4th Grade Multiplying a Fraction by a Whole Number Test Solutions and Scoring (PDF)

4th Grade math test solutions: Multiplying a Fraction by a Whole Number – Maths PDF

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This multiply fraction whole test answers for 4th Grade covers multiplying a fraction by a whole number (Common Core 4.NF.B.4a, 4.NF.B.4b, 4.NF.B.4c), with a free PDF to print.

Use this answer key and scoring guide to grade the test. Each solution shows the multiplication and the mixed number, and the scoring notes explain partial credit out of 20 points.

Grade 4 · Common Core State Standards: 4.NF.B.4a, 4.NF.B.4b, 4.NF.B.4c

Multiply fraction whole test answers: worked solutions

Question 1 – Unit fractions [2 pts]

(a) Each shaded part is \(\frac{1}{6}\), and there are 5 of them.

Five copies of \(\frac{1}{6}\).

(b) Five parts of \(\frac{1}{6}\) added together.

(a) \(5 \times \frac{1}{6}\) (b) \(\frac{1}{6} + \frac{1}{6} + \frac{1}{6} + \frac{1}{6} + \frac{1}{6}\)

Scoring: 1 point for each part.

Question 2 – Unit fraction products [2 pts]

(a) \(3 \times 1 = 3\), so \(\frac{3}{8}\).

(b) \(\frac{7}{5}\) = \(1\frac{2}{5}\).

(a) \(\frac{3}{8}\) (b) \(\frac{7}{5}\) = \(1\frac{2}{5}\)

Scoring: 1 point for each part.

Question 3 – Multiply by a fraction [2 pts]

\(4 \times 3 = 12\), so \(\frac{12}{5}\).

\(12 \div 5 = 2\) remainder 2.

\(\frac{12}{5}\) = \(2\frac{2}{5}\)

Scoring: 1 point for the fraction; 1 point for the mixed number.

Question 4 – Jumps on a number line [2 pts]

There are 3 jumps and each jump is \(\frac{3}{4}\).

The jumps land at \(\frac{3}{4}\), \(\frac{6}{4}\) and \(\frac{9}{4}\).

\(3 \times \frac{3}{4} = \frac{9}{4} = 2\frac{1}{4}\).

\(3 \times \frac{3}{4} = \frac{9}{4}\), or \(2\frac{1}{4}\)

Scoring: 1 point for the equation; 1 point for the product.

Question 5 – Larger product [2 pts]

\(8 \times 5 = 40\), so \(\frac{40}{12}\).

\(40 \div 12 = 3\) remainder 4.

\(3\frac{4}{12}\)

Scoring: 1 point for \(\frac{40}{12}\); 1 point for the mixed number.

Question 6 – Morning runs [3 pts]

(a) \(4 \times \frac{5}{6} = \frac{20}{6}\).

(b) \(20 \div 6 = 3\) remainder 2, so \(3\frac{2}{6}\).

(a) \(4 \times \frac{5}{6} = \frac{20}{6}\) (b) \(3\frac{2}{6}\) miles (c) yes

Scoring: 1 point for each part.

Question 7 – Batches of muffins [3 pts]

(a) \(6 \times \frac{3}{4} = \frac{18}{4}\).

(b) \(18 \div 4 = 4\) remainder 2, so \(4\frac{2}{4}\).

Six groups of \(\frac{3}{4}\) cup.

(a) \(6 \times \frac{3}{4} = \frac{18}{4}\) (b) \(4\frac{2}{4}\) cups (c) \(\frac{2}{4}\) cup

Scoring: 1 point for each part.

Question 8 – Products for nine fourths [2 pts]

\(\frac{9}{4} = 9 \times \frac{1}{4}\) and \(\frac{9}{4} = 3 \times \frac{3}{4}\).

\(9 \times \frac{1}{4}\) and \(3 \times \frac{3}{4}\)

Scoring: 1 point for each correct product.

Question 9 – Diego's mistake [2 pts]

Diego multiplied the denominator by 3. The denominator names the size of the pieces, and it does not change. Only the number of pieces changes: \(3 \times 2 = 6\) fifths.

\(3 \times \frac{2}{5} = \frac{6}{5}\)

Scoring: 1 point for the explanation; 1 point for \(\frac{6}{5}\).

Total score

Total

20 points

Key facts behind this multiply fraction whole test answers

Key facts

A fraction a/b is a multiple of the unit fraction 1/b, so a/b = a x 1/b.
n x (a/b) = (n x a)/b. Multiply the whole number by the numerator and keep the denominator.
Repeated jumps on a number line show the same product.
Write improper fraction products as mixed numbers when it helps.
Equal groups in word problems signal fraction times whole number.

How to use this multiply fraction whole test answers

Score your test with the point values shown for each question. Then read the worked solution of every question where you lost points and note the method to review.

Download the multiply fraction whole test answers as a PDF with the button below and keep it with your notes.

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