MATHEMATICSNumber & Arithmetic

CURRENT TOPICRatio & Proportion

NAVIGATION

2:3

● Master Topic Guide Verified 11+ Curriculum

Ratio & Proportion Master Guide ⚖️

Master ratio definitions, simplifying ratios, equivalent ratios, sharing amounts, recipe scaling, map scale problems, and 11+ word problems!

Practice Levels:Warm-Up Core Mode Pro Mode

Practice Papers

RATIO OVERVIEW

A ratio compares two or more quantities. It shows how much of one thing there is compared to another.

1. WHAT IS A RATIO?

A ratio compares the size of two or more amounts. Written using a colon (:) or "to".

2 to 32 : 3

4 to 14 : 1

5 to 25 : 2

⚠️ Order matters! 2 : 3 is NOT the same as 3 : 2

2. WRITING RATIOS

Write the ratio of the first amount to the second amount.

Ex 1: 6 red balls & 4 blue balls

🔴🔴🔴🔴🔴🔴 🔵🔵🔵🔵

Red to blue ═ 6 : 4

Ex 2: 3 apples & 5 oranges

🍎🍎🍎 🍊🍊🍊🍊🍊

Apples to oranges ═ 3 : 5

3. SIMPLIFYING RATIOS

Divide both parts by their highest common factor (HCF).

Simplify 12 : 18 (HCF = 6)

12 ÷ 6 : 18 ÷ 6 ═ 2 : 3

Simplify 15 : 25 (HCF = 5)

15 ÷ 5 : 25 ÷ 5 ═ 3 : 5

💡 2:3 and 3:5 are in simplest form!

4. EQUIVALENT RATIOS

Equivalent ratios show the same relationship. Multiply or divide both parts by the same number.

Scaling 2 : 3:

× 2 ➔ 4 : 6

× 3 ➔ 6 : 9

× 4 ➔ 8 : 12

÷ 2 ➔ 1 : 1.5

Recipe Flour & Sugar Table:

Flour	Sugar	Ratio
2	3	2:3
4	6	4:6
6	9	6:9
8	12	8:12

5. PART TO PART & PART TO WHOLE

4 boys and 6 girls (Total = 10 children).

Part to Part:

Compare one part to another.

Boys : Girls ═ 4 : 6

Part to Whole:

Compare part to total.

Boys : Total ═ 4 : 10

Girls : Total ═ 6 : 10

6. USING RATIOS TO SHARE AMOUNTS

Example: Share 60 in the ratio 2 : 3

1. Add parts: 2 + 3 ═ 5 parts

2. Value of 1 part: 60 ÷ 5 ═ 12

3. First amount: 2 × 12 ═ 24

4. Second amount: 3 × 12 ═ 36

Answer: 24 and 36

7. REAL LIFE EXAMPLES

Class Ratio Problem:

Boys to girls = 2:3. 20 students total.

1 part = 20÷5 = 4 ➔ 8 boys, 12 girls

Recipe Batch Problem:

Flour to sugar = 2:3. Using 4 cups flour.

Flour ×2 ➔ Sugar 3×2 ═ 6 cups sugar

⚖️

RATIO & PROPORTION WORD PROBLEMS

A ratio compares two or more amounts. A proportion is an equivalent ratio.

KEY IDEAS

★ Use ratios to compare quantities.
★ Set up a proportion to solve.
★ Keep parts in the same ratio.

1. WHAT IS A RATIO?

Shows how much of one thing there is compared to another.

Apples : Oranges ═ 2 : 3
Total parts ═ 2 + 3 ═ 5

2. SIMPLIFYING RATIOS

Divide each part by Highest Common Factor (HCF).

12 : 18 ➔ ÷6 ➔ 2 : 3

3. PROPORTION

Two ratios are in proportion if equal (2/3 = 4/6).

Cross multiply: 2×6 ═ 12 and 3×4 ═ 12 ✔️

HOW TO SOLVE RATIO & PROPORTION WORD PROBLEMS

1Read question carefully

2Identify ratio compared

3Set up ratio/proportion

4Solve via cross-mult

5Check your answer

5. WORKED EXAMPLES

A. SHARING IN A RATIO

Share £45 between Alex and Ben in the ratio 2 : 3.

Total parts: 2 + 3 ═ 5

Alex: (2/5) × 45 ═ £18

Ben: (3/5) × 45 ═ £27

Answer: Alex £18, Ben £27

B. FINDING A MISSING PART

Ratio of girls to boys is 3 : 2. There are 15 girls. How many boys?

3 parts ═ 15 girls

1 part ═ 15 ÷ 3 ═ 5

Boys ═ 2 parts ═ 2 × 5 ═ 10

Answer: 10 boys

C. USING PROPORTION

Recipe: flour to sugar is 2 : 3. Using 400 g flour, how much sugar?

2 : 3 ═ 400 : x

2x ═ 3 × 400 ═ 1200

x ═ 600 g

Answer: 600 g of sugar

D. SCALE PROBLEMS

Map scale is 1 : 1000. Map distance is 7 cm. What is actual distance?

1 cm ➔ 1000 cm

7 cm ➔ 7 × 1000 cm ═ 7000 cm

7000 cm ═ 70 m

Answer: 70 metres

8. PRACTICE QUESTIONS

1. Divide 72 sweets between Tom & Sara in ratio 3 : 5Tom 27, Sara 45

2. Red to blue marbles 4 : 3. 28 red marbles. How many blue?21 blue

3. Boys to girls 5 : 7. 35 girls. How many boys?25 boys

4. Paint mixed 2 : 1 (red : white). 6 L red paint. White paint?3 L white

5. Model car scale 1 : 50. Model length 12 cm. Real car length?600 cm (6 m)

🏆 9. CHALLENGE

Ratio Year 5 to Year 6 is 4 : 5. There are 180 more Year 6 than Year 5 students. Total students?

Diff ═ 5−4 ═ 1 part ═ 180
Total parts ═ 4+5 ═ 9
Total students ═ 9 × 180 ═ 1620

10. REMEMBER

• Ratio compares amounts.

• Proportion keeps the same relationship.

• Use equivalent ratios or cross-multiplication.

INTERACTIVE RATIO CHAMPION QUIZ11+ Exam Practice

1. Simplify the ratio 18 : 24 to lowest terms:

2. Share £50 in the ratio 2 : 3 (find larger amount):

3. Ratio boys to girls is 4 : 5. If 20 boys, how many girls?

4. Scale 1 : 100. Map length 5 cm. Actual length in metres?

🚀 Ready to Test Your Knowledge?

Take our graded 11+ Ratio & Proportion assessment now!