Year 6 Arithmetic (SATs): Ratio language and fractions
Part of the Year 6 Arithmetic (SATs) ratio and proportion chapter. Chapter overview · whole chapter on one page
Ratio language and fractions
Rule
A ratio compares two amounts and is written a:b. Simplify it by dividing both parts by their highest common factor: 12:20 = 3:5.
The total parts are a + b. The first part is a/(a + b) of the whole, and the second part is b/(a + b).
For the full work on ratio, read Year 6 maths, chapter 5.
Key ideas
- A ratio is written a:b, and it compares two quantities.
- Simplify a ratio by dividing both parts by the same number.
- Add the parts to find the total number of parts.
- The fraction for the first part is a/(a + b).
Method. Divide both parts by the highest common factor.
- Find the highest common factor of the two numbers. The biggest number that divides into 12 and 20 is 4.HCF = 4
- Divide both parts of the ratio by it. Dividing both parts by the same number keeps the ratio the same.12 ÷ 4 = 3 and 20 ÷ 4 = 5
- Write the answer. 3:5
Check. 3 × 4 = 12 and 5 × 4 = 20. ✓
Watch out. Simplify fully: 6:10 is not the simplest form, 3:5 is.
Method. Find the total number of parts, then write the boys' parts as a fraction of the total.
- Add the parts. 3 + 5 = 8 parts altogether.3 + 5 = 8
- Write the boys as a fraction. Boys are 3 of the 8 parts.3/8
- Write the answer. 3/8
Check. The girls are 5/8, and 3/8 + 5/8 = 1. ✓
Method. Share the 24 pupils into the parts of the ratio.
- Add the parts of the ratio. 3 + 5 = 8, so the total is shared into 8 equal parts.3 + 5 = 8 parts
- Find the value of one part. Share the total into 8 equal parts.24 ÷ 8 = 3
- Find each share. Multiply the value of one part by each number in the ratio.3 × 3 = 9 and 5 × 3 = 15
- Write the answer. 9
Check. 9 boys and 15 girls make 24 pupils. ✓
Exercise 5A Practice: ratio language and fractions
Non-calculatorMethod. Divide both parts by the highest common factor.
- Find the highest common factor of the two numbers. The biggest number that divides into 12 and 20 is 4.HCF = 4
- Divide both parts of the ratio by it. Dividing both parts by the same number keeps the ratio the same.12 ÷ 4 = 3 and 20 ÷ 4 = 5
- Write the answer. 3:5
Check. 3 and 5 have no common factor. ✓
Method. Divide both parts by the highest common factor.
- Find the highest common factor of the two numbers. The biggest number that divides into 9 and 6 is 3.HCF = 3
- Divide both parts of the ratio by it. Dividing both parts by the same number keeps the ratio the same.9 ÷ 3 = 3 and 6 ÷ 3 = 2
- Write the answer. 3:2
Check. 3 and 2 have no common factor. ✓
Method. Divide both parts by the highest common factor.
- Find the highest common factor of the two numbers. The biggest number that divides into 14 and 21 is 7.HCF = 7
- Divide both parts of the ratio by it. Dividing both parts by the same number keeps the ratio the same.14 ÷ 7 = 2 and 21 ÷ 7 = 3
- Write the answer. 2:3
Check. 2 and 3 have no common factor. ✓
Method. Divide both parts by the highest common factor.
- Find the highest common factor of the two numbers. The biggest number that divides into 15 and 45 is 15.HCF = 15
- Divide both parts of the ratio by it. Dividing both parts by the same number keeps the ratio the same.15 ÷ 15 = 1 and 45 ÷ 15 = 3
- Write the answer. 1:3
Check. 1 and 3 have no common factor. ✓
Method. Divide both parts by the highest common factor.
- Find the highest common factor of the two numbers. The biggest number that divides into 8 and 24 is 8.HCF = 8
- Divide both parts of the ratio by it. Dividing both parts by the same number keeps the ratio the same.8 ÷ 8 = 1 and 24 ÷ 8 = 3
- Write the answer. 1:3
Check. 1 and 3 have no common factor. ✓
Method. Divide both parts by the highest common factor.
- Find the highest common factor of the two numbers. The biggest number that divides into 16 and 40 is 8.HCF = 8
- Divide both parts of the ratio by it. Dividing both parts by the same number keeps the ratio the same.16 ÷ 8 = 2 and 40 ÷ 8 = 5
- Write the answer. 2:5
Check. 2 and 5 have no common factor. ✓
Method. Divide both parts by the highest common factor.
- Find the highest common factor of the two numbers. The biggest number that divides into 30 and 45 is 15.HCF = 15
- Divide both parts of the ratio by it. Dividing both parts by the same number keeps the ratio the same.30 ÷ 15 = 2 and 45 ÷ 15 = 3
- Write the answer. 2:3
Check. 2 and 3 have no common factor. ✓
Method. Add the parts, then write the first part over the total.
- Add the parts. 3 + 4 = 7.7 parts
- Write the fraction. The first part is 3 of the 7 parts.3/7
- Write the answer. 3/7
Check. The second part is 4/7, and 3/7 + 4/7 = 1. ✓
Method. Add the parts, then write the second part over the total.
- Add the parts. 3 + 4 = 7.7 parts
- Write the fraction. The second part is 4 of the 7 parts.4/7
- Write the answer. 4/7
Check. 3/7 + 4/7 = 1. ✓
Method. Share the pupils in the ratio 4 : 5.
- Add the parts of the ratio. 4 + 5 = 9, so the total is shared into 9 equal parts.4 + 5 = 9 parts
- Find the value of one part. Share the total into 9 equal parts.45 ÷ 9 = 5
- Find each share. Multiply the value of one part by each number in the ratio.4 × 5 = 20 and 5 × 5 = 25
- Write the answer. 20
Check. 20 boys and 25 girls make 45. ✓
Method. Find the total parts, then the amount of one part.
- Find the total parts. 1 + 4 = 5 parts.5 parts
- Find one part. 500 ml ÷ 5 = 100 ml.100 ml
- Find the orange. Orange is 1 part, so 100 ml.100 ml
- Write the answer. 100 ml
Check. 100 ml of orange and 400 ml of water make 500 ml. ✓
Method. Divide both parts of 2 : 6 by 2.
- Divide both parts by 2. 2 ÷ 2 = 1 and 6 ÷ 2 = 3.1 : 3
- Write the answer. Yes
Check. Dividing both parts by 2 gives 1 : 3. ✓
Method. Add the parts to get the total.
- Add the parts. 2 + 3 = 5 parts.5 parts
- Find the blue fraction. Blue is 3 parts out of 5.3/5
- Write the answer. Because there are 2 + 3 = 5 parts in total, and blue is 3 of those 5 parts.
Check. 2/5 + 3/5 = 1. ✓