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## Course: 7th grade > Unit 4

- Worked example: Solving proportions
- Writing proportions example
- Proportion word problem: cookies
- Proportion word problem: hot dogs

## Multi-step ratio and percent problems

- 10 10 1 0 10 parts gold yarn
- 7 7 7 7 parts bronze yarn
- 3 3 3 3 parts silver yarn
- 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

## Problem 2: Soccer

- On Monday, Joel exercises for 20 20 2 0 20 minutes before school, and 25 % 25\% 2 5 % 25, percent of that time is spent playing soccer.
- On Monday, Joel exercises for 60 60 6 0 60 minutes after school, and 40 % 40\% 4 0 % 40, percent of that time is spent playing soccer.

## Problem 3: Candles

- 2 2 2 2 parts red wax
- 5 5 5 5 parts yellow wax
- 3 3 3 3 parts white wax
- (Choice A) 5 10 \dfrac5{10} 1 0 5 start fraction, 5, divided by, 10, end fraction quarts A 5 10 \dfrac5{10} 1 0 5 start fraction, 5, divided by, 10, end fraction quarts
- (Choice B) 1 1 1 1 quart B 1 1 1 1 quart
- (Choice C) 2 1 2 2\dfrac12 2 2 1 2, start fraction, 1, divided by, 2, end fraction quarts C 2 1 2 2\dfrac12 2 2 1 2, start fraction, 1, divided by, 2, end fraction quarts
- (Choice D) 25 25 2 5 25 quarts D 25 25 2 5 25 quarts

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In order to access this I need to be confident with:

Dividing a quantity into a ratio

## Ratio Problem Solving

## What is ratio problem solving?

- What is the ratio involved?
- What order are the quantities in the ratio?
- What is the total amount / what is the part of the total amount known?
- What are you trying to calculate ?

Let’s look at a couple of methods we can use when given certain pieces of information.

Charlie and David share 40 sweets, how many sweets do they each get?

We use the ratio to divide 40 sweets into 8 equal parts.

Then we multiply each part of the ratio by 5.

This means that Charlie will get 15 sweets and David will get 25 sweets.

Step-by-step guide: Dividing ratios (coming soon)

## Ratios and fractions (proportion problems)

Step-by-step guide: Ratios and fractions (coming soon)

## Simplifying and equivalent ratios

## Units and conversions ratio questions

Units and conversions are usually equivalent ratio problems (see above).

- If £1:\$1.37 and we wanted to convert £10 into dollars, we would multiply both sides of the ratio by 10 to get £10 is equivalent to \$13.70.
- The scale on a map is 1:25,000. I measure 12cm on the map. How far is this in real life, in kilometres? After multiplying both parts of the ratio by 12 you must then convert 12 \times 25000=300000 \ cm to km by dividing the solution by 100 \ 000 to get 3km.

Top tip: if you are converting units, always write the units in your ratio.

## How to do ratio problem solving

In order to solve problems including ratios:

Identify key information within the question.

Know what you are trying to calculate.

Use prior knowledge to structure a solution.

## Explain how to do ratio problem solving

## Ratio problem solving worksheet

## Related lessons on ratio

## Ratio problem solving examples

Where the letter above each part of the ratio links to the question.

We know that 465 students have school dinner.

2 Know what you are trying to calculate.

We need to find the value of p.

3 Use prior knowledge to structure a solution.

So the value of p is equal to 7 \times 93=651.

There are 651 students that have a packed lunch.

## Example 2: unit conversions

The table below shows the currency conversions on one day.

Use the table above to convert £520 (GBP) to Euros € (EUR).

Use the table above to convert \bf{£520} (GBP) to Euros \bf{€} (EUR).

## Example 3: writing a ratio 1:n

So we can also express the ratio as 500:2000 which will help us in later steps.

We want to simplify the ratio 500:2000 into the form 1:n.

So the ratio of plant food to water in the form 1:n is 1:4.

## Example 4: forming and solving an equation

We also know that Luke receives £8.

We want to calculate the total amount of pocket money for the three siblings.

The total amount of pocket money is therefore 4+7+8=£19.

## Example 5: simplifying ratios

Below is a bar chart showing the results for the colours of counters in a bag.

Express this data as a ratio in its simplest form.

From the bar chart, we can read the frequencies to create the ratio.

We need to simplify this ratio.

Dividing all the parts of the ratio by 2 , we get

## Example 6: combining two ratios

We are trying to find the ratio of all 3 components: silica, lime and soda.

## Example 7: using bar modelling

We know that the initial ratio is 5:2 and that India has three more parts than Beau.

We want to find the original quantity.

Drawing a bar model of this problem, we have

Where India has 5 equal shares, and Beau has 2 equal shares.

We can find the value of one share by working out 75 \div 3=25g.

We can fill in each share to be 25g.

The total amount of popcorn was 125+50=175g.

## Common misconceptions

## Practice ratio problem solving questions

8-3=5 computer games sold for every 3 board games.

4. The angles in a triangle are written as the ratio x:2x:3x. Calculate the size of each angle.

## Ratio problem solving GCSE questions

1. One mole of water weighs 18 grams and contains 6.02 \times 10^{23} water molecules.

Write this in the form 1gram:n where n represents the number of water molecules in standard form.

Calculate the length of the plank of wood.

5-3=2 \ parts = 36cm so 1 \ part = 18cm

(b) Sally is 16 years younger than Kim. Calculate the sum of their ages.

## Learning checklist

- Relate the language of ratios and the associated calculations to the arithmetic of fractions and to linear functions
- Develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multi-step problems
- Make and use connections between different parts of mathematics to solve problems

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## Corbettmaths

Videos, worksheets, 5-a-day and much more, ratio practice questions, click here for questions, click here for answers.

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## Edexcel GCSE Foundation Unit 11 - Ratio & Proportion

Subject: Mathematics

Age range: 14-16

Resource type: Unit of work

Each upload is a unit for the EdExcel GCSE spec. Each PowerPoint includes starters, class work, examples, plenary + answers. I teach these myself and I upload them as I create them. If I reteach anything, I update it on here. Most material is made from things I've accumulated over the years from others or things I have created myself. I don't remember every item I have used and who from (hence my stuff is all free), as it was when I first used it. If you want to get me a coffee: Paypal @abhawtin

Last updated

17 January 2022

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Following the Pearson Edexcel GCSE SOW for foundation students, Unit 11 - Ratio & Proportion. Simplifying, Writing Ratios, Ratio & Fractions, Sharing in Ratio, Ratio Part Given, Ratio Difference Given, Problem Solving, Best Buys, Recipes, Exchange Rates, Direct Proportion, Inverse Proportion . Each PowerPoint is a full lesson including starter, examples, questions and plenary. The retrieval starter will link to the prior lessons here and in prior units I’ve uploaded. Credits to Mr Barton, Corbett maths, drfrostmaths and others from whom i have sourced some questions and slides. Some are my own too. I’ll upload files as I go along

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## Lorraine2705

Amazing resources. Thank you!

You're welcome, thank you for saying!

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Fantastic set of resources. Thank you for sharing,

You're welcome, glad they are helpful!

## onyiedede11

It cover quite a lot of topics and is good for long term memory recall of previous and future learning.

Thank you for you review!

## x_nihilism_x

These resources are phenomenal - thank you very much. Did you happen to do Unit 7 for Foundation on Averages as i can't find it

Thank you for your comments. Unit 5, 6 & 7 was when I had a trainee with me so never planned my own stuff (I only started uploading this last year from scratch). It's in the pipeline at some point though, but may be next academic year before I get to teaching it again.

Amazing sequence of lessons! Thank you!

You're welcome, glad i could help and thank you for you comments

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## COMMENTS

LESSON 3 Solving Proportion Problems 12 | Math Foundation Unit—Grade 7: Intro setting the direction Here is a summary of the properties of equality: Properties of Equality Re#exive Property of Equality a = a. Symmetric Property of Equality If a = b, then b = a. Transitive Property of Equality If a = b and b = c, then a = c. Addition Property of Equality If a = b, then a + c = b + c.

Things to remember. A ratio is a comparison of two quantities. A proportion is an equality of two ratios. To write a ratio: Determine whether the ratio is part to part or part to whole. Calculate the parts and the whole if needed. Plug values into the ratio. Simplify the ratio if needed.

In other words, 150/20 is 7.5 so we already have half of the ratio (The answer must be an equivalent ratio to 3 : 20). __:150. To get the last half of the answer, we must multiply 7.5 by 3 because we already found out that 150/20 is 7.5. 3 x 7.5 is 22.5 so the answer is 22.5 : 150.

Ratio tables are another technique for solving ratio problems. How to solve a proportion problem. As we have seen, ratio and proportion are strongly linked. ... (Foundation) Ratio GCSE exam questions foundation. 7. The students in Ellie's class walk, cycle or drive to school in the ratio 2:1:4. If 8 students walk, how many students are there ...

Ratio: Problem Solving Textbook Exercise - Corbettmaths. October 7, 2019 corbettmaths.

Ratio problem solving GCSE questions. 1. One mole of water weighs 18 18 grams and contains 6.02 \times 10^ {23} 6.02 × 1023 water molecules. Write this in the form 1gram:n 1gram: n where n n represents the number of water molecules in standard form. 2.

pptx, 1.83 MB. GCSE Maths Problem Solving Foundation Questions. This KS4 GCSE-Style Questions - Foundation Set 3 Question Set contains GCSE-Style questions that typically appear on foundation papers. There are a variety of topics and skills tested in order to prepare students for the GCSE exam. Registering for an LbQ account will give you ...

This plan builds on what Mathletes already know about ratios to introduce the definition of probability as a ratio of desired outcomes to total outcomes. Mathletes will then practice calculating the likelihood of single events. Download the Mathlete handout. Download the coaches version with solutions.

The Math Learning Center grants permission to writers to quote passages and illustrations, with attribution, for academic publications or research purposes. Suggested attribution: "Learning to Think Mathematically with the Ratio Table," Jeffrey Frykholm, 2013. The Math Learning Center is a nonprofit organization serving the education community.

Ready-to-use mathematics resources for Key Stage 3, Key Stage 4 and GCSE maths classes.

Draw 3 parts for lions and 2 parts for tigers, with a total of 55. Divide the total number of big cats (55) in the ratio 3 : 2. To find the value of one part, divide the amount (55) by the total ...

The Corbettmaths Practice Questions on Ratio. Videos, worksheets, 5-a-day and much more

Following the Pearson Edexcel GCSE SOW for foundation students, Unit 11 - Ratio & Proportion. Simplifying, Writing Ratios, Ratio & Fractions, Sharing in Ratio, Ratio Part Given, Ratio Difference Given, Problem Solving, Best Buys, Recipes, Exchange Rates, Direct Proportion, Inverse Proportion . Each PowerPoint is a full lesson including starter ...

Explore how to divide a value into a given ratio, and understand links between ratios and fractions with this BBC Bitesize Maths article. For students ages 11 to 14. Solving ratio problems