4th Grade Multiplying a Fraction by a Whole Number Lesson (Free PDF)

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

To multiply a whole number by a fraction, multiply the whole number by the numerator and keep the denominator: 3 x 2/5 = 6/5. A fraction such as 5/6 is a multiple of the unit fraction 1/6, because it is 5 x 1/6. Change an improper fraction to a mixed number to read the answer more easily.

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

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.

What does a fraction mean as a multiple of a unit fraction?

A unit fraction has a numerator of 1, like \(\frac{1}{6}\). Every fraction is built from unit fractions. The fraction \(\frac{5}{6}\) is 5 pieces that are each \(\frac{1}{6}\), so \(\frac{5}{6} = 5 \times \frac{1}{6}\).

1/61/61/61/61/65/6 = 5 × 1/6
Five sixths is five copies of one sixth.
Multiplying a whole number by a fraction

\(n \times \frac{a}{b} = \frac{n \times a}{b}\). Multiply the whole number by the numerator. Keep the denominator, because the size of the pieces does not change.

How do you multiply a whole number by a fraction?

Example: Find \(3 \times \frac{2}{5}\).

  1. Think of 3 groups of \(\frac{2}{5}\).
  2. Multiply the whole number by the numerator: \(3 \times 2 = 6\).
  3. Keep the denominator: \(\frac{6}{5}\).
  4. Change to a mixed number if you like: \(\frac{6}{5} = 1\frac{1}{5}\).
2/52/52/5
Three groups of \(\frac{2}{5}\) make 6 fifths, which is more than 1 whole.

How can you show it on a number line?

Make equal jumps. For \(4 \times \frac{3}{8}\), start at 0 and make 4 jumps of \(\frac{3}{8}\). The last jump lands at \(\frac{12}{8}\), which is \(1\frac{4}{8}\).

0123/83/83/86/83/89/83/812/8
Four jumps of \(\frac{3}{8}\) land at \(\frac{12}{8}\).

How do you solve a word problem?

Look for equal groups. If each of 4 batches uses \(\frac{3}{4}\) cup of milk, the total is \(4 \times \frac{3}{4} = \frac{12}{4} = 3\) cups.

? cups in all3/43/43/43/4
A tape diagram with 4 equal parts of \(\frac{3}{4}\) cup.

When the answer is an improper fraction, write it as a mixed number or a whole number so it is easier to understand. Divide the numerator by the denominator: the quotient is the whole number and the remainder is the new numerator.

What mistakes should you avoid?

  • Multiplying the denominator. In \(3 \times \frac{2}{5}\), the answer is \(\frac{6}{5}\), not \(\frac{6}{15}\). The pieces are still fifths.
  • Stopping at an improper fraction when the problem asks how many cups or miles. Write a mixed number so the amount is easy to picture.
  • Forgetting the groups. In a word problem, find how many equal groups there are and what fraction is in each group.

A quick check: \(\frac{6}{5}\) is a little more than 1 whole, and 3 groups of two fifths should be a little more than 1 too. If your answer looks far too big or too small, try the number line again.

Questions about multiplying a fraction by a whole number

How do you multiply a fraction by a whole number?

Multiply the whole number by the numerator and keep the same denominator. For 3 times 2/5, multiply 3 times 2 to get 6, so the answer is 6/5.

Why is 3/4 the same as 3 times 1/4?

Three fourths means three pieces that are each one fourth. Putting 3 equal pieces together is the same as multiplying 3 by 1/4.

Does the denominator change when you multiply by a whole number?

No. The denominator tells the size of each piece, and multiplying by a whole number only changes how many pieces there are.

How do you change an improper fraction answer to a mixed number?

Divide the numerator by the denominator. The quotient is the whole number part and the remainder is the numerator of the fraction part. For 12/8, 12 divided by 8 is 1 remainder 4, so it is 1 4/8.

How can you tell a word problem needs fraction times whole number?

Look for equal groups where each group is a fraction, such as 5 days of 2/3 mile each. The total is the number of groups times the fraction.

Practice this chapter

All Grade 4 chapters: Grade 4 math.

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