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Ratio

Use ratio notation, simplify ratios, and divide a quantity into parts based on a given ratio.

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This is level 6: dividing a quantity in a given ratio. You will be awarded a trophy if you get at least 7 answers correct and you do this activity online.

1

Tom and Sean are window cleaners. Tom cleans 7 windows and Sean cleans 5 windows. Altogether they earn £36. How much will Tom get if they share the money in the same ratio as the number of windows they have cleaned?
Window Cleaning

2

Share £72 in the ratio 8:1. How much will the smaller share be?

3

Share 72kg in the ratio 1:5. How heavy will the larger share be?

4

The ratio of boys to girls in a school is 5:6. How many girls are at the school if there are 1210 students altogether.

5

The ratio of sunny days to cloudy days in the month of June was 3:2. How many sunny days were there?
Sun

6

One kilogram of sugar is shared between a jar and a jug in the ratio 3:7. How many grams of sugar went into the jar?

7

In the winter the ratio of daylight to darkness on a particular day is 5:7. How many hours of daylight were there?

8

To make orange squash you need to mix cordial and water in the ratio 1:8. How much cordial would you need to make 72 cups of squash?

9

Samantha is 8 years old. Her brother Kevin is 5 years old. The pocket money they receive is in the same ratio as their ages. How many pence does Kevin receive if their pocket money totals £7.80 ?

10

A toy car and a battery together costs £68. The ratio of the cost of the car to the battery is 16:1. How much did the battery cost?

Check

This is Ratio level 6. You can also try:
Level 1 Level 2 Level 3 Level 4 Level 5 Level 7 Level 8

There is also a related exercise on the Unitary Method.

Instructions

Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.

Why am I learning this?

Mathematicians are not the people who find Maths easy; they are the people who enjoy how mystifying, puzzling and hard it is. Are you a mathematician?

Comment recorded on the 24 May 'Starter of the Day' page by Ruth Seward, Hagley Park Sports College:

"Find the starters wonderful; students enjoy them and often want to use the idea generated by the starter in other parts of the lesson. Keep up the good work"

Comment recorded on the 19 October 'Starter of the Day' page by E Pollard, Huddersfield:

"I used this with my bottom set in year 9. To engage them I used their name and favorite football team (or pop group) instead of the school name. For homework, I asked each student to find a definition for the key words they had been given (once they had fun trying to guess the answer) and they presented their findings to the rest of the class the following day. They felt really special because the key words came from their own personal information."

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Maths Mind Reader

This spectacular magic trick never fails to amaze people of all ages assuming they can add and subtract very simple numbers. The mathematics comes in finding out how the trick works.

Answers

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Go Maths

Learning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths page is an alphabetical list of free activities designed for students in Secondary/High school.

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Are you looking for something specific? An exercise to supplement the topic you are studying at school at the moment perhaps. Navigate using our Maths Map to find exercises, puzzles and Maths lesson starters grouped by topic.

Teachers

If you found this activity useful don't forget to record it in your scheme of work or learning management system. The short URL, ready to be copied and pasted, is as follows:

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It may be worth remembering that if Transum.org should go offline for whatever reason, there is a mirror site at Transum.info that contains most of the resources that are available here on Transum.org.

When planning to use technology in your lesson always have a plan B!

Ms Michelle,

Monday, November 9, 2020

"5 STARS!!
My class absolutely loves these activities, they look forward to maths everyday!!"

Lizi, Camden School For Girls!

Friday, May 3, 2024

"Super great! My classmates really enjoy this website! Keep goin'!"

Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.

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Description of Levels

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Level 1 - Identifying ratios from pictures

Level 2 - Simplifying ratios

Level 3 - Simplifying ratios with mixed units

Level 4 - Reducing a ratio to the form 1:n or n:1

Level 5 - Simplifying ratios with fractional parts

Level 6 - Dividing a quantity in a given ratio

Level 7 - Comparing the parts of a ratio

Level 8 - Using ratios in real life

Retro: Real life problems adapted from an old Mathematics textbook

Exam Style Questions - A collection of problems in the style of GCSE or IB/A-level exam paper questions (worked solutions are available for Transum subscribers).

More on this topic including lesson Starters, visual aids, investigations and self-marking exercises.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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Curriculum Reference

See the National Curriculum page for links to related online activities and resources.

Introduction to Ratios

Please be aware that the levels referenced in this video pertain to the structure of the exercise when it consisted of only seven levels. Following the production of the video, I introduced a new Level 4, focused on simplifying ratios to the form 1:n. Consequently, the previous Level 4 was reassigned as Level 5, Level 5 advanced to Level 6, and this pattern continued accordingly. I am confident you will be able to navigate these changes; my apologies for any inconvenience caused.

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly. You can double-click the 'Check' button to make it float at the bottom of your screen.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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