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Solving word problems by adding and subtracting fractions and mixed numbers, learn how to solve fraction word problems with examples and interactive exercises.
Example 1: Rachel rode her bike for one-fifth of a mile on Monday and two-fifths of a mile on Tuesday. How many miles did she ride altogether?
Analysis: To solve this problem, we will add two fractions with like denominators.
Answer: Rachel rode her bike for three-fifths of a mile altogether.
Analysis: To solve this problem, we will subtract two fractions with unlike denominators.
Answer: Stefanie swam one-third of a lap farther in the morning.
Analysis: To solve this problem, we will add three fractions with unlike denominators. Note that the first is an improper fraction.
Answer: It took Nick three and one-fourth hours to complete his homework altogether.

Analysis: To solve this problem, we will add two mixed numbers, with the fractional parts having like denominators.
Answer: Diego and his friends ate six pizzas in all.
Analysis: To solve this problem, we will subtract two mixed numbers, with the fractional parts having like denominators.
Answer: The Cocozzelli family took one-half more days to drive home.
Analysis: To solve this problem, we will add two mixed numbers, with the fractional parts having unlike denominators.
Answer: The warehouse has 21 and one-half meters of tape in all.
Analysis: To solve this problem, we will subtract two mixed numbers, with the fractional parts having unlike denominators.
Answer: The electrician needs to cut 13 sixteenths cm of wire.
Analysis: To solve this problem, we will subtract a mixed number from a whole number.
Answer: The carpenter needs to cut four and seven-twelfths feet of wood.
Summary: In this lesson we learned how to solve word problems involving addition and subtraction of fractions and mixed numbers. We used the following skills to solve these problems:
- Add fractions with like denominators.
- Subtract fractions with like denominators.
- Find the LCD.
- Add fractions with unlike denominators.
- Subtract fractions with unlike denominators.
- Add mixed numbers with like denominators.
- Subtract mixed numbers with like denominators.
- Add mixed numbers with unlike denominators.
- Subtract mixed numbers with unlike denominators.
Directions: Subtract the mixed numbers in each exercise below. Be sure to simplify your result, if necessary. Click once in an ANSWER BOX and type in your answer; then click ENTER. After you click ENTER, a message will appear in the RESULTS BOX to indicate whether your answer is correct or incorrect. To start over, click CLEAR.
Note: To write the fraction three-fourths, enter 3/4 into the form. To write the mixed number four and two-thirds, enter 4, a space, and then 2/3 into the form.

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Word problems - fraction addition (different denominators).
Description : This packet helps students practice solving word problems that require addition with fractions with different denominators. Each page contains 6 problems. Each page also has a speed and accuracy guide to help students see how fast and how accurately they should be doing these problems. After doing all 12 problems, students should be more comfortable doing these problems and have a clear understanding of how to solve them.
Claudia ordered pizza. So far, she has eaten $\dfrac{3}{9}$ of the large pizza. Her dad has eaten $\dfrac{1}{6}$ of the large pizza. How much of the pizza has been eaten so far?
Practice problems require knowledge of how to add, subtract, and multiply whole numbers
Adding Fractions with Unlike Denominators

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Unit 4: Lesson 5
Adding fractions word problem: paint.
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Video transcript
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Practice Means Progress

Lesson: Word Problems: Adding and Subtracting Fractions with Unlike Denominators Mathematics • 5th Grade
In this lesson, we will learn how to solve problems by adding and subtracting up to three proper fractions with different denominators by finding common denominators.
Lesson Plan
Students will be able to
- find the least common denominator,
- add or subtract fractions with unlike denominators to solve word problems.
Lesson Worksheet
Jackson eats 1 2 of a pizza, while Olivia eats 1 3 of it. How much do they eat in total?
Isabella colored 1 2 of a drawn figure, and her sister colored 1 3 of it. How much is left uncolored?
Chloe is building a tower using red, green, and yellow blocks. If the height of the red blocks is equal to 1 4 of a meter, the height of the green blocks is equal to 3 2 0 of a meter, and the height of the yellow blocks is equal to 1 5 of a meter, find the total height of the tower.
Hint : Give your answer in the simplest form.
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Add & subtract fractions word problems
Like & unlike denominators.
Below are our grade 5 math word problem worksheet on adding and subtracting fractions. The problems include both like and unlike denominators , and may include more than two terms.

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Worksheet on Add and Subtract Fractions
Recall the topic carefully and practice the questions given in the math worksheet on add and subtract fractions. The question mainly covers addition with the help of a fraction number line, subtraction with the help of a fraction number line, add the fractions with the same denominator, subtract the fractions with the same denominator and word problems on add and subtract fractions.
1. Add with the help of a fraction number line: (a) ²/₃ + ¹/₃
(b) ³/₇ + ²/₇
(c) ⁶/₁₀ + ¹/₁₀
2. Subtract with the help of a fraction number line: (a) ⁹/₁₀ - ³/₁₀
(b) ⁵/₆ - ²/₆
(c) ⁷/₈ - ⁴/₈
3. Add:
(a) ⁷/₁₀ + ²/₁₀
(b) ⁶/₈ + ⁴/₈
(c) ⁵/₉ + ²/₉ + ¹/₉
(d) ⁸/₁₁ + ²/₁₁
(e) ⁴/₉ + ⁷/₉
(f) ³/₈ + ⁵/₈ + ²/₈
(g) ⁴/₆ + ²/₆ + ¹/₆
(h) ⁷/₁₂ + ⁵/₁₂ + ⁶/₁₂
4. Find the difference. Remember to show the answer in the simplest form: (a) ⁹/₁₄ - ⁴/₁₄
(b) ⁶/₁₁ - ³/₁₁
(c) ⁸/₁₂ - ⁴/₁₂
(d) ¹²/₁₅ - ⁹/₁₅
(e) ¹²/₁₃ - ⁹/₁₃
(f) ⁶/₁₀ - ²/₁₀
(g) ⁹/₁₆ - ⁵/₁₆
(h) ¹²/₁₄ - ⁸/₁₄
Worksheet on Word Problems on Addition and Subtraction of Like Fractions:
5. Solve these problems: (a) ¹/₃ of the school garden has vegetable and another ¹/₃ has flowers. What part of the garden is left to grow grass? (b) Sam spent ¹/₆ of his Sunday doing home work and ³/₆ of the day watching cricket. What part of the day was left to do other things? (c) My mother ate ¹/₈ of the cake and my father ³/⁸. How much of the cake has been eaten and how much is left? (d) Pearl bought ²/₃ of her school books last week. What part is still left to be bought? (e) Sonia walked ³/₈ of the distance to school and ran ⁵/₈ of the distance. How much more of the distance does she need to cover?
(f) Emma likes chocolate. One day she bought a chocolate and ate \(\frac{5}{8}\) of it in the morning and \(\frac{2}{8}\) in the evening. How much part of the chocolate has she eaten?
(g) James and Lucas are eating a pizza. James ate \(\frac{3}{4}\) of the pizza and Lucas ate \(\frac{1}{4}\) of pizza. Who ate more pizza?
(h) Sophia completed \(\frac{2}{5}\) of her homework before going out for play. She did \(\frac{1}{5}\) of her homework after the play. How much homework did she complete altogether?
(i) David distributed \(\frac{19}{24}\) apples in his class and gave \(\frac{2}{24}\) to his friend Richard. What fraction of apples he gave away in all?
(j) Mary read \(\frac{2}{9}\) of her book in the morning and \(\frac{5}{9}\) in the evening. What fraction of the book has she read?
(k) A piece of ribbon is \(\frac{12}{15}\) m long. A piece of \(\frac{4}{15}\) m is cut from it. What is the fraction of the remaining ribbon?
(l) Nancy saves \(\frac{2}{7}\) of her salary and uses \(\frac{1}{7}\) for paying the house rent. How much salary is she left with?

Answers for the worksheet on add and subtract fractions are given below to check the exact answers of the above questions on adding & subtracting fractions.
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Here we will learn Reciprocal of a fraction. What is 1/4 of 4? We know that 1/4 of 4 means 1/4 × 4, let us use the rule of repeated addition to find 1/4× 4. We can say that \(\frac{1}{4}\) is the reciprocal of 4 or 4 is the reciprocal or multiplicative inverse of 1/4

Multiplying Fractions | How to Multiply Fractions? |Multiply Fractions
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Subtraction of Unlike Fractions | Subtracting Fractions | Examples
To subtract unlike fractions, we first convert them into like fractions. In order to make a common denominator, we find LCM of all the different denominators of given fractions and then make them equivalent fractions with a common denominators.

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Subtraction of Fractions having the Same Denominator | Like Fractions
To find the difference between like fractions we subtract the smaller numerator from the greater numerator. In subtraction of fractions having the same denominator, we just need to subtract the numerators of the fractions.

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The associative and commutative properties of natural numbers hold good in the case of fractions also.

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To add unlike fractions, we first convert them into like fractions. In order to make a common denominator we find the LCM of all different denominators of the given fractions and then make them equivalent fractions with a common denominator.

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To add two or more like fractions we simplify add their numerators. The denominator remains same.

Fractions in Descending Order |Arranging Fractions an Descending Order
We will discuss here how to arrange the fractions in descending order. Solved examples for arranging in descending order: 1. Arrange the following fractions 5/6, 7/10, 11/20 in descending order. First we find the L.C.M. of the denominators of the fractions to make the

Fractions in Ascending Order | Arranging Fractions an Ascending Order
We will discuss here how to arrange the fractions in ascending order. Solved examples for arranging in ascending order: 1. Arrange the following fractions 5/6, 8/9, 2/3 in ascending order. First we find the L.C.M. of the denominators of the fractions to make the denominators

Comparison of Unlike Fractions | Compare Unlike Fractions | Comparing
In comparison of unlike fractions, we change the unlike fractions to like fractions and then compare. To compare two fractions with different numerators and different denominators, we multiply by a number to convert them to like fractions. Let us consider some of the
● Fractional Numbers - worksheets
Worksheet on Equivalent Fractions.
Worksheet on Fractions.
Worksheet on Comparison of Like Fractions.
Worksheet on Conversion of Fractions.
Worksheet on Changing Fractions.
Worksheet on Types of Fractions.
Worksheet on Reducing Fraction.
Worksheet on Addition of Fractions having the Same Denominator.
Worksheet on Subtraction of Fractions having the Same Denominator.
Worksheet on Add and Subtract Fractions.
Worksheet on Fractional Numbers.
4th Grade Math Activities From Worksheet on Add and Subtract Fractions to HOME PAGE
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