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In this guided practice lesson, we will work through fraction equivalence problems step-by-step together. You'll learn strategies for finding equivalent fractions and simplifying them efficiently.

Key Strategies

Multiply or divide both parts: To find an equivalent fraction, multiply or divide both the numerator and denominator by the same number.
Use visual models: Drawing fraction bars or circles can help you see equivalence.
Check your work: Cross-multiply to verify two fractions are equivalent.
Find the GCF: When simplifying, find the greatest common factor of the numerator and denominator.

Examples

Work through these examples to see the concepts in action.

Example 1: Finding an Equivalent Fraction

Find a fraction equivalent to 2/3 with a denominator of 12.

Solution: Since 3 x 4 = 12, multiply both parts by 4: 2/3 = 8/12

Example 2: Simplifying a Fraction

Simplify 12/16 to lowest terms.

Solution: The GCF of 12 and 16 is 4. Divide both by 4: 12/16 = 3/4

✏️ Practice

Test your understanding with these practice questions.

Practice Questions

0/4 correct

Question 1

If y = 3x represents a proportional relationship, what is the constant of proportionality?

A 1

B 3

C x

D y

Explanation: In y = kx, the constant of proportionality k is the coefficient of x. Here k = 3.

Question 2

A recipe uses 2 cups of flour for every 3 cups of sugar. If you use 6 cups of flour, how many cups of sugar do you need?

A 4 cups

B 9 cups

C 12 cups

D 8 cups

Explanation: Set up the proportion: 2/3 = 6/x. Cross multiply: 2x = 18, so x = 9 cups.

Question 3

Which equation represents a proportional relationship?

A y = 2x + 1

B y = 5x

C y = x²

D y = 3

Explanation: A proportional relationship has the form y = kx where k is a constant. Only y = 5x fits this form.

Question 4

The table shows x: 2, 4, 6 and y: 8, 16, 24. What is the constant of proportionality?

A 2

B 4

C 6

D 8

Explanation: Divide any y-value by its corresponding x-value: 8÷2 = 4, 16÷4 = 4, 24÷6 = 4. The constant is 4.

Check Your Understanding

Test yourself with these 10 quiz questions. Click on each question to reveal the answer.

Question 1: Find a fraction equivalent to 1/2 with a denominator of 8.

Answer: 4/8. Multiply both numerator and denominator by 4: 1x4/2x4 = 4/8

Question 2: Simplify 6/9 to lowest terms.

Answer: 2/3. The GCF of 6 and 9 is 3. Divide both by 3: 6/9 = 2/3

Question 3: Are 3/4 and 9/12 equivalent fractions?

Answer: Yes. 3x3=9 and 4x3=12, so 3/4 = 9/12. You can also cross-multiply: 3x12=36 and 4x9=36.

Question 4: Find a fraction equivalent to 2/5 with a denominator of 20.

Answer: 8/20. Since 5x4=20, multiply both parts by 4: 2x4/5x4 = 8/20

Question 5: Simplify 15/25 to lowest terms.

Answer: 3/5. The GCF of 15 and 25 is 5. Divide both by 5: 15/25 = 3/5

Question 6: What is the missing numerator? __/6 = 2/3

Answer: 4. Since 3x2=6, multiply the numerator by 2 as well: 2x2=4, so 4/6 = 2/3

Question 7: Are 4/10 and 2/5 equivalent fractions?

Answer: Yes. 4/10 simplifies to 2/5 when you divide both by 2.

Question 8: Find the simplest form of 8/12.

Answer: 2/3. The GCF of 8 and 12 is 4. Divide both by 4: 8/12 = 2/3

Question 9: What is the missing denominator? 3/4 = 12/__

Answer: 16. Since 3x4=12, multiply the denominator by 4 as well: 4x4=16, so 3/4 = 12/16

Question 10: Simplify 20/32 to lowest terms.

Answer: 5/8. The GCF of 20 and 32 is 4. Divide both by 4: 20/32 = 5/8

Next Steps

Review any concepts that felt challenging
Move on to the next lesson when ready
Return to practice problems periodically for review