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.