Operations with Fractions

Adding, subtracting, multiplying, and dividing fractions

Operations with Fractions

Adding and Subtracting Fractions

Same denominator: Add or subtract numerators, keep denominator $\frac{a}{c} + \frac{b}{c} = \frac{a + b}{c}$

Example: $\frac{2}{7} + \frac{3}{7} = \frac{5}{7}$

Different denominators: Find common denominator first!

Example: $\frac{1}{3} + \frac{1}{4}$

LCD = 12: $\frac{1}{3} = \frac{4}{12}, \quad \frac{1}{4} = \frac{3}{12}$ $\frac{4}{12} + \frac{3}{12} = \frac{7}{12}$

Multiplying Fractions

Multiply numerators, multiply denominators $\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$

Example: $\frac{2}{3} \times \frac{4}{5} = \frac{8}{15}$

Tip: Simplify before multiplying when possible!

Dividing Fractions

Multiply by the reciprocal $\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$

Example: $\frac{2}{3} \div \frac{4}{5} = \frac{2}{3} \times \frac{5}{4} = \frac{10}{12} = \frac{5}{6}$

Memory aid: "Keep, Change, Flip"

Simplifying Fractions

Divide numerator and denominator by their GCF: $\frac{12}{18} = \frac{12 \div 6}{18 \div 6} = \frac{2}{3}$

📚 Practice Problems

1Problem 1easy

❓ Question:

Calculate: $\frac{3}{8} + \frac{1}{8}$

💡 Show Solution

Same denominator: add numerators, keep denominator.

$\frac{3}{8} + \frac{1}{8} = \frac{3 + 1}{8} = \frac{4}{8}$

Simplify: $\frac{4}{8} = \frac{1}{2}$

Answer: $\frac{1}{2}$

2Problem 2medium

❓ Question:

Calculate: $\frac{2}{5} \times \frac{3}{4}$

💡 Show Solution

Multiply numerators and denominators:

$\frac{2}{5} \times \frac{3}{4} = \frac{2 \times 3}{5 \times 4} = \frac{6}{20}$

Simplify (divide by 2): $\frac{6}{20} = \frac{3}{10}$

Answer: $\frac{3}{10}$

3Problem 3hard

❓ Question:

Calculate: $\frac{3}{4} \div \frac{2}{3}$

💡 Show Solution

Keep, Change, Flip: Multiply by the reciprocal

$\frac{3}{4} \div \frac{2}{3} = \frac{3}{4} \times \frac{3}{2}$

Multiply: $\frac{3 \times 3}{4 \times 2} = \frac{9}{8}$

Convert to mixed number: $\frac{9}{8} = 1\frac{1}{8}$

Answer: $\frac{9}{8}$ or $1\frac{1}{8}$

4Problem 4medium

❓ Question:

Calculate: 2/3 × 3/4

💡 Show Solution

Step 1: Multiply numerators. 2 × 3 = 6

Step 2: Multiply denominators. 3 × 4 = 12

Step 3: Write the result. 6/12

Step 4: Simplify. GCF of 6 and 12 is 6 6/12 = 1/2

Answer: 1/2

5Problem 5hard

❓ Question:

A recipe calls for 2 1/4 cups of flour. You want to make 2/3 of the recipe. How much flour do you need?

💡 Show Solution

Step 1: Convert mixed number to improper fraction. 2 1/4 = 9/4

Step 2: Multiply by 2/3. 9/4 × 2/3

Step 3: Multiply numerators and denominators. (9 × 2)/(4 × 3) = 18/12

Step 4: Simplify. GCF of 18 and 12 is 6 18/12 = 3/2

Step 5: Convert to mixed number. 3/2 = 1 1/2

Answer: 1 1/2 cups of flour

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