Adding and Subtracting Fractions Worksheet for primary students, featuring exercises on finding LCM, solving fraction operations, and real-world application with jumpers.

Problem Analysis and Solution

The worksheet provided involves three main sections:
1. Finding the Least Common Multiple (LCM) of fraction pairs.
2. Solving addition and subtraction problems involving fractions.
3. Applying fraction operations to solve real-world problems related to stock levels of jumpers.

Let's solve each section step by step.

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Section 1: Finding the LCM of Fraction Pairs

#### Task:
Match the fraction pairs to their LCM.

#### Given Pairs:
1. \( \frac{3}{4} \) and \( \frac{7}{8} \)
2. \( \frac{6}{9} \) and \( \frac{2}{3} \)
3. \( \frac{5}{7} \) and \( \frac{1}{2} \)
4. \( \frac{8}{9} \) and \( \frac{4}{6} \)
5. \( \frac{7}{8} \) and \( \frac{11}{12} \)
6. \( \frac{1}{4} \) and \( \frac{3}{9} \)

#### Possible LCMs:
- 14
- 8
- 24
- 9
- 18
- 36

#### Solution:
To find the LCM of two fractions, we need the LCM of their denominators.

1. Pair: \( \frac{3}{4} \) and \( \frac{7}{8} \)
- Denominators: 4 and 8
- LCM(4, 8) = 8
- Match: 8

2. Pair: \( \frac{6}{9} \) and \( \frac{2}{3} \)
- Denominators: 9 and 3
- LCM(9, 3) = 9
- Match: 9

3. Pair: \( \frac{5}{7} \) and \( \frac{1}{2} \)
- Denominators: 7 and 2
- LCM(7, 2) = 14
- Match: 14

4. Pair: \( \frac{8}{9} \) and \( \frac{4}{6} \)
- Denominators: 9 and 6
- LCM(9, 6) = 18
- Match: 18

5. Pair: \( \frac{7}{8} \) and \( \frac{11}{12} \)
- Denominators: 8 and 12
- LCM(8, 12) = 24
- Match: 24

6. Pair: \( \frac{1}{4} \) and \( \frac{3}{9} \)
- Denominators: 4 and 9
- LCM(4, 9) = 36
- Match: 36

#### Final Matches:
- \( \frac{3}{4} \) and \( \frac{7}{8} \): 8
- \( \frac{6}{9} \) and \( \frac{2}{3} \): 9
- \( \frac{5}{7} \) and \( \frac{1}{2} \): 14
- \( \frac{8}{9} \) and \( \frac{4}{6} \): 18
- \( \frac{7}{8} \) and \( \frac{11}{12} \): 24
- \( \frac{1}{4} \) and \( \frac{3}{9} \): 36

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Section 2: Solving Fraction Calculations

#### Task:
Solve the following calculations and simplify the answers.

#### Problems:
a) \( \frac{1}{4} + \frac{5}{8} \)
b) \( \frac{2}{3} + \frac{1}{9} \)
c) \( \frac{3}{8} + \frac{2}{16} \)
d) \( \frac{1}{2} - \frac{3}{10} \)
e) \( \frac{4}{5} - \frac{7}{15} \)
f) \( \frac{13}{16} - \frac{5}{32} \)

#### Solution:

1. a) \( \frac{1}{4} + \frac{5}{8} \)
- LCM of 4 and 8 is 8.
- Convert \( \frac{1}{4} \) to \( \frac{2}{8} \).
- Add: \( \frac{2}{8} + \frac{5}{8} = \frac{7}{8} \)
- Answer: \( \frac{7}{8} \)

2. b) \( \frac{2}{3} + \frac{1}{9} \)
- LCM of 3 and 9 is 9.
- Convert \( \frac{2}{3} \) to \( \frac{6}{9} \).
- Add: \( \frac{6}{9} + \frac{1}{9} = \frac{7}{9} \)
- Answer: \( \frac{7}{9} \)

3. c) \( \frac{3}{8} + \frac{2}{16} \)
- LCM of 8 and 16 is 16.
- Convert \( \frac{3}{8} \) to \( \frac{6}{16} \).
- Add: \( \frac{6}{16} + \frac{2}{16} = \frac{8}{16} \)
- Simplify: \( \frac{8}{16} = \frac{1}{2} \)
- Answer: \( \frac{1}{2} \)

4. d) \( \frac{1}{2} - \frac{3}{10} \)
- LCM of 2 and 10 is 10.
- Convert \( \frac{1}{2} \) to \( \frac{5}{10} \).
- Subtract: \( \frac{5}{10} - \frac{3}{10} = \frac{2}{10} \)
- Simplify: \( \frac{2}{10} = \frac{1}{5} \)
- Answer: \( \frac{1}{5} \)

5. e) \( \frac{4}{5} - \frac{7}{15} \)
- LCM of 5 and 15 is 15.
- Convert \( \frac{4}{5} \) to \( \frac{12}{15} \).
- Subtract: \( \frac{12}{15} - \frac{7}{15} = \frac{5}{15} \)
- Simplify: \( \frac{5}{15} = \frac{1}{3} \)
- Answer: \( \frac{1}{3} \)

6. f) \( \frac{13}{16} - \frac{5}{32} \)
- LCM of 16 and 32 is 32.
- Convert \( \frac{13}{16} \) to \( \frac{26}{32} \).
- Subtract: \( \frac{26}{32} - \frac{5}{32} = \frac{21}{32} \)
- Answer: \( \frac{21}{32} \)

#### Final Answers:
a) \( \frac{7}{8} \)
b) \( \frac{7}{9} \)
c) \( \frac{1}{2} \)
d) \( \frac{1}{5} \)
e) \( \frac{1}{3} \)
f) \( \frac{21}{32} \)

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Section 3: Applying Fractions to Stock Levels

#### Task:
Determine the fractions of jumpers left in stock or sold based on the given fractions.

#### Given Fractions:
- Black: \( \frac{1}{2} \)
- Red: \( \frac{7}{10} \)
- Orange: \( \frac{1}{3} \)
- Blue: \( \frac{2}{6} \)
- Green: \( \frac{3}{4} \)
- Pink: \( \frac{4}{5} \)
- White: \( \frac{1}{8} \)

#### Problems:
a) What fraction of the orange and blue jumpers are left in stock?
b) What fraction of the green and white jumpers are left in stock?
c) What fraction of the pink and black jumpers have been sold?
d) What fraction of the red and pink jumpers have been sold?

#### Solution:

1. a) Fraction of orange and blue jumpers left in stock
- Orange: \( \frac{1}{3} \)
- Blue: \( \frac{2}{6} = \frac{1}{3} \) (simplified)
- Add: \( \frac{1}{3} + \frac{1}{3} = \frac{2}{3} \)
- Answer: \( \frac{2}{3} \)

2. b) Fraction of green and white jumpers left in stock
- Green: \( \frac{3}{4} \)
- White: \( \frac{1}{8} \)
- LCM of 4 and 8 is 8.
- Convert \( \frac{3}{4} \) to \( \frac{6}{8} \).
- Add: \( \frac{6}{8} + \frac{1}{8} = \frac{7}{8} \)
- Answer: \( \frac{7}{8} \)

3. c) Fraction of pink and black jumpers sold
- Pink: \( \frac{4}{5} \) left, so \( 1 - \frac{4}{5} = \frac{1}{5} \) sold.
- Black: \( \frac{1}{2} \) left, so \( 1 - \frac{1}{2} = \frac{1}{2} \) sold.
- Add: \( \frac{1}{5} + \frac{1}{2} \)
- LCM of 5 and 2 is 10.
- Convert \( \frac{1}{5} \) to \( \frac{2}{10} \) and \( \frac{1}{2} \) to \( \frac{5}{10} \).
- Add: \( \frac{2}{10} + \frac{5}{10} = \frac{7}{10} \)
- Answer: \( \frac{7}{10} \)

4. d) Fraction of red and pink jumpers sold
- Red: \( \frac{7}{10} \) left, so \( 1 - \frac{7}{10} = \frac{3}{10} \) sold.
- Pink: \( \frac{4}{5} \) left, so \( 1 - \frac{4}{5} = \frac{1}{5} \) sold.
- Add: \( \frac{3}{10} + \frac{1}{5} \)
- LCM of 10 and 5 is 10.
- Convert \( \frac{1}{5} \) to \( \frac{2}{10} \).
- Add: \( \frac{3}{10} + \frac{2}{10} = \frac{5}{10} \)
- Simplify: \( \frac{5}{10} = \frac{1}{2} \)
- Answer: \( \frac{1}{2} \)

#### Final Answers:
a) \( \frac{2}{3} \)
b) \( \frac{7}{8} \)
c) \( \frac{7}{10} \)
d) \( \frac{1}{2} \)

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Final Answer Summary

1. Section 1 Matches:
- \( \frac{3}{4} \) and \( \frac{7}{8} \): 8
- \( \frac{6}{9} \) and \( \frac{2}{3} \): 9
- \( \frac{5}{7} \) and \( \frac{1}{2} \): 14
- \( \frac{8}{9} \) and \( \frac{4}{6} \): 18
- \( \frac{7}{8} \) and \( \frac{11}{12} \): 24
- \( \frac{1}{4} \) and \( \frac{3}{9} \): 36

2. Section 2 Answers:
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. Section 3 Answers:
a) \( \frac{2}{3} \)
b) \( \frac{7}{8} \)
c) \( \frac{7}{10} \)
d) \( \frac{1}{2} \)

Boxed Final Answer:
\[
\boxed{
\begin{array}{l}
\text{Section 1: } 8, 9, 14, 18, 24, 36 \\
\text{Section 2: } \frac{7}{8}, \frac{7}{9}, \frac{1}{2}, \frac{1}{5}, \frac{1}{3}, \frac{21}{32} \\
\text{Section 3: } \frac{2}{3}, \frac{7}{8}, \frac{7}{10}, \frac{1}{2}
\end{array}
}
\]