Mathematics • Year 7 • Unit 1 • Lesson 8
Adding and Subtracting Fractions
Build the rules: same denominator means just combine the tops; different denominators means find the lowest common denominator first. Mixed numbers? Handle whole and fraction parts.
1. I do — fully worked example
Read every line. Each step has a short reason on the right so you can see why, not just what.
Problem. Calculate 2/5 + 1/3 and write the answer in lowest terms.
Step 1 — Find the LCD (lowest common denominator).
Multiples of 5: 5, 10, 15, 20, … Multiples of 3: 3, 6, 9, 12, 15, …
First multiple they share = 15. So LCD = 15.
Reason: fractions can only be added when their slices are the same size — that means same denominator.
Step 2 — Convert each fraction to fifteenths.
2/5 = (2 × 3)/(5 × 3) = 6/15
1/3 = (1 × 5)/(3 × 5) = 5/15
Reason: multiplying top and bottom by the same number gives an equivalent fraction.
Step 3 — Add the numerators, keep the denominator.
6/15 + 5/15 = 11/15
Reason: 6 fifteenths + 5 fifteenths = 11 fifteenths. The size of each slice doesn't change.
Step 4 — Simplify if possible.
HCF(11, 15) = 1, so 11/15 is already simplest form.
Answer: 11/15.
2. We do — fill in the missing steps
Same structure as Section 1, but with the working faded. Fill in each blank line. 4 marks
Problem. Calculate 5/6 − 1/4 and write the answer in lowest terms.
Step 1 — Find LCD of 6 and 4:
Multiples of 6: 6, 12, 18, … Multiples of 4: 4, 8, _____, _____, …
LCD = _____.
Step 2 — Convert each fraction:
5/6 = (5 × _____)/(6 × _____) = _____ / _____
1/4 = (1 × _____)/(4 × _____) = _____ / _____
Step 3 — Subtract the numerators, keep the denominator:
_____ / _____ − _____ / _____ = _____ / _____
Step 4 — Simplify if possible. HCF of your top and bottom? _____. Final answer: _____.
3. You do — independent practice
Show your working in the space under each problem. The first four are foundation, the middle two are standard, and the last two are extension.
Foundation — single step
3.1 3/7 + 2/7 = ? 1 mark
3.2 7/9 − 4/9 = ? 1 mark
3.3 1/2 + 1/4 = ? (Hint: change 1/2 to quarters first.) 1 mark
3.4 5/8 − 1/4 = ? (Hint: change 1/4 to eighths first.) 1 mark
Standard — combine two ideas
3.5 3/8 + 5/12. Find the LCD, convert both, then add. Simplify if possible. 2 marks
3.6 2 1/5 + 1 3/5. (Hint: add the wholes first, then add the fractions.) 2 marks
Extension — push your thinking
3.7 4 1/6 − 2 5/6. The fraction part will go negative — explain how you borrow 1 from the whole, then finish the calculation. 3 marks
3.8 2/3 + 4/5. Find the LCD, convert, add, then write the answer as a mixed number. 2 marks
How did this worksheet feel?
What I'll revisit before next class:
Section 2 — We do (5/6 − 1/4)
Step 1: Multiples of 4: 4, 8, 12, 16, … LCD = 12.
Step 2: 5/6 = (5 × 2)/(6 × 2) = 10/12. 1/4 = (1 × 3)/(4 × 3) = 3/12.
Step 3: 10/12 − 3/12 = 7/12.
Step 4: HCF(7, 12) = 1. Final answer = 7/12.
3.1 — 3/7 + 2/7
Same denominator: add tops. 3 + 2 = 5. Keep 7. = 5/7.
3.2 — 7/9 − 4/9
Same denominator: 7 − 4 = 3. Keep 9. = 3/9 = 1/3 (simplify by 3).
3.3 — 1/2 + 1/4
Change 1/2 to quarters: 1/2 = 2/4. Then 2/4 + 1/4 = 3/4.
3.4 — 5/8 − 1/4
Change 1/4 to eighths: 1/4 = 2/8. Then 5/8 − 2/8 = 3/8. (HCF(3, 8) = 1, already simplified.)
3.5 — 3/8 + 5/12
LCD(8, 12) = 24. Convert: 3/8 = 9/24, 5/12 = 10/24. Sum: 9/24 + 10/24 = 19/24. HCF(19, 24) = 1, already simplified.
3.6 — 2 1/5 + 1 3/5
Wholes: 2 + 1 = 3. Fractions: 1/5 + 3/5 = 4/5. Combine: 3 4/5.
3.7 — 4 1/6 − 2 5/6
Fractions: 1/6 − 5/6 = −4/6, which is negative. Borrow 1 from the 4 wholes: 4 1/6 = 3 + 6/6 + 1/6 = 3 7/6.
Now subtract: 3 7/6 − 2 5/6. Wholes: 3 − 2 = 1. Fractions: 7/6 − 5/6 = 2/6 = 1/3.
Answer: 1 1/3.
3.8 — 2/3 + 4/5
LCD(3, 5) = 15. Convert: 2/3 = 10/15, 4/5 = 12/15. Sum: 10/15 + 12/15 = 22/15. As a mixed number: 22 ÷ 15 = 1 remainder 7, so 1 7/15.