4th Grade Math Practice Test — Units 7–8

Covers Unit 7 (Equivalent fractions and comparing) and Unit 8 (Add and subtract fractions & mixed numbers).

Unit 7 — Equivalent Fractions & Comparing Fractions

Concept 1

Generating Equivalent Fractions (The Golden Rule)

The Golden Rule: You create an equivalent fraction by multiplying (or dividing) both the numerator (top) and the denominator (bottom) by the exact same non-zero number. You are multiplying by 1 in disguise!

Worked Example: Find equivalent fractions for 3/4

• Multiply top and bottom by 2: (3 × 2) / (4 × 2) = 6/8
• Multiply top and bottom by 3: (3 × 3) / (4 × 3) = 9/12
• Multiply top and bottom by 5: (3 × 5) / (4 × 5) = 15/20
3/4 = 6/8 = 9/12 = 15/20. All represent the exact same amount of the whole.

Check Yourself:

Find the missing number: 2/5 = ?/20

Show Answer

Bottom: 5 × 4 = 20. So multiply top by 4: 2 × 4 = 8. So 2/5 = 8/20.

Understanding:

Concept 2

Comparing Fractions with Benchmarks (0, 1/2, 1)

The Big Idea: Before doing common denominators, compare fractions to the benchmark 1/2:

If the numerator is less than half the denominator, the fraction is less than 1/2 (e.g., 2/6 is less than 1/2 because half of 6 is 3).
If the numerator is greater than half the denominator, the fraction is greater than 1/2 (e.g., 5/8 is greater than 1/2 because half of 8 is 4).

Worked Example: Compare 3/8 and 4/6

• 3/8 is less than 1/2 (since 4/8 = 1/2).
• 4/6 is greater than 1/2 (since 3/6 = 1/2).
• Therefore: 3/8 < 4/6 without needing common denominators!

Check Yourself:

Compare using <, >, or =: 5/12 [ ? ] 7/10

Show Answer

Half of 12 is 6, so 5/12 < 1/2. Half of 10 is 5, so 7/10 > 1/2. Therefore: 5/12 < 7/10.

Understanding:

Concept 3

Comparing Using Common Denominators

The Big Idea: When benchmarks are too close, make the denominators equal by finding a common multiple, then compare the numerators.

Worked Example: Compare 3/5 and 2/3

Common multiple of 5 and 3 is 15:
• 3/5 = (3 × 3) / (5 × 3) = 9/15
• 2/3 = (2 × 5) / (3 × 5) = 10/15
Since 9/15 < 10/15, 3/5 < 2/3.

Check Yourself:

Compare 3/4 [ ? ] 5/6 by finding a common denominator.

Show Answer

Common denominator is 12: 3/4 = 9/12 and 5/6 = 10/12. Since 9/12 < 10/12, 3/4 < 5/6.

Understanding:

Unit 8 — Add & Subtract Fractions and Mixed Numbers

Concept 4

Adding Fractions with Like Denominators & Decomposing

The Core Rule: When denominators are the same, add the numerators and KEEP the denominator! Never add the denominators together!

Worked Example: 2/7 + 3/7

Add numerators: 2 + 3 = 5. Keep denominator 7.
2/7 + 3/7 = 5/7.

Decomposing: 5/7 can be broken into unit fractions: 1/7 + 1/7 + 1/7 + 1/7 + 1/7 or 2/7 + 3/7 or 1/7 + 4/7.

Check Yourself:

Find 4/9 + 3/9. What is the sum?

Show Answer

4 + 3 = 7. Denominator stays 9. Answer: 7/9.

Understanding:

Concept 5

Subtracting Fractions & Regrouping from Whole Numbers

The Big Idea: To subtract a fraction from a whole number 1, rename 1 as a fraction with matching top and bottom: 1 = 8/8 = 5/5 = 12/12.

Worked Example: 1 − 3/8

Rewrite 1 as 8/8:
8/8 − 3/8 = (8 − 3)/8 = 5/8.

Check Yourself:

Calculate: 1 − 5/12

Show Answer

12/12 − 5/12 = 7/12.

Understanding:

Concept 6

Adding and Subtracting Mixed Numbers with Regrouping

Subtracting with Regrouping: When the top fraction numerator is smaller than the bottom fraction, borrow 1 from the whole number and turn it into a fraction!

Worked Example: 4 1/5 − 1 4/5

You cannot subtract 4/5 from 1/5. Regroup 4 into 3 + 5/5:
• 4 1/5 = 3 + (5/5 + 1/5) = 3 6/5.
• Now subtract: 3 6/5 − 1 4/5 = (3 − 1) + (6/5 − 4/5) = 2 2/5.

Check Yourself:

Calculate: 5 2/7 − 2 5/7

Show Answer

Regroup 5 2/7 → 4 (7/7 + 2/7) = 4 9/7.
4 9/7 − 2 5/7 = 2 4/7.

Understanding: