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## Math Problems and Solutions on Integers

Problems related to integer numbers in mathematics are presented along with their solutions.

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## What Is An Integer? — Definition & Examples

## Integer definition

Common numbering systems you may encounter include all these:

Avoid confusing the different groups of numbers with the different ways we represent them.

## Set of integers

We understand that the negative numbers keep going, and so do the positive whole numbers.

Below are two different sets of numbers. What do each of them mean?

The first is a set of all positive integers. The second is a set of all non-negative, even integers.

A set of integers is represented by the symbol Z . A set is written as Z={...} .

## Integers that are not whole numbers

A negative number that is not a decimal or fraction is an integer but not a whole number.

## Integer examples

Negative integers: -1, -2, -3, -4, -5 and so on, without end.

Non-negative integers: 0 and all positive whole numbers like 6, 7, 8, 9, 10 and so on.

Positive integers: 1, 2, 3, 4, 5 and so on, without end.

## Non-integers examples

Non-integers are any number that is a decimal, fraction, or mixed unit. These are all not integers:

Fractions: 1 2 \frac{1}{2} 2 1

Mixed units: 3 1 2 3\frac{1}{2} 3 2 1

## Where do we use integers?

Integers pop up in most things you count each day:

Temperatures: 45 ° C 45°C 45° C or 76 ° F 76°F 76° F

Teams: 11 football players; 9 baseball players

Altitude: Commercial planes fly at 35,000 feet

Coins: You have three quarters and two dimes so you have 0.95 cents.

3 7 8 \mathbf{3}\frac{\mathbf{7}}{\mathbf{8}} 3 8 7 becomes the integer 4

98.6 ° F 98.6° F 98.6° F becomes the integer 99 ° F 99 °F 99° F

364.75 miles becomes the integer 365 miles .

## Characteristics of integers

Testing to see if a number is an integer is as easy as asking two questions:

Is it a whole number? – Integer!

Is it the number 0 ? – Integer!

Is it negative of a whole number? – Integer!

Does it include multiple parts, such as 5'6" or $1.97 – Not an integer!

## Which of the following are integers?

Answers 1, 3, and 5 are integers.

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## {FREE} Add & Subtract Integers: Real Life Lesson

## Teaching Integer Operations Through Problem Solving

## How to Add & Subtract Integers

Students will then need a set of word problem cards .

You want them to see that at the end, they all end up with the same final balance .

Then they could go through them in order , without cutting the cards out.

Finally, you will need to give everyone a starting balance .

If the starting balance is $0, they will end the assignment with $277 in the bank .

Need more practice and visuals to teaching addition & subtraction with integers? Grab this complete lesson and games collection: Add & Subtract Integers Lessons & Games .

## Extension and Follow Up Questions

After discussing ideas, estimations and strategies, work out each problem.

This shows what happens as you add & subtract integers using +/- tables.

Find more helpful pre-algebra lessons in this post .

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## Integers: Word Problems On Integers

## Word problems on integers Examples:

Total amount deposited= Rs. 150

Amount overdrew by Shyak= Rs. 38

Amount charged by bank= Rs. 20

Total amount debited = (-38) + (-20) = -58

Current balance= Total deposit +Total Debit

Hence, the current balance is Rs. 92.

Optimum temperature for bacteria X = -31˚C

Optimum temperature for bacteria Y= -56˚C

Temperature difference= Optimum temperature for bacteria X – Optimum temperature for bacteria Y

Hence, temperature difference is 25˚C.

Initial position = 20 m (above sea level)

Final position = 250 m (below sea level)

Total depth it submerged = (250+20) = 270 m

Thus, the submarine travelled 270 m below sea level.

Time taken to submerge 1 meter = 1/5 minutes

Time taken to submerge 270 m = 270 (1/5) = 54 min

Hence, the submarine will reach 250 m below sea level in 54 minutes.

## Leave a Comment Cancel reply

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## Integer Word Problems Worksheets

## Benefits of Integers Word Problems Worksheets

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## Integers - practice problems

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## Search form

What is an integer, integers lesson and integer examples.

top, bottom | increase, decrease | forward, backward | positive, negative

## Definitions

- The number line goes on forever in both directions. This is indicated by the arrows.
- Whole numbers greater than zero are called positive integers (+) . These numbers are to the right of zero on the number line.
- Whole numbers less than zero are called negative integers (-) . These numbers are to the left of zero on the number line.
- Zero is neutral. It is neither positive nor negative.
- Two numbers are opposites if they are each the same distance away from zero, but on opposite sides of the number line. One will have a positive sign, the other a negative sign. In the number line above, + 3 and - 3 are labeled as opposites.

Let's revisit the problem from the top of this page.

Solution: We can represent the elevation using positive and negative numbers:

Example 1: Write a number using positive or negative signs numberto represent each situation:

Example 2: Name the opposite of each integer.

Example 3: Name 4 real life situations in which integers can be used.

Rising and falling temperatures.

Stock market gains and losses.

Gaining and losing yards in a football game.

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## How to Solve Integers and Their Properties

## Using Addition and Subtraction Properties

- a + b = c (where both a and b are positive numbers the sum c is also positive)
- For example: 2 + 2 = 4

- -a + -b = -c (where both a and b are negative, you get the absolute value of the numbers then you proceed to add, and use the negative sign for the sum)
- For example: -2+ (-2)=-4

- a + (-b) = c (when your terms are of different signs, determine the larger number's value, then get the absolute value of both terms and subtract the lesser value from the larger value. Use the sign of the larger number for the answer.)
- For example: 5 + (-1) = 4

- -a +b = c (get the absolute value of the numbers and again, proceed to subtract the lesser value from the larger value and assume the sign of the larger value)
- For example: -5 + 2 = -3

- An example of the additive identity is: a + 0 = a
- Mathematically, the additive identity looks like: 2 + 0 = 2 or 6 + 0 = 6

- The additive inverse is when a number is added to the negative equivalent of itself.
- For example: a + (-b) = 0, where b is equal to a
- Mathematically, the additive inverse looks like: 5 + -5 = 0

## Using Multiplication Properties

- When a and b are positive numbers and not equal to zero: +a * + b = +c
- When a and b are both negative numbers and not equal to zero: -a*-b = +c

- For example: a(b+c) = ab + ac
- Mathematically, this looks like: 5(2+3) = 5(2) + 5(3)
- Note that there is no inverse property for multiplication because the inverse of a whole number is a fraction, and fractions are not an element of integer.

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## What are Integers?

Let’s discuss the definition, types, and properties of integers and conduct arithmetic operations!

Integer examples: $-7$, $-1$, 0, 2, 7, 15, etc.

Non-integer examples: 85, 3.14, 7, etc.

Integer symbol: The set of integers are represented by the symbol ℤ .

## How to Represent Integers on a Number Line?

All three categories of integers can be visually represented on an integer number line.

The more the integer is positive, the greater it is. For example, $+15$ is greater than $+12$.

The more the integer is negative, the smaller it is. For example, $-33$ is smaller than $-19$.

## How to Perform Arithmetic Operations on Integers?

The four basic mathematical operations are:

## Addition of Integers

The resultant integer will have the same sign as the given integers.

Here, 7 and 3 are positive. So, the answer is +10 or simply 10.

The rules for addition are summarized in the table below:

## Subtraction of Integers

- Convert the subtraction operation into an addition operation by changing the sign of the second number that is being subtracted.
- Apply the rules for adding integers as discussed above to get the answer.
- $(–$$6)$ $–$ $(+7) = (–$$6) + ($$–$$7) = –$$13$

## Multiplication of Integers

- If both integers have the same sign, the resultant product will have a positive (+) sign.
- If the integers have different signs, the resultant product will have a negative (–) sign.

The rules are summarized in the table below:

## Division of Integers

- If both integers have the same sign, the result will have a positive $(+)$ sign.
- If the integers have different signs, the result will have a negative $(–)$ sign.

## Properties of Integers

- Closure Property
- Commutative Property
- Associative Property
- Distributive Property
- Additive Inverse Property
- Multiplicative Inverse Property
- Identity Property

## 1. Closure Property

- $a + b =$ Integer
- $a$ $–$ $b =$ Integer
- $a \times b =$ Integer
- $–5 + 4 = –1$
- $8$ $–$ $5 = 3$
- $2 \times 3 = 6$

For example: $15 \div 2 = 7.5$

## 2. Commutative Property

So, for two integers a and b :

## 3. Associative Property

So, for any three integers a, b, and c:

## 4. Distributive Property

So, for three integers a, b , and c :

$a \times (b + c) = (a \times b) + (a \times c)$

- $5 \times (4 + 3) = (5 \times 4 + 5 \times 3) = 35$
- $–2 \times (6 + 1) = {(–$$2) \times 6 + (–$$2) \times 1} = –$$14$

## 5. Additive Inverse Property

## 6. Multiplicative Inverse Property

## 7. Identity Property

- $a + 0 = 0 + a = a$
- $a \times 1 = 1 \times a = a$
- $10 + 0 = 0 + 10 = 10$
- $10 \times 1 = 1 \times 10 = 10$

1. Sort the numbers as integers and non-integers.

Non-integers $= 7.5$, $37$, $–4.25$

So, $(–$$8)$ $–$ $(–$5) =$ $–$$8 + 5$

Step 2: Then we follow the addition operation

Since the signs are different, we need to find the difference in their absolute value.

The sign of the resultant integer will be the sign of the integer with the highest absolute value.

Here, 8 is the integer with the highest absolute value, and its sign is negative.

3. Using the number line, find the integer which is:

Attend this quiz & Test your knowledge.

## Which of the following comparisons are true? $+10$ . . . $–10$ $+5$ . . . $+15$ $–8$ . . . $0$ $–20$ . . . $+2$

Integers including 0 and positive integers are whole numbers.

Whole numbers: 0, 1, 2, 3, 4, …

Are all integers rational numbers?

Is $–1$ an integer? Is $–2$ an integer?

Yes. Integers include negative numbers that are whole (without fractions or decimals).

No. Integers do not include fractions. So, $-16$ is not an integer.

What are consecutive integers?

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## Examples on Multiplication of Integers | Questions on Multiplication of Integers

## Worked out Multiplication of Integers Problems

## Key Points to Remember on Properties of Integers Multiplication

- The Closure Integer Property of multiplication defines that the product value of two or three integer numbers will be an integer number.
- The commutative Integer Multiplication property defines that swapping two or three integers will not differ the value of the final result.
- The associative Integer Multiplication property defines that the grouping of integer values together will not affect the final result.
- The distributive Integer property of multiplication defines that the distribution concept of 1 operation value on other mathematical integer values within the given braces.
- Multiplication by zero defines the product value of any negative or positive integer number by zero
- Multiplicative Integer defines the final result as 1 when any integer number is multiplied with 1.

## Integer Multiplication Rules on Problems

Also. given that it decreases for 4 hours.

The total drop in temperature is (-4) * (4) = -16

Therefore, the total drop in temperature is 16 degrees C

Thus, the final result is -16 degree C

Jason borrowed $2 a day to buy a launch. She now owes $60. How many days did Jason borrow $2?

As given in the question, Jason borrowed to buy a launch = $2

No of days Jason borrowed money = 60/2 = 30

Therefore, the total days = 30 days

Thus, the final result is 30 days.

As given in the question, A football team lost yards = -12 yards

Team total change in position for 4 plays = (-12) * (4) = 48

Therefore, the total change = -48 yards

Thus, the final answer is -48 yards.

As per the given question, The temperature changed at the rate = -2 degree F

The change happened for days = 5 days

No of days there was a change = (-2)*5 = -10

Therefore, there was a change for days = 10 days

Thus, the final solution is 10 days.

Amount of deposited money = $7

The overall change in the account = 6 * ($7) = 42

Therefore, the change in money = 42

Thus, the final solution is $42

## Questions on Multiplication of Integers

The price of the winter coat is reduced by $15, Therefore it is negative = -$15

The absolute values of |3| and |-15| are 3 and 15

The coat reduced in price = 3*15 = 45

Therefore, the total change in price = $45

Netflix charges $9 per month. Therefore, it is negative.

Given, the bill will be deducted automatically for months = 6

The absolute values of |6| and |9| are 6 and 9.

The amount of money deducted from customers bank account = 6*9 = 54

Therefore, the total amount after determining the signs = -$54

Hence, the final solution is -$54

In 3 months, she cut 2 inches off her hair. This is also negative.

For the month of June and July, the length of the hair she cut = 2 * (-3) = -6

For the months August, September, and October, the length of the hair she cut = 3 * (-2) = -6

Therefore, the total length = (-6) + (-6) = -12 inches

Thus. the complete length she cut = 12 inches

Hence, the final solution is -12 inches

The depth of the water in a pool decreases each week = 2 inches

As the water level decreases, it will be negative.

The decrease in water for weeks = 4

The change in depth of water = (-2)*4 = -8

Therefore, the water level decreases by 8 inches.

Thus, the final solution is -8 inches

The temperature drops by 3 degrees. Therefore, it will be negative.

Also given for every 1000 feet it is 3 degrees. Thus for every 5000 feet, it is 5 degrees.

The temperature change = (-3)*5 = -15

Thus, for every 5000 feet, the temperature changes by -15 degrees.

Hence, the final solution is -15 degrees.

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## Class 7 math (India)

## Word problems involving negative numbers

- Your answer should be
- an integer, like 6 6 6 6
- a simplified proper fraction, like 3 / 5 3/5 3 / 5 3, slash, 5
- a simplified improper fraction, like 7 / 4 7/4 7 / 4 7, slash, 4
- a mixed number, like 1 3 / 4 1\ 3/4 1 3 / 4 1, space, 3, slash, 4
- an exact decimal, like 0.75 0.75 0 . 7 5 0, point, 75
- a multiple of pi, like 12 pi 12\ \text{pi} 1 2 pi 12, space, start text, p, i, end text or 2 / 3 pi 2/3\ \text{pi} 2 / 3 pi 2, slash, 3, space, start text, p, i, end text

## How to Add and Subtract Positive and Negative Numbers

Numbers can be positive or negative.

## No Sign Means Positive

If a number has no sign it usually means that it is a positive number.

## Play with it!

On the Number Line positive goes to the right and negative to the left.

Try the sliders below and see what happens:

## Balloons and Weights

Let us think about numbers as balloons (positive) and weights (negative):

This basket has balloons and weights tied to it:

## Adding a Positive Number

Adding positive numbers is just simple addition.

We can add balloons (we are adding positive value)

the basket gets pulled upwards (positive)

## Example: 2 + 3 = 5

"Positive 2 plus Positive 3 equals Positive 5"

We could write it as (+2) + (+3) = (+5)

## Subtracting A Positive Number

Subtracting positive numbers is just simple subtraction.

We can take away balloons (we are subtracting positive value)

the basket gets pulled downwards (negative)

## Example: 6 − 3 = 3

"Positive 6 minus Positive 3 equals Positive 3"

We could write it as (+6) − (+3) = (+3)

## Adding A Negative Number

Now let's see what adding and subtracting negative numbers looks like:

We can add weights (we are adding negative values)

## Example: 6 + (−3) = 3

"Positive 6 plus Negative 3 equals Positive 3"

We could write it as (+6) + (−3) = (+3)

So these have the same result :

In other words subtracting a positive is the same as adding a negative .

## Subtracting A Negative Number

Lastly, we can take away weights (we are subtracting negative values)

## Example: What is 6 − (−3) ?

Yes indeed! Subtracting a Negative is the same as adding!

## What Did We Find?

## Example: What is 5 + (−7) ?

## Subtracting a negative ...

It can all be put into two rules :

They are "like signs" when they are like each other (in other words: the same).

So, all you have to remember is:

Two like signs become a positive sign

Two unlike signs become a negative sign

## Example: What is 5+(−2) ?

+(−) are unlike signs (they are not the same), so they become a negative sign .

## Example: What is 25−(−4) ?

−(−) are like signs, so they become a positive sign .

## Starting Negative

What if we start with a negative number?

Using The Number Line can help:

## Example: What is −3+(+2) ?

+(+) are like signs, so they become a positive sign .

## Example: What is −3+(−2) ?

+(−) are unlike signs, so they become a negative sign .

## Now Play With It!

And there is a "common sense" explanation:

If I say "Eat!" I am encouraging you to eat (positive)

If I say "Do not eat!" I am saying the opposite (negative).

So, two negatives make a positive, and if that satisfies you, then you are done!

## Another Common Sense Explanation

## A Bank Example

Example: last year the bank subtracted $10 from your account by mistake, and they want to fix it..

So the bank must take away a negative $10 .

Let's say your current balance is $80, so you will then have:

So you get $10 more in your account.

## A Long Example You Might Like

Ally can be naughty or nice. So Ally's parents have said

So when we subtract a negative, we gain points (i.e. the same as adding points).

See: both " 15 − (+3) " and " 15 + (−3) " result in 12.

## Try These Exercises ...

Now try This Worksheet , and see how you go.

- 3.1 Use a Problem-Solving Strategy
- Introduction
- 1.1 Introduction to Whole Numbers
- 1.2 Use the Language of Algebra
- 1.3 Add and Subtract Integers
- 1.4 Multiply and Divide Integers
- 1.5 Visualize Fractions
- 1.6 Add and Subtract Fractions
- 1.7 Decimals
- 1.8 The Real Numbers
- 1.9 Properties of Real Numbers
- 1.10 Systems of Measurement
- Key Concepts
- Review Exercises
- Practice Test
- 2.1 Solve Equations Using the Subtraction and Addition Properties of Equality
- 2.2 Solve Equations using the Division and Multiplication Properties of Equality
- 2.3 Solve Equations with Variables and Constants on Both Sides
- 2.4 Use a General Strategy to Solve Linear Equations
- 2.5 Solve Equations with Fractions or Decimals
- 2.6 Solve a Formula for a Specific Variable
- 2.7 Solve Linear Inequalities
- 3.2 Solve Percent Applications
- 3.3 Solve Mixture Applications
- 3.4 Solve Geometry Applications: Triangles, Rectangles, and the Pythagorean Theorem
- 3.5 Solve Uniform Motion Applications
- 3.6 Solve Applications with Linear Inequalities
- 4.1 Use the Rectangular Coordinate System
- 4.2 Graph Linear Equations in Two Variables
- 4.3 Graph with Intercepts
- 4.4 Understand Slope of a Line
- 4.5 Use the Slope-Intercept Form of an Equation of a Line
- 4.6 Find the Equation of a Line
- 4.7 Graphs of Linear Inequalities
- 5.1 Solve Systems of Equations by Graphing
- 5.2 Solving Systems of Equations by Substitution
- 5.3 Solve Systems of Equations by Elimination
- 5.4 Solve Applications with Systems of Equations
- 5.5 Solve Mixture Applications with Systems of Equations
- 5.6 Graphing Systems of Linear Inequalities
- 6.1 Add and Subtract Polynomials
- 6.2 Use Multiplication Properties of Exponents
- 6.3 Multiply Polynomials
- 6.4 Special Products
- 6.5 Divide Monomials
- 6.6 Divide Polynomials
- 6.7 Integer Exponents and Scientific Notation
- 7.1 Greatest Common Factor and Factor by Grouping
- 7.2 Factor Trinomials of the Form x2+bx+c
- 7.3 Factor Trinomials of the Form ax2+bx+c
- 7.4 Factor Special Products
- 7.5 General Strategy for Factoring Polynomials
- 7.6 Quadratic Equations
- 8.1 Simplify Rational Expressions
- 8.2 Multiply and Divide Rational Expressions
- 8.3 Add and Subtract Rational Expressions with a Common Denominator
- 8.4 Add and Subtract Rational Expressions with Unlike Denominators
- 8.5 Simplify Complex Rational Expressions
- 8.6 Solve Rational Equations
- 8.7 Solve Proportion and Similar Figure Applications
- 8.8 Solve Uniform Motion and Work Applications
- 8.9 Use Direct and Inverse Variation
- 9.1 Simplify and Use Square Roots
- 9.2 Simplify Square Roots
- 9.3 Add and Subtract Square Roots
- 9.4 Multiply Square Roots
- 9.5 Divide Square Roots
- 9.6 Solve Equations with Square Roots
- 9.7 Higher Roots
- 9.8 Rational Exponents
- 10.1 Solve Quadratic Equations Using the Square Root Property
- 10.2 Solve Quadratic Equations by Completing the Square
- 10.3 Solve Quadratic Equations Using the Quadratic Formula
- 10.4 Solve Applications Modeled by Quadratic Equations
- 10.5 Graphing Quadratic Equations in Two Variables

## Learning Objectives

By the end of this section, you will be able to:

- Approach word problems with a positive attitude
- Use a problem-solving strategy for word problems
- Solve number problems

## Be Prepared 3.1

Before you get started, take this readiness quiz.

## Be Prepared 3.2

Solve: 2 3 x = 24 . 2 3 x = 24 . If you missed this problem, review Example 2.16 .

Solve: 3 x + 8 = 14 . 3 x + 8 = 14 . If you missed this problem, review Example 2.27 .

## Approach Word Problems with a Positive Attitude

“If you think you can… or think you can’t… you’re right.”—Henry Ford

Use a Problem-Solving Strategy for Word Problems

## Use a Problem-Solving Strategy to Solve Word Problems.

- Step 1. Read the problem. Make sure all the words and ideas are understood.
- Step 2. Identify what we are looking for.
- Step 3. Name what we are looking for. Choose a variable to represent that quantity.
- Step 4. Translate into an equation. It may be helpful to restate the problem in one sentence with all the important information. Then, translate the English sentence into an algebraic equation.
- Step 5. Solve the equation using good algebra techniques.
- Step 6. Check the answer in the problem and make sure it makes sense.
- Step 7. Answer the question with a complete sentence.

## Example 3.1

If this were a homework exercise, our work might look like this:

Let’s try this approach with another example.

## Example 3.2

## Example 3.3

The difference of a number and six is 13. Find the number.

The difference of a number and eight is 17. Find the number.

The difference of a number and eleven is −7 . −7 . Find the number.

## Example 3.4

The sum of twice a number and seven is 15. Find the number.

The sum of four times a number and two is 14. Find the number.

The sum of three times a number and seven is 25. Find the number.

## Example 3.5

One number is five more than another. The sum of the numbers is 21. Find the numbers.

One number is six more than another. The sum of the numbers is twenty-four. Find the numbers.

## Try It 3.10

The sum of two numbers is fifty-eight. One number is four more than the other. Find the numbers.

## Example 3.6

## Try It 3.11

## Try It 3.12

The sum of two numbers is −18 . −18 . One number is 40 more than the other. Find the numbers.

## Example 3.7

One number is ten more than twice another. Their sum is one. Find the numbers.

## Try It 3.13

One number is eight more than twice another. Their sum is negative four. Find the numbers.

## Try It 3.14

One number is three more than three times another. Their sum is −5 . −5 . Find the numbers.

## Example 3.8

The sum of two consecutive integers is 47. Find the numbers.

## Try It 3.15

The sum of two consecutive integers is 95 . 95 . Find the numbers.

## Try It 3.16

The sum of two consecutive integers is −31 . −31 . Find the numbers.

## Example 3.9

Find three consecutive integers whose sum is −42 . −42 .

## Try It 3.17

Find three consecutive integers whose sum is −96 . −96 .

## Try It 3.18

Find three consecutive integers whose sum is −36 . −36 .

## Example 3.10

Find three consecutive even integers whose sum is 84.

## Try It 3.19

Find three consecutive even integers whose sum is 102.

## Try It 3.20

Find three consecutive even integers whose sum is −24 . −24 .

## Example 3.11

## Try It 3.21

## Try It 3.22

## Section 3.1 Exercises

Use the Approach Word Problems with a Positive Attitude

In the following exercises, prepare the lists described.

In the following exercises, solve each number word problem.

The sum of a number and eight is 12. Find the number.

The sum of a number and nine is 17. Find the number.

The difference of a number and 12 is three. Find the number.

The difference of a number and eight is four. Find the number.

The sum of three times a number and eight is 23. Find the number.

The sum of twice a number and six is 14. Find the number.

The difference of twice a number and seven is 17. Find the number.

The difference of four times a number and seven is 21. Find the number.

Three times the sum of a number and nine is 12. Find the number.

Six times the sum of a number and eight is 30. Find the number.

One number is six more than the other. Their sum is 42. Find the numbers.

One number is five more than the other. Their sum is 33. Find the numbers.

The sum of two numbers is 20. One number is four less than the other. Find the numbers.

The sum of two numbers is 27. One number is seven less than the other. Find the numbers.

The sum of two numbers is −45 . −45 . One number is nine more than the other. Find the numbers.

The sum of two numbers is −61 . −61 . One number is 35 more than the other. Find the numbers.

The sum of two numbers is −316 . −316 . One number is 94 less than the other. Find the numbers.

The sum of two numbers is −284 . −284 . One number is 62 less than the other. Find the numbers.

One number is one more than twice another. Their sum is −5 . −5 . Find the numbers.

One number is six more than five times another. Their sum is six. Find the numbers.

The sum of two numbers is 14. One number is two less than three times the other. Find the numbers.

The sum of two numbers is zero. One number is nine less than twice the other. Find the numbers.

The sum of two consecutive integers is 77. Find the integers.

The sum of two consecutive integers is 89. Find the integers.

The sum of two consecutive integers is −23 . −23 . Find the integers.

The sum of two consecutive integers is −37 . −37 . Find the integers.

The sum of three consecutive integers is 78. Find the integers.

The sum of three consecutive integers is 60. Find the integers.

Find three consecutive integers whose sum is −3 . −3 .

Find three consecutive even integers whose sum is 258.

Find three consecutive even integers whose sum is 222.

Find three consecutive odd integers whose sum is 171.

Find three consecutive odd integers whose sum is 291.

Find three consecutive even integers whose sum is −36 . −36 .

Find three consecutive even integers whose sum is −84 . −84 .

Find three consecutive odd integers whose sum is −213 . −213 .

Find three consecutive odd integers whose sum is −267 . −267 .

## Everyday Math

Buying in Bulk Alicia bought a package of eight peaches for $3.20. Find the cost of each peach.

## Writing Exercises

What has been your past experience solving word problems?

When you start to solve a word problem, how do you decide what to let the variable represent?

What are consecutive odd integers? Name three consecutive odd integers between 50 and 60.

ⓑ If most of your checks were:

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Access for free at https://openstax.org/books/elementary-algebra-2e/pages/1-introduction

- Authors: Lynn Marecek, MaryAnne Anthony-Smith, Andrea Honeycutt Mathis
- Publisher/website: OpenStax
- Book title: Elementary Algebra 2e
- Publication date: Apr 22, 2020
- Location: Houston, Texas
- Book URL: https://openstax.org/books/elementary-algebra-2e/pages/1-introduction
- Section URL: https://openstax.org/books/elementary-algebra-2e/pages/3-1-use-a-problem-solving-strategy

## Understanding Integers

## Rules of Integers

The sum of any two positive integers will result in an integer.

The sum of any two negative integers is an integer.

The product of two positive integers will give an integer.

The product of two negative integers will be given an integer.

The sum of any integer and its inverse will be equal to zero.

The product of an integer and its reciprocal will be equal to 1.

## The Addition of Signed Integer Numbers

## Subtraction of Signed Integer Numbers

## Multiplication and Division of Signed Integer Numbers

## Properties of Integers

Multiplicative inverse property

## Closure Property:

For example, 2 + 5 = 7, which is an integer, and 2 x 5 = 10, which is also an integer.

## Commutative Property:

According to the associative property, if a, b, and c are integers, then:

For example, 2 + (3 + 4) = (2 + 3) + 4 = 9 and 2 x (3 x 4) = (2 x 3) x 4 = 24.

This property is only valid when it comes to addition and multiplication.

## Distributive Property:

LHS = 3 x (5 + 1) = 3 x 6 = 18

RHS = 3 x 5 + 3 x 1 = 15 + 3 = 18

## Additive Inverse Property:

## Multiplicative Inverse Property:

## Identity Property of Integers:

## Types of Integers

## Positive Integers:

## Negative Integers:

## Fun Facts About Integers

The word integer comes from the Latin word “ integer ” which literally means whole.

## FAQs on Word Problems on Integers

1. What are integers and what is their importance?

2. What are the rules for adding and subtracting integers?

There are some rules to be noted while adding two or more integers. They are as follows:

The sum of an integer and its additive inverse is always zero.

When you add an integer with zero, you will get the same number as the answer.

There are some rules to be noted while subtracting two or more integers. They are as follows:

3. State the principles that the addition and subtraction of integers on a number line is based on.

The principles upon which the addition of integers on a number line is based are as follows:

The principles upon which the subtraction of integers on a number line is based are as follows:

Every subtraction fact can also be written as an addition fact.

4. Is multiplying rational numbers just like multiplying integers? If so, how?

## Algebra: Consecutive Integer Problems

In these lessons, we will learn how to solve

- consecutive integer word problems
- consecutive even integer word problems
- consecutive odd integer word problems

## What Are Consecutive Integers?

Consecutive integer problems are word problems that involve consecutive integers .

The following are common examples of consecutive integer problems.

Step 2: Solve the equation Combine like terms 2x + 2 = 60

Answer: The 3 consecutive numbers are 29, 30 and 31.

Step 2: Write out the formula for perimeter of triangle . P = sum of the three sides

Step 3: Plug in the values from the question and from the sketch. 45 = x + x + 2 + x + 4

Combine like terms 45 = 3x + 6

Isolate variable x 3x = 45 – 6 3x = 39 x =13

Step 3: Check your answer 13 + 13 + 2 + 13 + 4 = 45

Be careful! The question requires the length of the longest side. The length of longest = 13 + 4 =17

Answer: The length of longest side is 17

Step 2: Convert 5 feet to inches 5 × 12 = 60

Step 3: Sum of the 4 shelves is 60 x + x + 2 + x + 4 + x + 6 = 60

Combine like terms 4x + 12 = 60

Isolate variable x 4x = 60 – 12 4x = 48 x = 12

Step 3: Check your answer 12 + 12 + 2 + 12 + 4 + 12 + 6 = 60

The lengths of the shelves should be 12, 14, 16 and 18.

Answer: The lengths of the shelves in inches should be 12, 14, 16 and 18.

- The sum of three consecutive integers is 657; find the integers.
- The sum of two consecutive integers is 519; find the integers.
- The sum of three consecutive even integers is 528; find the integers.
- The sum of three consecutive odd integers is 597; find the integers.

The following video shows how to solve the integer word problems.

- The sum of two consecutive integers is 99. Find the value of the smaller integer.
- The sum of two consecutive odd integers is 40. What are the integers?
- The sum of three consecutive even integers is 30. Find the integers.

How to solve consecutive integer word problems?

Example: The sum of three consecutive integers is 24. Find the integers.

## IMAGES

## VIDEO

## COMMENTS

Solution to Problem 1: Let x and x + 1 (consecutive integers differ by 1) be the two numbers. Use the fact that their sum is equal to 129 to write the equation x + (x + 1) = 129 Solve for x to obtain x = 64 The two numbers are x = 64 and x + 1 = 65 We can see that the sum of the two numbers is 129.

Integers examples Non-integers examples. Non-integers are any number that is a decimal, fraction, or mixed unit. These are all not integers: Decimals: 3.14. Fractions: 1 2 \frac{1}{2} 2 1 Mixed units: 3 1 2 3\frac{1}{2} 3 2 1 Non-integer examples Where do we use integers? Integers pop up in most things you count each day:

For example, what is better for Bob, working 5 hours at $15 an hour or working 10 hours for $10 an hour? After discussing ideas, estimations and strategies, work out each problem. Finally, you can then discuss what they noticed about integers and as them to explain in their own words how to add negative numbers, or how to subtract negative numbers.

Examples of Integers: - 1, -12, 6, 15. Symbol The integers are represented by the symbol 'Z'. Z= {……-8,-7,-6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8,……} Types of Integers Integers come in three types: Zero (0) Positive Integers (Natural numbers) Negative Integers (Additive inverse of Natural Numbers) Zero

Word problems on integers Examples: Example 1: Shyak has overdrawn his checking account by Rs.38. The bank debited him Rs.20 for an overdraft fee. Later, he deposited Rs.150. What is his current balance? Solution: Given, Total amount deposited= Rs. 150 Amount overdrew by Shyak= Rs. 38 ⇒ Debit amount = -38 [Debit is represented as negative integer]

When subtracting integers, be sure to subtract the smaller integer from the larger integer. The smaller integer is farther to the left on the number line. 1. Mt. Everest, the highest elevation in Asia, is 29,028 feet above sea level. The Dead Sea, the lowest elevation, is 1,312 feet below sea level.

An integer is defined as a number that can be written without a fractional component. For example, 11, 8, 0, and −1908 are integers whereas √5, Π are not integers. The set of integers consists of zero, the positive natural numbers, and their additive inverses. Integers are closed under the operations of addition and multiplication.

Answers to these sample questions appear at the bottom of the page. This page does not grade your responses. Want unlimited math worksheets? Learn more about our online math practice software. See some of our other supported math practice problems. Complexity=1 Solve. Complexity=2 Solve. Answers Complexity=1 Solve. Complexity=2 Solve.

Integers - practice problems Number of problems found: 271 Unknown 72284 The unknown number is twice less than 80 Celsius degrees The temperature on Monday was 5 celsius. The temperature on Thursday was 7 degrees less than the temperature on Monday. What was the temperature on Thursday? Degrees Fahrenheit

Here are four great examples about adding integers word problems. Read the solution carefully, so you will know how to do similar problems. Problem #1: Maria saved 200 dollars and then she spent 150 dollars. How much money does Maria have now? Solution The problem has 3 important components shown in bold below.

Example: (1) Find three consecutive positive integers such that the sum of the two smaller integers exceed the largest integer by 5. (2) The sum of a number and three times its additive inverse is 16. Find the number. Show Video Lesson Example: The largest of five consecutive even integers is 2 less than twice the smallest.

Summary: Integers are the set of whole numbers and their opposites. Whole numbers greater than zero are called positive. Whole numbers less than zero are called negative. Zero is neither positive nor negative, and has no sign. Two integers are opposites if they are each the same distance away from zero, but on opposite sides of the number line.

For example: When a and b are positive numbers and not equal to zero: +a * + b = +c When a and b are both negative numbers and not equal to zero: -a*-b = +c If a and b have unlike signs, the sign of the product is negative. For example: When a is positive and b is negative: +a * -b = -c

Apply the rules for adding integers as discussed above to get the answer. For example: ( - 6) - ( + 7) = ( - 6) + ( - 7) = - 13 Here, we first convert the problem into addition by changing the sign of 7. Then, we follow the rules for addition. The absolute value of the integers is 6 and 7, and their sum is 13.

Division of Integers Rules and Examples Question 1: Find the value of ||-17|+17| / ||-25|-42| Solution: ||-17|+17| / ||-25|-42| = |17+17| / |25-42| = |34| / |-17| = 34 / 17 = 2 Question 2: Simplify: {36 / (-9)} / { (-24) / 6} Solution: {36 / (-9)} / { (-24) / 6} = {36/-9} / {-24/6} = - (36/9) / - (24/6) = -4/-4 = 4/4 =1

Get detailed solutions to your math problems with our Integers step-by-step calculator. Practice your math skills and learn step by step with our math solver. ... Solved example of integers. $20+90+51$ 2. Add the values $20$ and $90$ $110+51$ 3. Add the values $110$ and $51$ $161$ Final Answer. $161$

Integer Multiplication Rules on Problems Question 1: The temperature in an area drops by 4 degrees for 4 hours. How much is the total drop in the temperature? Solution: As given in the question, the temperature drops by 4 degrees. Therefore, the temperature is a negative factor. Also. given that it decreases for 4 hours.

Word problems involving negative numbers. Google Classroom. A flying fish deep under the sea dreams of reaching the clouds one day. The fish is at a depth of 200 200 feet below sea level right under the clouds. It has to fly 6700 6700 feet to reach the clouds.

Example: 6 + (−3) = 3. is really saying. "Positive 6 plus Negative 3 equals Positive 3". We could write it as (+6) + (−3) = (+3) The last two examples showed us that taking away balloons (subtracting a positive) or adding weights (adding a negative) both make the basket go down. So these have the same result:

Use a Problem-Solving Strategy to Solve Word Problems. Step 1. Read the problem. Make sure all the words and ideas are understood. Step 2. ... Examples of consecutive even integers are: 18, 20, 22 64, 66, 68 −12, −10, −8 18, 20, 22 64, 66, 68 −12, −10, −8. Notice each integer is 2 more than the number preceding it.

For example, 2 + 5 = 7, which is an integer, and 2 x 5 = 10, which is also an integer. Commutative Property: According to this property, if a and b are two integers, then a + b = b + a and a x b = b x a. For example, 3 + 8 = 8 x 3 = 24 and 3 + 8 = 8 + 3 = 11.

The following diagram shows an example of a consecutive integer problem. Scroll down the page for more examples and solutions on consecutive integer problems. Consecutive Integer Problems. Consecutive integer problems are word problems that involve consecutive integers. The following are common examples of consecutive integer problems. Example: