Adding and Subtracting Fractions Worksheet for primary students.

Let's solve each part of this "Adding and Subtracting Fractions Worksheet" step by step.

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1. Draw lines to match the fraction pairs to their LCM

We are given pairs of fractions and need to find the Least Common Multiple (LCM) of their denominators.

#### Step-by-step:

| Fraction Pair | Denominators | LCM |
|---------------|--------------|-----|
| 3/4, 7/8 | 4, 8 | LCM(4,8) = 8 → But wait, the options are: 14, 8, 24, 9, 18, 36. So we check which one matches.
Wait — actually, the numbers below are LCMs for the pairs, but they’re not in order. Let’s go through each pair.

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a) 3/4 and 7/8
Denominators: 4 and 8
LCM of 4 and 8 is 8 ✔ → Match with yellow box: 8

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b) 6/9 and 2/3
Simplify first:
6/9 = 2/3 → So both are equivalent to 2/3
But we still look at original denominators: 9 and 3
LCM(9,3) = 9 ✔ → Match with green box: 9

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c) 5/7 and 1/2
Denominators: 7 and 2
LCM(7,2) = 14 ✔ → Match with red box: 14

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d) 8/9 and 4/6
Simplify 4/6 = 2/3
Denominators: 9 and 6
LCM(9,6):
Multiples of 9: 9, 18, 27...
Multiples of 6: 6, 12, 18...
→ LCM = 18 ✔ → Match with blue box: 18

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e) 7/8 and 11/12
Denominators: 8 and 12
LCM(8,12):
8 = 2³, 12 = 2²×3 → LCM = 2³×3 = 24 ✔ → Match with orange box: 24

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f) 1/4 and 3/9
Simplify 3/9 = 1/3
Denominators: 4 and 3
LCM(4,3) = 12? Wait — but 12 is not listed!
Wait, let’s check the available LCMs: 14, 8, 24, 9, 18, 36

Hmm — but 1/4 and 3/9 → denominators 4 and 9
LCM(4,9):
4 = 2², 9 = 3² → LCM = 2²×3² = 36 ✔ → Match with purple box: 36

So final matching:

| Fraction Pair | LCM | Box Color |
|---------------|-----|-----------|
| 3/4, 7/8 | 8 | Yellow |
| 6/9, 2/3 | 9 | Green |
| 5/7, 1/2 | 14 | Red |
| 8/9, 4/6 | 18 | Blue |
| 7/8, 11/12 | 24 | Orange |
| 1/4, 3/9 | 36 | Purple |

✔ Answer:
- 3/4 & 7/8 → 8
- 6/9 & 2/3 → 9
- 5/7 & 1/2 → 14
- 8/9 & 4/6 → 18
- 7/8 & 11/12 → 24
- 1/4 & 3/9 → 36

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2. Solve the following calculations. Give the answer in its simplest form.

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#### a) $ \frac{1}{4} + \frac{5}{8} $

LCM of 4 and 8 is 8
Convert $ \frac{1}{4} = \frac{2}{8} $
$ \frac{2}{8} + \frac{5}{8} = \frac{7}{8} $

✔ Answer: $ \frac{7}{8} $

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#### b) $ \frac{2}{3} + \frac{1}{9} $

LCM of 3 and 9 is 9
$ \frac{2}{3} = \frac{6}{9} $
$ \frac{6}{9} + \frac{1}{9} = \frac{7}{9} $

✔ Answer: $ \frac{7}{9} $

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#### c) $ \frac{3}{8} + \frac{2}{16} $

Simplify $ \frac{2}{16} = \frac{1}{8} $
Now: $ \frac{3}{8} + \frac{1}{8} = \frac{4}{8} = \frac{1}{2} $

✔ Answer: $ \frac{1}{2} $

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#### d) $ \frac{1}{2} - \frac{3}{10} $

LCM of 2 and 10 is 10
$ \frac{1}{2} = \frac{5}{10} $
$ \frac{5}{10} - \frac{3}{10} = \frac{2}{10} = \frac{1}{5} $

✔ Answer: $ \frac{1}{5} $

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#### e) $ \frac{4}{5} - \frac{7}{15} $

LCM of 5 and 15 is 15
$ \frac{4}{5} = \frac{12}{15} $
$ \frac{12}{15} - \frac{7}{15} = \frac{5}{15} = \frac{1}{3} $

✔ Answer: $ \frac{1}{3} $

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#### f) $ \frac{13}{16} - \frac{5}{32} $

LCM of 16 and 32 is 32
$ \frac{13}{16} = \frac{26}{32} $
$ \frac{26}{32} - \frac{5}{32} = \frac{21}{32} $

✔ Answer: $ \frac{21}{32} $

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3. Jim’s Jumping Jumperium – Fraction Problems

Jumper fractions:
- Black: $ \frac{1}{2} $
- Red: $ \frac{7}{10} $
- Orange: $ \frac{1}{3} $
- Blue: $ \frac{2}{6} = \frac{1}{3} $
- Green: $ \frac{3}{4} $
- Pink: $ \frac{4}{5} $
- White: $ \frac{1}{8} $

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#### a) What fraction of the orange and blue jumpers are left in stock?

Orange: $ \frac{1}{3} $, Blue: $ \frac{2}{6} = \frac{1}{3} $

Add: $ \frac{1}{3} + \frac{1}{3} = \frac{2}{3} $

✔ Answer: $ \frac{2}{3} $

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#### b) What fraction of the green and white jumpers are left in stock?

Green: $ \frac{3}{4} $, White: $ \frac{1}{8} $

LCM of 4 and 8 is 8
$ \frac{3}{4} = \frac{6}{8} $
$ \frac{6}{8} + \frac{1}{8} = \frac{7}{8} $

✔ Answer: $ \frac{7}{8} $

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#### c) What fraction of the pink and black jumpers have been sold?

Left in stock:
- Pink: $ \frac{4}{5} $ → So sold = $ 1 - \frac{4}{5} = \frac{1}{5} $
- Black: $ \frac{1}{2} $ → Sold = $ 1 - \frac{1}{2} = \frac{1}{2} $

Total sold: $ \frac{1}{5} + \frac{1}{2} $

LCM of 5 and 2 is 10
$ \frac{1}{5} = \frac{2}{10}, \frac{1}{2} = \frac{5}{10} $
$ \frac{2}{10} + \frac{5}{10} = \frac{7}{10} $

✔ Answer: $ \frac{7}{10} $

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#### d) What fraction of the red and pink jumpers have been sold?

Red: $ \frac{7}{10} $ in stock → Sold = $ 1 - \frac{7}{10} = \frac{3}{10} $

Pink: $ \frac{4}{5} $ in stock → Sold = $ 1 - \frac{4}{5} = \frac{1}{5} $

Now add: $ \frac{3}{10} + \frac{1}{5} $

$ \frac{1}{5} = \frac{2}{10} $
$ \frac{3}{10} + \frac{2}{10} = \frac{5}{10} = \frac{1}{2} $

✔ Answer: $ \frac{1}{2} $

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✔ Final Answers Summary:

#### 1. Matching LCMs
- 3/4, 7/8 → 8
- 6/9, 2/3 → 9
- 5/7, 1/2 → 14
- 8/9, 4/6 → 18
- 7/8, 11/12 → 24
- 1/4, 3/9 → 36

#### 2. Calculations
a) $ \frac{7}{8} $
b) $ \frac{7}{9} $
c) $ \frac{1}{2} $
d) $ \frac{1}{5} $
e) $ \frac{1}{3} $
f) $ \frac{21}{32} $

#### 3. Jumper Problems
a) $ \frac{2}{3} $
b) $ \frac{7}{8} $
c) $ \frac{7}{10} $
d) $ \frac{1}{2} $

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