Simplifying ratios

To simplify a ratio, divide both parts by their greatest common factor: 12 : 18 = 2 : 3. A quiz for kids, parent help below.

🧒 Kids: make the numbers small!

Find a number that divides into both parts. Divide both. Keep going until you can’t. Then try the quiz!

▶ Quiz 🔢 More practice

💡 Trick: 12 and 18 both divide by 6. 12 ÷ 6 = 2 and 18 ÷ 6 = 3, so 12 : 18 = 2 : 3!

More ratios: What is a ratio · Equivalent ratios · Simplifying ratios · Ratio tables · Tape diagrams · Unit rates

For parents and teachers ↓

This part is for grown-ups: the key idea, pictures to draw, what to say, common mistakes, questions with answers and a free worksheet.

The trick: divide by the greatest common factor

A ratio is in simplest form when the only number that divides into all its parts is 1. Find the greatest common factor and divide every part by it. Dividing by a smaller common factor works too, but takes more steps.

Patterns to spot

See it: pictures to draw with your child

Draw these on paper or a whiteboard. A quick sketch makes the idea concrete before any rules.

12 blue and 18 orange: lots of shapes to count.
Put them into 6 equal groups. Each group has 2 blue and 3 orange, so 12 : 18 = 2 : 3.
Blue66= 12Orange666= 18
In a tape diagram, each box is 6. 2 boxes and 3 boxes: 12 : 18 in simplest form is 2 : 3.

What your child already knows

Children already know how to find factors and how to simplify fractions like 6/8 = 3/4. Simplifying a ratio uses exactly the same skill on two (or more) numbers.

In real life: A recipe for 12 people with 6 eggs and 9 cups of flour is 2 : 3 eggs to flour. The simple ratio is easier to remember and to scale for any number of people.

Ratios with decimals, units and three parts

For decimals, multiply every part by 10 or 100 first. 1.5 : 2.5 becomes 15 : 25, which simplifies to 3 : 5.

For different units, change to the same unit first. For example, 40 cm : 2 m is 40 cm : 200 cm. That simplifies to 1 : 5.

A three-part ratio simplifies the same way: divide every part by a factor they all share. For example, 6 : 9 : 12 divides by 3 to give 2 : 3 : 4.

Worked examples

Example 1: Find the GCF

  1. Simplify 24 : 36.
  2. The factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24.
  3. The largest that also divides 36 is 12. 24 ÷ 12 = 2 and 36 ÷ 12 = 3.
  4. So 24 : 36 = 2 : 3.

Example 2: Step by step

  1. Simplify 40 : 60.
  2. Both end in 0, so divide by 10: 4 : 6.
  3. Both are even, so divide by 2: 2 : 3.
  4. No more common factors, so 2 : 3 is the simplest form.

Example 3: With units

  1. Simplify 30 minutes : 2 hours. 2 hours is 120 minutes, so the ratio is 30 : 120.
  2. Divide both by 30: 1 : 4.

Common mistakes

Stopping too earlyWrites 24 : 36 as 12 : 18.Fix: check again: 12 and 18 still share 6, so keep going to 2 : 3.
Dividing only one partWrites 12 : 18 as 2 : 18.Fix: divide every part by the same number.
Ignoring unitsWrites 30 minutes : 2 hours as 15 : 1.Fix: change both to minutes first: 30 : 120 = 1 : 4.

What to say to your child

A short script for your first session. Pause after each line and let your child answer.

  1. “What number goes into 12 and into 18?” (2, 3 or 6.)
  2. “Which is the biggest?” (6.)
  3. “Divide both by 6. What do you get?” (2 : 3.)
  4. “Can 2 and 3 both be divided again?” (No.)
  5. “So 2 : 3 is the simplest form. It is the same mix with smaller numbers.”

Questions to try (answers below)

Ask these out loud or write them down. The last one is a stretch.

  1. Simplify 6 : 8
  2. Simplify 10 : 25
  3. Simplify 14 : 21
  4. Simplify 9 : 27
  5. Simplify 16 : 40
  6. Simplify 45 : 30
  7. Simplify 8 : 12 : 20
  8. Simplify 0.5 : 2
  9. Stretch: simplify 75 cm : 3 m
Show the answers
  1. 3 : 4
  2. 2 : 5
  3. 2 : 3
  4. 1 : 3
  5. 2 : 5
  6. 3 : 2
  7. 2 : 3 : 5
  8. 1 : 4
  9. 1 : 4

Games to play at home

Factor hunt

Write two numbers, list their factors and circle the biggest one they share.

Lego groups

Make 12 red and 18 blue bricks into equal groups and read the simple ratio.

Recipe trim

Take a big recipe and write each ratio in its simplest form.

A 5-day plan for simplifying ratios

Ten minutes a day is enough. Short, regular practice works far better than one long session.

By grade

Grade 6 uses common factors (Common Core 6.NS.B.4) to write ratios and fractions in simplest form. It also learns ratio language (6.RP.A.1). In India, simplest form of a ratio is part of the class 6 ratio and proportion chapter.

More for each grade: Grade 6 math and the CBSE class 6 maths guide.

What comes next

Use simplest forms to check equivalent ratios, or try the ratio calculator. For more on factors, see simplifying fractions.

Worksheet and more practice

Print a free worksheet with an answer key, or keep practicing online with ratio practice.

Printable PDFs: ratios worksheet · unit rates worksheet · make a fresh ratio test

← Equivalent ratiosRatio tables →

More: ratios for kids · ratio calculator · unit rate calculator · ratio practice · percentages for kids · fractions for kids

Last reviewed

Questions parents ask

How do you simplify a ratio?

Divide every part by the greatest common factor. 12 : 18 ÷ 6 = 2 : 3.

What is the simplest form of a ratio?

The equivalent ratio whose parts share no common factor except 1, like 2 : 3.

How do you simplify a ratio with decimals?

Multiply every part by 10 or 100 to make whole numbers, then simplify. 1.5 : 2.5 = 15 : 25 = 3 : 5.

How do you simplify a ratio with different units?

Change both amounts to the same unit first. 40 cm : 2 m = 40 : 200 = 1 : 5.

What grade learns simplifying ratios?

Grade 6 under Common Core 6.RP.A.1 and 6.NS.B.4. In India, class 6.