Mini Minds Hub · Free printable
Simplifying Ratios: Free Printable Worksheet for Year 7
- ForYear 7
- StageKey Stage 3
- CostFree
- FormatPrintable PDF
Simplifying Ratios is a free printable maths worksheet for Year 7 (ages 11 to 12), in Key Stage 3. Children simplify ratios by dividing both parts by the same number, choosing the highest common factor so that nothing is left to simplify. It takes about 15 minutes, needs only a pencil, and page 2 gives the grown-up help ideas, a stretch task and the answers.
It comes from the Mini Minds Hub, the free library of printables from Jaques of London, the British games and toy company that has been making games for families since 1795. Print both pages, give page 1 to your child and keep page 2 for yourself. Black and white printing works well.
What is on the sheet
Children meet a set of ratios written with a colon, such as two part ratios and one ratio with three parts. Each one needs writing in its simplest form. To do this, they look for a number that divides into every part, divide each part by it, and check that nothing more can be done. There is space to answer each question.
- 4 : 8
- 6 : 9
- 12 : 16
- 20 : 5
- 15 : 25
- 9 : 27
- 8 : 20
- 6 : 9 : 12
A worked example
Simplify 21 : 49.
This is a different question from the ones on the sheet. It shows one way to find the answer and one way to check it.
Method 1: list the factors- Factors of 21: 1, 3, 7, 21.
- Factors of 49: 1, 7, 49.
- The biggest factor they share is 7.
- Divide both parts by 7: 21 ÷ 7 = 3 and 49 ÷ 7 = 7.
- So 21 : 49 simplifies to 3 : 7.
- Multiply each part of your answer by 7: 3 × 7 = 21 and 7 × 7 = 49.
- You are back at the start, so the ratio keeps its value.
- Now look at 3 and 7. They share no factor other than 1, so the ratio cannot be simplified any further.
What does it mean to simplify a ratio?
A ratio compares two or more quantities. Written with a colon, it shows how much of one thing there is for each amount of another. Simplifying a ratio means writing it with smaller whole numbers while keeping the same relationship. The ratio is not changed, only written more neatly. It works in the same way as simplifying a fraction.
The rule is simple. Whatever you do to one part, you must do to every other part. Dividing both sides by the same number keeps the ratio equivalent. A ratio is in its simplest form when the parts share no common factor other than 1. That is why finding the highest common factor saves time, because it gets you there in one step.
Skills and curriculum link
- Ratio notation
- Finding factors
- Highest common factor
- Simplifying
- Checking answers
Ideas behind the sheet
- Equivalent ratiosDifferent ratios can describe the same relationship. Multiplying or dividing every part by the same number gives an equivalent ratio.
- Common factorsA common factor is a number that divides exactly into every part. Finding these is the key step in simplifying.
- Highest common factorDividing by the highest common factor reaches the simplest form in one step. Smaller common factors work too, but need repeating.
- Order mattersA ratio compares parts in a set order. Keep the parts in the same order after simplifying.
Key words
- RatioA way to compare two or more amounts. It is written with a colon between the parts.
- PartOne of the numbers in a ratio, on one side of a colon.
- FactorA whole number that divides exactly into another number.
- Highest common factorThe biggest number that is a factor of every part in a ratio.
- Simplest formA ratio whose parts share no common factor other than 1.
- Equivalent ratiosRatios that show the same relationship, such as 1 : 2 and 3 : 6.
How to use it
- Print both pages. Page 1 is for your child. Keep page 2, which has the notes and answers.
- Work through the first ratio together. Ask your child to say what they could divide both parts by.
- Let them try the rest alone. It should take about 15 minutes. Remind them to check that both parts share no common factor other than 1.
- Check against the answers on page 2. Ask, "How did you know that was the biggest factor?" The reasoning matters as much as the answer.
- Come back to it on another day and redo any that felt tricky. Repeating a familiar sheet builds confidence.
Help, stretch and game ideas
If it feels too hard
List the factors of each number first, then circle the biggest one they share. Divide both parts by that number. Try the ratios with smaller numbers first, and come back to the harder ones later. Say each division out loud.
To stretch confident children
Choose a simplest ratio of your own. Write three different ratios that simplify to it, and explain how you made them. Then swap with a friend and see whether they can simplify yours back again.
Make it a game
Play ratio snap. Make cards in pairs, with one ratio that is not simplified and one in its simplest form. Shuffle them, turn them over one at a time and call snap when two cards match. Check each snap together.
Mistakes to watch for
Watch forA child divides only one part of the ratio, so the two sides no longer match.
Try thisSay the rule aloud: whatever you do to one part, you do to every part. Check by multiplying back to the start.
Watch forA child divides by a small common factor, such as 2 for 24 : 36, and stops too soon.
Try thisAsk, "Do both parts still share a factor?" Keep dividing until the only shared factor is 1, or find the highest common factor first.
Watch forA child swaps the order of the parts when writing the answer.
Try thisUnderline the first part before dividing. The first part of the answer must come from the first part of the question.
Talk about it
- How do you decide which number to divide by?
- How can you check that a ratio is in its simplest form?
- Why must you divide every part by the same number?
- What is the same and what is different between simplifying a ratio and simplifying a fraction?
- Which ratio on the sheet did you find easiest, and why?
- Can you think of a time when a ratio is used in real life?
Take it off the page
Counter ratios
Use two colours of counters, buttons or bricks. Make a group of 14 of one colour and 21 of another. Share them into equal smaller groups to see the simplest ratio.
Squared paper rectangles
Draw rectangles on squared paper with different sides, such as 6 by 9. Write each side length as a ratio and simplify it. Then draw a smaller rectangle with the same ratio.
Ratio hunt
Look around the house for two things you can count, such as red and blue pens. Write their ratio, then simplify it and explain what it tells you.
Who it is for
Parents
Sit beside your child for the first ratio, then let them lead. About 15 minutes is plenty. If they get stuck, ask them to list the factors of each number and look for the biggest one they share.
Teachers
Use it as a starter, plenary, early finisher task, homework or supply cover. It needs no preparation beyond printing. Page 2 has help and stretch ideas for mixed ability groups, and the answers for quick marking.
Home educators
Print it as part of your wider maths plan. It fits well after work on factors and multiples. You can print it again later for revision, or for brothers and sisters.
Where this fits
Before this, children need secure times tables, and to be able to find factors and common factors. Simplifying fractions is a close cousin of this skill, so it helps if that idea is already familiar.
After this, children can move on to sharing amounts in a given ratio, comparing ratios and solving problems with proportion. Simplifying ratios is a foundation for the Key Stage 3 strand on ratio, proportion and rates of change.
Questions parents and teachers ask
- What age is Simplifying Ratios for?
It is written for Year 7 (ages 11 to 12), in Key Stage 3. It also works as revision for older children, or as a stretch task for confident learners in upper Key Stage 2.
- What will children practise?
Children practise simplifying ratios by dividing both parts by the same number. They find factors, look for the highest common factor and check that the answer cannot be simplified further.
- How long does it take?
It takes about 15 minutes for most children working alone. You can make it shorter by doing only the first few ratios, or longer by adding the stretch idea on page 2.
- What if it feels too hard?
Start by listing the factors of each number, then circle the biggest one they share. Work through the first ratio together and try the easier ones first. Come back to the harder ones another day.
- Is it free?
Yes. It is free to print for home and classroom use. You can print it again for brothers, sisters or revision a few weeks later.
- Can teachers use it in class?
Yes. Teachers can use it as a starter, plenary, early finisher task, homework or table activity. It needs no preparation beyond printing, and page 2 has the answers.
- Do I need to print in colour?
No. It prints well in black and white on plain A4 paper. Page 1 is for the child and page 2 is for the grown-up.
Preview the full PDF
Made by Jaques of London, making games for families since 1795. A printable supports classroom learning and does not replace a teacher.