📊 Part 1: Finding the Highest Common Factor (HCF)

1. Find the HCF of 12 and 18.

Answer: 6

Working:

Factors of 12: 1, 2, 3, 4, 6, 12

Factors of 18: 1, 2, 3, 6, 9, 18

Common factors: 1, 2, 3, 6

Highest Common Factor = 6

2. Find the HCF of 24 and 30.

Answer: 6

Working:

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30

Common factors: 1, 2, 3, 6

Highest Common Factor = 6

3. Find the HCF of 15 and 25.

Answer: 5

Working:

Factors of 15: 1, 3, 5, 15

Factors of 25: 1, 5, 25

Common factors: 1, 5

Highest Common Factor = 5

🔢 Part 2: Simplifying Fractions

4. Simplify 8/12 to its lowest terms.

Answer: 2/3

Working:

Step 1: Find HCF of 8 and 12

Factors of 8: 1, 2, 4, 8

Factors of 12: 1, 2, 3, 4, 6, 12

HCF = 4

Step 2: Divide numerator and denominator by HCF

8 ÷ 4 = 2

12 ÷ 4 = 3

Therefore: 8/12 = 2/3

5. Simplify 15/25 to its lowest terms.

Answer: 3/5

Working:

Step 1: Find HCF of 15 and 25

HCF = 5 (from question 3)

Step 2: Divide numerator and denominator by HCF

15 ÷ 5 = 3

25 ÷ 5 = 5

Therefore: 15/25 = 3/5

6. Simplify 18/24 to its lowest terms.

Answer: 3/4

Working:

Step 1: Find HCF of 18 and 24

Factors of 18: 1, 2, 3, 6, 9, 18

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

HCF = 6

Step 2: Divide numerator and denominator by HCF

18 ÷ 6 = 3

24 ÷ 6 = 4

Therefore: 18/24 = 3/4

✅ Part 3: Equivalent Fractions Recognition

7. Circle the fractions that are equivalent to 1/2:

✓

2/4

3/5

✓

4/8

5/12

✓

6/12

Explanation: 2/4 = 1/2, 4/8 = 1/2, and 6/12 = 1/2 when simplified.

8. Which fraction is 12/16 equivalent to when simplified?

1/2

✓

3/4

2/3

4/5

Working: HCF of 12 and 16 is 4. So 12÷4 = 3 and 16÷4 = 4, giving us 3/4.

📝 Part 4: Word Problems

9. Sarah ate 6 out of 8 slices of pizza. What fraction of the pizza did she eat in its simplest form?

Answer: 3/4

Working:

Sarah ate 6/8 of the pizza

HCF of 6 and 8 = 2

6 ÷ 2 = 3

8 ÷ 2 = 4

Therefore: 6/8 = 3/4

10. A recipe calls for 20/30 of a cup of flour. Simplify this fraction.

Answer: 2/3

Working:

Original fraction: 20/30

HCF of 20 and 30 = 10

20 ÷ 10 = 2

30 ÷ 10 = 3

Therefore: 20/30 = 2/3 of a cup

11. In a class of 24 students, 16 students like maths. What fraction of the class likes maths in its simplest form?

Answer: 2/3

Working:

Fraction who like maths: 16/24

HCF of 16 and 24 = 8

16 ÷ 8 = 2

24 ÷ 8 = 3

Therefore: 16/24 = 2/3 of the class

🎯 Part 5: Challenge Questions

12. Simplify 36/48 using prime factorisation.

Answer: 3/4

Working using prime factorisation:

36 = 2² × 3²

48 = 2⁴ × 3

Common factors: 2² × 3 = 4 × 3 = 12

HCF = 12

36 ÷ 12 = 3

48 ÷ 12 = 4

Therefore: 36/48 = 3/4

13. True or False: 14/21 and 2/3 are equivalent fractions.

✓

True

False

Explanation: 14/21 simplified: HCF of 14 and 21 is 7. So 14÷7 = 2 and 21÷7 = 3, giving us 2/3. Therefore, they are equivalent.

💡 Key Learning Points

Remember these steps to simplify fractions:

1. Find all factors of the numerator (top number)

2. Find all factors of the denominator (bottom number)

3. Identify the common factors

4. Find the Highest Common Factor (HCF)

5. Divide both numerator and denominator by the HCF

6. Check if the fraction can be simplified further

Important vocabulary:

• Numerator: The top number in a fraction

• Denominator: The bottom number in a fraction

• Factor: A number that divides evenly into another number

• HCF: The largest number that divides both numbers evenly

• Equivalent fractions: Fractions that represent the same value

• Simplest form: When the HCF of numerator and denominator is 1

Simplifying Fractions Answers

Simplifying Fractions Answers

📊 Part 1: Finding the Highest Common Factor (HCF)

🔢 Part 2: Simplifying Fractions

✅ Part 3: Equivalent Fractions Recognition

📝 Part 4: Word Problems

🎯 Part 5: Challenge Questions

💡 Key Learning Points

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