Question 1
Unit Fraction Multiples
Which expression is equivalent to the fraction 5/6?
Solution: 5/6 = 5 × (1/6). Any fraction a/b is equal to a × (1/b).
4th Grade Math Diagnostic Test — Units 9–10
Multiplying Fractions & Decimal Concepts. Limit: 60 Minutes.
Question 2
Multiplying Whole Number by Unit Fraction
Calculate: 8 × (1/9) = /
Solution: 8 × (1/9) = (8 × 1)/9 = 8/9.
Question 3
Repeated Addition to Multiplication
Which multiplication expression represents 2/7 + 2/7 + 2/7?
Solution: Adding 2/7 three times is 3 groups of 2/7, written as 3 × (2/7).
Question 4
Calculating Repeated Fraction Product
Calculate the product: 3 × (2/7) = /
Solution: 3 × 2 = 6 in numerator. Product is 6/7.
Question 5
Multiplying Non-Unit Fractions
What is 4 × (2/5) written as an improper fraction?
Solution: 4 × 2 = 8. Denominator remains 5 → 8/5. Do NOT multiply the denominator!
Question 6
Converting Product to Mixed Number
Convert the improper fraction 8/5 into a mixed number:
Whole: • Fraction: /
Solution: 8 ÷ 5 = 1 with a remainder of 3. So 8/5 = 1 3/5.
Question 7
Fraction Multiplication Product
Calculate: 6 × (3/8) = /
Solution: 6 × 3 = 18. Denominator is 8. Product = 18/8 (or 9/4).
Question 8
Word Problem: Ribbon
Each of 3 students needs 3/4 yard of ribbon for an art project. How many total yards of ribbon are needed?
Mixed number: Whole: • Fraction: / yards.
Solution: 3 × 3/4 = 9/4 = 2 1/4 yards.
Question 9
Tenths to Decimals
What is 7/10 written as a decimal?
Solution: 7/10 has 7 in the tenths place, written as 0.7.
Question 10
Hundredths to Decimals
What is 6/100 written as a decimal?
Solution: 6/100 has 0 in the tenths place and 6 in the hundredths place → 0.06. 0.6 is 6/10.
Question 11
Hundredths to Decimal
Write 35/100 as a decimal:
Solution: 35/100 = 0.35 (3 tenths and 5 hundredths).
Question 12
Decimals to Fractions
Write the decimal 0.8 as a fraction: /
Solution: 0.8 = 8/10 (or simplified to 4/5).
Question 13
Adding Tenths and Hundredths
What is 4/10 + 23/100 expressed as a fraction?
Solution: Convert 4/10 to hundredths: 4/10 = 40/100. Then 40/100 + 23/100 = 63/100.
Question 14
Sum as a Decimal
Write the fraction 63/100 as a decimal:
Solution: 63/100 = 0.63.
Question 15
Comparing Decimals
Which comparison statement is true?
Solution: 0.5 = 0.50. Comparing 50 hundredths to 47 hundredths, 0.50 > 0.47.
Question 16
Decimal Comparison in Word Problem
In a race, Aiden ran 0.7 kilometers and Ben ran 0.65 kilometers.
Part A: Who ran farther?
Part B: By how many kilometers did he run farther? km.
Solution: 0.7 = 0.70 km. Since 0.70 > 0.65, Aiden ran farther. Difference: 0.70 − 0.65 = 0.05 km.