Printable worksheet for practicing adding and subtracting fractions, including matching fractions to their LCM and solving real-life scenarios with jumpers.

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, so let’s compute them properly.

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 = 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 → but again, use original 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
But denominators: 4 and 9
LCM(4,9):
- 4 = 2²
- 9 = 3²
→ LCM = 2²×3² = 36 ✔ → Match with purple box: 36

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✔ Matching Summary:

| Fraction Pairs | LCM | Color Box |
|--------------------------|-----|-----------|
| 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 |

> So draw lines accordingly.

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

#### 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: $ \boxed{\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: $ \boxed{\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: $ \boxed{\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: $ \boxed{\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: $ \boxed{\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: $ \boxed{\frac{21}{32}} $

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3. Jim’s Jumping Jumperium – Fraction Word Problems

Jumpers and fractions left in stock:

- 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: $ \boxed{\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: $ \boxed{\frac{7}{8}} $

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

- Sold means: 1 - (fraction left)

So:
- Pink: $ 1 - \frac{4}{5} = \frac{1}{5} $
- Black: $ 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: $ \boxed{\frac{7}{10}} $

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

- Red: $ 1 - \frac{7}{10} = \frac{3}{10} $
- Pink: $ 1 - \frac{4}{5} = \frac{1}{5} $
- Add: $ \frac{3}{10} + \frac{1}{5} $

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

✔ Answer: $ \boxed{\frac{1}{2}} $

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✔ Final Answers:

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

Let me know if you'd like this as a printable solution or with diagrams!