Year 6: Ratio notation: a:b
Part of the Year 6 ratio and proportion chapter. Chapter overview · whole chapter on one page
Ratio notation: a:b
A ratio compares two amounts of the same kind. Suppose a bag holds 2 red counters and 3 blue counters. The ratio of red to blue is 2:3, which we read as ‘2 to 3’. The colon : means ‘to’.
The order matters. The ratio of blue to red is 3:2, which is a different ratio. Always keep the amounts in the order that the question gives them.
A ratio can be simplified just like a fraction. Divide both numbers by their highest common factor (HCF). For example, 4:6 divided by 2 is 2:3. A ratio does not tell us the actual amounts: 2:3 could mean 2 red and 3 blue, or 20 red and 30 blue.
Key ideas
- A ratio is written as a:b, with a colon between the two numbers.
- The order matters: the first number is the first amount named in the question.
- Write a ratio in its simplest form by dividing both numbers by their HCF.
- A ratio does not give the real amounts. Two numbers in a ratio are parts, not the total.
Key words. A ratio compares two amounts of the same kind. We write it with a colon: 2:3 is read ‘2 to 3’. The order matters, because the first number is the first amount named.
Method. Divide both numbers by their highest common factor (HCF).
- Write the ratio in the order the question gives. The order of the numbers must not change.4:6
- Find the highest common factor (HCF) of the two numbers. It is the biggest number that divides into both.HCF of 4 and 6 is 2
- Divide both numbers by the HCF. This keeps the same ratio but uses smaller numbers.4 ÷ 2 = 2, and 6 ÷ 2 = 3
- Write the answer. 2:3
Check. 2 × 2 = 4 and 3 × 2 = 6. ✓
Watch out. Divide both numbers by the same number. Keep the order the question gives.
Key words. A ratio compares two amounts of the same kind. We write it with a colon: 2:3 is read ‘2 to 3’. The order matters, because the first number is the first amount named.
Method. Divide both numbers by their highest common factor (HCF).
- Write the ratio in the order the question gives. The order of the numbers must not change.12:8
- Find the highest common factor (HCF) of the two numbers. It is the biggest number that divides into both.HCF of 12 and 8 is 4
- Divide both numbers by the HCF. This keeps the same ratio but uses smaller numbers.12 ÷ 4 = 3, and 8 ÷ 4 = 2
- Write the answer. 3:2
Check. 3 × 4 = 12 and 2 × 4 = 8. ✓
Watch out. Divide both numbers by the same number. Keep the order the question gives.
Key words. A ratio compares two amounts of the same kind. We write it with a colon: 2:3 is read ‘2 to 3’. The order matters, because the first number is the first amount named.
Method. Divide both numbers by their highest common factor (HCF).
- Write the ratio in the order the question gives. The order of the numbers must not change.10:15
- Find the highest common factor (HCF) of the two numbers. It is the biggest number that divides into both.HCF of 10 and 15 is 5
- Divide both numbers by the HCF. This keeps the same ratio but uses smaller numbers.10 ÷ 5 = 2, and 15 ÷ 5 = 3
- Write the answer. 2:3
Check. 2 × 5 = 10 and 3 × 5 = 15. ✓
Watch out. Divide both numbers by the same number. Keep the order the question gives.
Watch out
2:3 is not the same as 3:2. Many pupils swap the numbers. Read the question again and ask: which amount comes first?
Exam tip
Grown-up tip. Ask the child to say the ratio out loud: “2 to 3”. Then ask: “Can both numbers be divided by 2?” If so, divide them both.
Exercise 7A Writing and simplifying ratios
Non-calculatorKey words. A ratio compares two amounts of the same kind. We write it with a colon: 2:3 is read ‘2 to 3’. The order matters, because the first number is the first amount named.
Method. Divide both numbers by their highest common factor (HCF).
- Write the ratio in the order the question gives. The first number stays first.5:7
- Find the highest common factor (HCF) of the two numbers. It is the biggest number that divides into both.HCF of 5 and 7 is 1
- Only 1 divides into both, so the ratio is already in its simplest form. Dividing by 1 changes nothing.5:7 is already simplest
- Write the answer. 5:7
Check. 5 × 1 = 5 and 7 × 1 = 7. ✓
Watch out. Divide both numbers by the same number. Keep the order the question gives.
Key words. A ratio compares two amounts of the same kind. We write it with a colon: 2:3 is read ‘2 to 3’. The order matters, because the first number is the first amount named.
Method. Divide both numbers by their highest common factor (HCF).
- Write the ratio in the order the question gives. The order of the numbers must not change.8:12
- Find the highest common factor (HCF) of the two numbers. It is the biggest number that divides into both.HCF of 8 and 12 is 4
- Divide both numbers by the HCF. This keeps the same ratio but uses smaller numbers.8 ÷ 4 = 2, and 12 ÷ 4 = 3
- Write the answer. 2:3
Check. 2 × 4 = 8 and 3 × 4 = 12. ✓
Watch out. Divide both numbers by the same number. Keep the order the question gives.
Key words. A ratio compares two amounts of the same kind. We write it with a colon: 2:3 is read ‘2 to 3’. The order matters, because the first number is the first amount named.
Method. Divide both numbers by their highest common factor (HCF).
- Write the ratio in the order the question gives. The order of the numbers must not change.6:9
- Find the highest common factor (HCF) of the two numbers. It is the biggest number that divides into both.HCF of 6 and 9 is 3
- Divide both numbers by the HCF. This keeps the same ratio but uses smaller numbers.6 ÷ 3 = 2, and 9 ÷ 3 = 3
- Write the answer. 2:3
Check. 2 × 3 = 6 and 3 × 3 = 9. ✓
Watch out. Divide both numbers by the same number. Keep the order the question gives.
Key words. A ratio compares two amounts of the same kind. We write it with a colon: 2:3 is read ‘2 to 3’. The order matters, because the first number is the first amount named.
Method. Divide both numbers by their highest common factor (HCF).
- Write the ratio in the order the question gives. The order of the numbers must not change.10:4
- Find the highest common factor (HCF) of the two numbers. It is the biggest number that divides into both.HCF of 10 and 4 is 2
- Divide both numbers by the HCF. This keeps the same ratio but uses smaller numbers.10 ÷ 2 = 5, and 4 ÷ 2 = 2
- Write the answer. 5:2
Check. 5 × 2 = 10 and 2 × 2 = 4. ✓
Watch out. Divide both numbers by the same number. Keep the order the question gives.
Key words. A ratio compares two amounts of the same kind. We write it with a colon: 2:3 is read ‘2 to 3’. The order matters, because the first number is the first amount named.
Method. Divide both numbers by their highest common factor (HCF).
- Write the ratio in the order the question gives. The order of the numbers must not change.9:12
- Find the highest common factor (HCF) of the two numbers. It is the biggest number that divides into both.HCF of 9 and 12 is 3
- Divide both numbers by the HCF. This keeps the same ratio but uses smaller numbers.9 ÷ 3 = 3, and 12 ÷ 3 = 4
- Write the answer. 3:4
Check. 3 × 3 = 9 and 4 × 3 = 12. ✓
Watch out. Divide both numbers by the same number. Keep the order the question gives.
Key words. A ratio compares two amounts of the same kind. We write it with a colon: 2:3 is read ‘2 to 3’. The order matters, because the first number is the first amount named.
Method. Divide both numbers by their highest common factor (HCF).
- Write the ratio in the order the question gives. The order of the numbers must not change.15:25
- Find the highest common factor (HCF) of the two numbers. It is the biggest number that divides into both.HCF of 15 and 25 is 5
- Divide both numbers by the HCF. This keeps the same ratio but uses smaller numbers.15 ÷ 5 = 3, and 25 ÷ 5 = 5
- Write the answer. 3:5
Check. 3 × 5 = 15 and 5 × 5 = 25. ✓
Watch out. Divide both numbers by the same number. Keep the order the question gives.
Key words. A ratio compares two amounts of the same kind. We write it with a colon: 2:3 is read ‘2 to 3’. The order matters, because the first number is the first amount named.
Method. Divide both numbers by their highest common factor (HCF).
- Write the ratio in the order the question gives. The order of the numbers must not change.20:12
- Find the highest common factor (HCF) of the two numbers. It is the biggest number that divides into both.HCF of 20 and 12 is 4
- Divide both numbers by the HCF. This keeps the same ratio but uses smaller numbers.20 ÷ 4 = 5, and 12 ÷ 4 = 3
- Write the answer. 5:3
Check. 5 × 4 = 20 and 3 × 4 = 12. ✓
Watch out. Divide both numbers by the same number. Keep the order the question gives.
Key words. A ratio compares two amounts of the same kind. We write it with a colon: 2:3 is read ‘2 to 3’. The order matters, because the first number is the first amount named.
Method. Divide both numbers by their highest common factor (HCF).
- Write the ratio in the order the question gives. The first number stays first.3:5
- Find the highest common factor (HCF) of the two numbers. It is the biggest number that divides into both.HCF of 3 and 5 is 1
- Only 1 divides into both, so the ratio is already in its simplest form. Dividing by 1 changes nothing.3:5 is already simplest
- Write the answer. 3:5
Check. 3 × 1 = 3 and 5 × 1 = 5. ✓
Watch out. Divide both numbers by the same number. Keep the order the question gives.
Key words. A ratio compares two amounts of the same kind. We write it with a colon: 2:3 is read ‘2 to 3’. The order matters, because the first number is the first amount named.
Method. Divide both numbers by their highest common factor (HCF).
- Write the ratio in the order the question gives. The order of the numbers must not change.2:6
- Find the highest common factor (HCF) of the two numbers. It is the biggest number that divides into both.HCF of 2 and 6 is 2
- Divide both numbers by the HCF. This keeps the same ratio but uses smaller numbers.2 ÷ 2 = 1, and 6 ÷ 2 = 3
- Write the answer. 1:3
Check. 1 × 2 = 2 and 3 × 2 = 6. ✓
Watch out. Divide both numbers by the same number. Keep the order the question gives.
Key words. A ratio compares two amounts of the same kind. We write it with a colon: 2:3 is read ‘2 to 3’. The order matters, because the first number is the first amount named.
Method. Divide both numbers by their highest common factor (HCF).
- Write the ratio in the order the question gives. The order of the numbers must not change.180:240
- Find the highest common factor (HCF) of the two numbers. It is the biggest number that divides into both.HCF of 180 and 240 is 60
- Divide both numbers by the HCF. This keeps the same ratio but uses smaller numbers.180 ÷ 60 = 3, and 240 ÷ 60 = 4
- Write the answer. 3:4
Check. 3 × 60 = 180 and 4 × 60 = 240. ✓
Watch out. Divide both numbers by the same number. Keep the order the question gives.
Key words. A ratio compares two amounts of the same kind. We write it with a colon: 2:3 is read ‘2 to 3’. The order matters, because the first number is the first amount named.
Method. Divide both numbers by their highest common factor (HCF).
- Write the ratio in the order the question gives. The order of the numbers must not change.18:27
- Find the highest common factor (HCF) of the two numbers. It is the biggest number that divides into both.HCF of 18 and 27 is 9
- Divide both numbers by the HCF. This keeps the same ratio but uses smaller numbers.18 ÷ 9 = 2, and 27 ÷ 9 = 3
- Write the answer. 2:3
Check. 2 × 9 = 18 and 3 × 9 = 27. ✓
Watch out. Divide both numbers by the same number. Keep the order the question gives.
Key words. A ratio compares two amounts of the same kind. We write it with a colon: 2:3 is read ‘2 to 3’. The order matters, because the first number is the first amount named.
Method. Divide both numbers by their highest common factor (HCF).
- Write the ratio in the order the question gives. The order of the numbers must not change.25:10
- Find the highest common factor (HCF) of the two numbers. It is the biggest number that divides into both.HCF of 25 and 10 is 5
- Divide both numbers by the HCF. This keeps the same ratio but uses smaller numbers.25 ÷ 5 = 5, and 10 ÷ 5 = 2
- Write the answer. 5:2
Check. 5 × 5 = 25 and 2 × 5 = 10. ✓
Watch out. Divide both numbers by the same number. Keep the order the question gives.
Key words. A ratio compares two amounts of the same kind. We write it with a colon: 2:3 is read ‘2 to 3’. The order matters, because the first number is the first amount named.
Method. Keep the order of the question: apples first, then oranges. Then simplify.
- Find the order in the question. The ratio is apples to oranges, so apples come first.4 apples : 10 oranges
- Write the ratio in that order. Sam has the numbers the wrong way round.4 : 10
- Simplify by dividing both numbers by 2. The HCF of 4 and 10 is 2.4 ÷ 2 = 2, and 10 ÷ 2 = 5
- Write the answer. No. 4:10 simplifies to 2:5.
Check. The ratio of oranges to apples would be 5:2, but the question asks for apples to oranges. ✓
Watch out. The order must match the question. Sam swapped the numbers.
Key words. A ratio compares two amounts of the same kind. We write it with a colon: 2:3 is read ‘2 to 3’. The order matters, because the first number is the first amount named.
Method. Simplify both ratios. If the simplest forms are the same, the ratios are equivalent.
- Simplify 6:9. Divide both numbers by their HCF, 3.6:9 = 2:3
- Simplify 3:2. Divide both numbers by their HCF, 1.3:2 = 3:2
- Compare the two simplest forms. The same simplest form means the ratios are equivalent.2:3 and 3:2 are different
- Write the answer. No
Check. 6 × 2 = 12 and 9 × 3 = 27, so the cross-products are not equal. ✓
Watch out. Compare the simplest forms, not the first numbers.
Key words. A ratio compares two amounts of the same kind. We write it with a colon: 2:3 is read ‘2 to 3’. The order matters, because the first number is the first amount named.
Method. Simplify each pair of numbers, then compare with 2:3.
- Simplify 10:15. The HCF of 10 and 15 is 5.10:15 = 2:3
- Simplify 12:18. The HCF of 12 and 18 is 6.12:18 = 2:3
- Compare with the club ratio, 2:3. Both simplify to the same ratio as the club.2:3 and 2:3 are the same
- Write the answer. Yes, both. 10:15 and 12:18 both simplify to 2:3.
Check. 10 ÷ 5 = 2 and 15 ÷ 5 = 3; 12 ÷ 6 = 2 and 18 ÷ 6 = 3. ✓
Watch out. Both amounts can be right, because each is the same ratio with a different total.