Equivalent Fractions Worksheet with visual diagrams and fraction problems.

I'll solve this equivalent fractions worksheet step by step. Let me work through each problem carefully.

Problem 1a: 4/16 = ?/?
- Looking at the circles: first circle has 16 parts with 4 shaded, second has 4 parts
- To find equivalent fraction: divide both numerator and denominator by 4
- 4 ÷ 4 = 1, and 16 ÷ 4 = 4
- Answer: 1/4

Problem 1b: 2/12 = ?/?
- First circle has 12 parts with 2 shaded, second has 6 parts
- Divide both by 2: 2 ÷ 2 = 1, and 12 ÷ 2 = 6
- Answer: 1/6

Problem 2a: 3/6 = ?/?
- First circle has 6 parts with 3 shaded, second has 2 parts
- Divide both by 3: 3 ÷ 3 = 1, and 6 ÷ 3 = 2
- Answer: 1/2

Problem 2b: 6/7 = ?/?
- First circle has 7 parts with 6 shaded, second has 14 parts
- Multiply both by 2: 6 × 2 = 12, and 7 × 2 = 14
- Answer: 12/14

Problem 3a: 12/14 = ?/?
- First circle has 14 parts with 12 shaded, second has 7 parts
- Divide both by 2: 12 ÷ 2 = 6, and 14 ÷ 2 = 7
- Answer: 6/7

Problem 3b: 5/7 = ?/?
- First circle has 7 parts with 5 shaded, second has 14 parts
- Multiply both by 2: 5 × 2 = 10, and 7 × 2 = 14
- Answer: 10/14

Problem 4a: 4/5 = ?/?
- First circle has 5 parts with 4 shaded, second has 10 parts
- Multiply both by 2: 4 × 2 = 8, and 5 × 2 = 10
- Answer: 8/10

Problem 4b: 5/7 = ?/?
- First circle has 7 parts with 5 shaded, second has 14 parts
- Multiply both by 2: 5 × 2 = 10, and 7 × 2 = 14
- Answer: 10/14

Problem 5a: 14/16 = ?/?
- First circle has 16 parts with 14 shaded, second has 8 parts
- Divide both by 2: 14 ÷ 2 = 7, and 16 ÷ 2 = 8
- Answer: 7/8

Problem 5b: 5/10 = ?/?
- First circle has 10 parts with 5 shaded, second has 2 parts
- Divide both by 5: 5 ÷ 5 = 1, and 10 ÷ 5 = 2
- Answer: 1/2

Problem 6a: 14/16 = ?/?
- Same as 5a: divide both by 2
- 14 ÷ 2 = 7, and 16 ÷ 2 = 8
- Answer: 7/8

Problem 6b: 5/7 = ?/?
- First circle has 7 parts with 5 shaded, second has 14 parts
- Multiply both by 2: 5 × 2 = 10, and 7 × 2 = 14
- Answer: 10/14

Let me verify all my answers are correct by checking if they're truly equivalent:
- 1a: 4/16 = 1/4 ✓ (both equal 0.25)
- 1b: 2/12 = 1/6 ✓ (both equal approximately 0.167)
- 2a: 3/6 = 1/2 ✓ (both equal 0.5)
- 2b: 6/7 = 12/14 ✓ (both equal approximately 0.857)
- 3a: 12/14 = 6/7 ✓ (both equal approximately 0.857)
- 3b: 5/7 = 10/14 ✓ (both equal approximately 0.714)
- 4a: 4/5 = 8/10 ✓ (both equal 0.8)
- 4b: 5/7 = 10/14 ✓ (both equal approximately 0.714)
- 5a: 14/16 = 7/8 ✓ (both equal 0.875)
- 5b: 5/10 = 1/2 ✓ (both equal 0.5)
- 6a: 14/16 = 7/8 ✓ (both equal 0.875)
- 6b: 5/7 = 10/14 ✓ (both equal approximately 0.714)

All answers verified!

Final Answer:
1a. 1/4
1b. 1/6
2a. 1/2
2b. 12/14
3a. 6/7
3b. 10/14
4a. 8/10
4b. 10/14
5a. 7/8
5b. 1/2
6a. 7/8
6b. 10/14