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Year 9 Fractions Guide

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Year 9 Fractions Guide

Year 9 Fractions Guide

Fractions worksheet illustration

🔢 Part 1: Adding and Subtracting Fractions

How to Add Fractions:

1. Find a common denominator (bottom number)

2. Convert fractions to equivalent fractions with the same denominator

3. Add the numerators (top numbers)

4. Keep the denominator the same

5. Simplify if possible

Example: 1/4 + 1/6 = 3/12 + 2/12 = 5/12

1. Calculate: 2/5 + 1/3
2. Calculate: 3/4 - 1/8
3. Calculate: 2/3 + 5/6 - 1/2

✖️ Part 2: Multiplying and Dividing Fractions

How to Multiply Fractions:

1. Multiply the numerators together

2. Multiply the denominators together

3. Simplify the result

How to Divide Fractions:

1. Keep the first fraction the same

2. Change division to multiplication

3. Flip the second fraction (reciprocal)

4. Multiply as normal

Example: 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6

4. Calculate: 3/7 × 2/5
5. Calculate: 4/9 ÷ 2/3
6. Which method do you use to divide fractions?

Multiply denominators and add numerators

Keep, change, flip (multiply by reciprocal)

Find common denominator first

Cross multiply

🔄 Part 3: Converting Between Forms

Converting Improper Fractions to Mixed Numbers:

1. Divide the numerator by the denominator

2. The whole number is your answer

3. The remainder becomes the new numerator

4. Keep the same denominator

Example: 17/5 = 3 2/5 (because 17 ÷ 5 = 3 remainder 2)

7. Convert to mixed numbers:

a) 23/7 = ____________

b) 19/4 = ____________

c) 31/6 = ____________

8. Convert to improper fractions:

a) 4 2/3 = ____________

b) 2 5/8 = ____________

c) 6 1/4 = ____________

9. Convert to decimals (show working):

a) 3/8 = ____________

b) 7/12 = ____________

📊 Part 4: Real-World Fraction Problems

Problem-Solving Steps:

1. Read the problem carefully

2. Identify what operation is needed

3. Set up the calculation

4. Solve step by step

5. Check if your answer makes sense

10. Sarah ate 2/5 of a pizza and Tom ate 1/4 of the same pizza. How much pizza did they eat altogether?
11. A recipe calls for 3/4 cup of flour, but you want to make 2/3 of the recipe. How much flour do you need?
12. A 5/6 metre piece of rope is cut into pieces that are each 1/12 metre long. How many pieces will you get?
13. Which of these fractions are equivalent to 1/2? (Check all that apply)

2/4

3/5

4/8

5/10

6/11

8/16

🎯 Part 5: Challenge Problems

14. Simplify: (2/3 + 1/4) × 3/5

Hint: Use order of operations - brackets first!

15. A tank is 3/4 full of water. If 2/5 of the water is used, what fraction of the tank is still full?
16. Match each fraction with its decimal equivalent:
1. 1/4
2. 3/5
3. 7/8
4. 2/3
A. 0.875
B. 0.25
C. 0.6
D. 0.667
17. Explain in your own words why we "flip and multiply" when dividing fractions:

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