4th Grade Multiplying a Fraction by a Whole Number Lesson (Free PDF)
This multiply fraction whole lesson 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.
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 in this multiply fraction whole lesson
- 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 \(\frac{5}{6} = 5 \times \frac{1}{6}\).
\(n \times \frac{a}{b} = \frac{n \times a}{b}\). 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 \(3 \times \frac{2}{5}\).
- Think of 3 groups of \(\frac{2}{5}\).
- Multiply the whole number by the numerator: \(3 \times 2 = 6\).
- Keep the denominator: \(\frac{6}{5}\).
- Change to a mixed number if you like: \(\frac{6}{5} = 1\frac{1}{5}\).
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 \(1\frac{4}{8}\).
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.
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.
Multiply fraction whole lesson: questions and answers
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.
How to use this multiply fraction whole lesson
Read the definitions first, then follow the worked method line by line and redo the example on paper without looking. When every step makes sense, move on to the worksheet, then check yourself with the quiz.
Download the multiply fraction whole lesson as a PDF with the button below and keep it with your notes.
Download the multiply fraction whole lesson as a PDF with the button below and keep it with your notes.
All Grade 4 chapters: Grade 4 math.
