Question 1
Generating Equivalent Fractions
Score: 1 / 1 pt
Which fraction is equivalent to 3/4?
Correct (1 / 1 pt)
Solution: 6/8. Multiplying numerator and denominator by 2 gives (3 × 2) / (4 × 2) = 6/8.
4th Grade Math Diagnostic Test — Units 7–8
Fractions: Equivalence, Comparing, Addition, Subtraction & Mixed Numbers • Completed & Locked
Question 2
Finding the Missing Numerator
Score: 0 / 1 pt
Find the missing numerator to make the fractions equivalent:
2/5 = / 20
Incorrect (0 / 1 pt)
Attempt History: First Take: 6 • Retake: 6
Solution: 8. Since 5 × 4 = 20, multiply the top by 4: 2 × 4 = 8. So 2/5 = 8/20.
Concept & Review Note • Missing Numerators in Equivalent Fractions
To keep fractions equivalent, whatever factor you multiply or divide the denominator by, you must multiply or divide the numerator by the exact same number.
In 2/5 = ?/20: look at the denominators 5 → 20. 5 × 4 = 20 (multiplier is 4). Multiply top by 4: 2 × 4 = 8. Do not add (2 + 4 is not how equivalent fractions work).
Question 3
Simplifying Fractions
Score: 1 / 1 pt
Which fraction is equivalent to 6/18 in simplest form (dividing top and bottom by 6)?
Correct (1 / 1 pt)
Solution: 1/3. 6 ÷ 6 = 1 and 18 ÷ 6 = 3, so 6/18 = 1/3.
Question 4
Dividing by a Common Factor
Score: 1 / 1 pt
Divide the numerator and denominator by 5 to find the equivalent fraction:
15/25 = / 5
Correct (1 / 1 pt)
Solution: 3. 15 ÷ 5 = 3 and 25 ÷ 5 = 5, so 15/25 = 3/5.
Question 5
Benchmark Comparison: 3/8 vs. 1/2
Score: 0 / 1 pt
Which statement correctly compares 3/8 to the benchmark fraction 1/2?
Incorrect (0 / 1 pt)
Attempt History: First Take: B (>) • Retake: B (>)
Solution: 3/8 < 1/2. Exactly half of 8 is 4 (4/8 = 1/2). Since 3/8 < 4/8, 3/8 is less than 1/2.
Concept & Review Note • Benchmark Comparison to 1/2
When comparing a fraction to 1/2, find half of the denominator:
The denominator of 3/8 is 8. Half of 8 is 4, which means 4/8 = 1/2. Since 3 is less than 4 (3/8 < 4/8), 3/8 is strictly less than 1/2. Never just compare top numbers (3 is greater than 1, but 3 eighths is smaller than 1 half!).
Question 6
Benchmark Comparison: 7/12 vs. 1/2
Score: 1 / 1 pt
Which statement correctly compares 7/12 to the benchmark fraction 1/2?
Correct (1 / 1 pt)
Solution: 7/12 > 1/2. Exactly half of 12 is 6 (6/12 = 1/2). Since 7 > 6, 7/12 is greater than 1/2.
Question 7
Comparing with Common Denominators
Score: 1 / 1 pt
Compare 3/5 and 2/3. Using common denominator 15 (3/5 = 9/15 and 2/3 = 10/15), which comparison is correct?
Correct (1 / 1 pt)
Solution: 3/5 < 2/3. In 15ths: 3/5 = 9/15, and 2/3 = 10/15. Since 9/15 < 10/15, 3/5 is smaller.
Question 8
Ordering Fractions
Score: 0.5 / 1 pt
Which list shows the fractions 1/4, 2/3, 5/12 in order from smallest to largest?
Corrected on Retake (+0.5 pt)
Attempt History: First Take selected D (1/4, 2/3, 5/12) • Retake corrected to A (1/4, 5/12, 2/3)
Solution: Choice A: 1/4, 5/12, 2/3. Converted to 12ths: 1/4 = 3/12, then 5/12, then 2/3 = 8/12. Order: 3/12 < 5/12 < 8/12.
Concept & Review Note • Ordering Fractions with Unlike Denominators
To order 1/4, 2/3, and 5/12, convert all to a common denominator of 12:
• 1/4 = 3/12 (multiply top & bottom by 3)
• 5/12 = 5/12
• 2/3 = 8/12 (multiply top & bottom by 4)
Comparing 12ths: 3/12 < 5/12 < 8/12, so the correct ascending order is 1/4, 5/12, 2/3.
Question 9
Decomposing into Unit Fractions
Score: 1 / 1 pt
How many 1/6 unit fractions must be added together to make 5/6?
Correct (1 / 1 pt)
Solution: 5 unit fractions. Five copies of 1/6 add up to 5/6.
Question 10
Breaking Apart Fractions
Score: 1 / 1 pt
Complete the equation to break apart 5/6 into two smaller fractions:
2/6 + / 6 = 5/6
Correct (1 / 1 pt)
Solution: 3. 2/6 + 3/6 = 5/6 (2 + 3 = 5).
Question 11
Adding Fractions with Like Denominators
Score: 1 / 1 pt
Add the numerators and keep the denominator the same:
3/8 + 4/8 = / 8
Correct (1 / 1 pt)
Solution: 7/8. 3 + 4 = 7, denominator stays 8.
Question 12
Adding Fractions with Like Denominators
Score: 1 / 1 pt
Calculate the sum:
5/12 + 6/12 = / 12
Correct (1 / 1 pt)
Solution: 11/12. 5 + 6 = 11, denominator stays 12.
Question 13
Subtracting a Fraction from 1 Whole
Score: 0.5 / 1 pt
Think of 1 as 7/7. Calculate:
1 − 3/7 = / 7
Corrected on Retake (+0.5 pt)
Attempt History: First Take: 2 • Retake: 4
Solution: 4/7. Rewrite 1 as 7/7: 7/7 − 3/7 = 4/7.
Concept & Review Note • Subtracting from 1 Whole
Whenever you subtract a fraction from 1 whole, rename the whole into a fraction matching the denominator:
Here, the denominator is 7, so 1 = 7/7. Now subtract like numerators: 7/7 − 3/7 = (7 − 3)/7 = 4/7. (First pass entered 2; on retake, correctly renamed 1 as 7/7 and computed 7 − 3 = 4).
Question 14
Subtracting Fractions with Like Denominators
Score: 1 / 1 pt
Subtract the numerators:
9/10 − 4/10 = / 10
Correct (1 / 1 pt)
Solution: 5/10. 9 − 4 = 5. (5/10 is also equivalent to 1/2).
Question 15
Adding Mixed Numbers
Score: 2 / 2 pts
Add the whole numbers and fractions: 2 1/6 + 3 4/6
Whole number: and fraction: / 6
Correct (2 / 2 pts: 1 pt whole, 1 pt fraction)
Solution: 5 5/6. Wholes: 2 + 3 = 5. Fractions: 1/6 + 4/6 = 5/6. Result: 5 5/6.
Question 16
Word Problem: Subtracting Mixed Numbers
Score: 1.0 / 2 pts
Maya had 3 1/8 cups of flour. She used 1 5/8 cups to bake muffins. How much flour is left?
Whole cups: and / 8 cups.
Corrected on Retake (+1.0 pt / 2 pts: +0.5 pt whole, +0.5 pt fraction)
Attempt History: First Take: Whole 3, Numerator 9 • Retake: Whole 1, Numerator 4
Solution: 1 4/8 cups (or 1 1/2 cups). Regroup 3 1/8 into 2 9/8. Then 2 9/8 − 1 5/8 = 1 4/8 cups.
Concept & Review Note • Subtracting Mixed Numbers with Regrouping
To subtract 3 1/8 − 1 5/8, notice you cannot subtract 5/8 from 1/8 without regrouping:
Step 1 (Regroup): Borrow 1 whole from 3 as 8/8: 3 wholes becomes 2 wholes + 8/8. Add 8/8 to 1/8 → 2 9/8.
Step 2 (Subtract): Whole numbers: 2 − 1 = 1. Fractions: 9/8 − 5/8 = 4/8.
Result: 1 4/8 cups (or 1 1/2 cups).
First Take successfully regrouped to 9/8 but stopped without subtracting 1 5/8; Retake completed both subtraction steps accurately.