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Multiply Fractions by Whole Number

- Grade 5 Math

After learning to add and subtract fractions with both like and unlike denominators, children now learn to multiply a fraction by a whole number. They understand that multiplying a fraction by a whole number is representing the fraction, whole number of times. In addition to direct multiplication, children practice multiplication as scaling. For example, the result of multiplying a number by a fraction less than 1 is less than the original number; therefore, it is like scaling down. Similarly, multiplying by a fraction greater than 1 is like scaling up.

What’s inside?

- Begin by expressing multiplication of a fraction ‘p/q’ with a whole number ‘a’ in  format.

- Encounter situations where multiplying fractions by a whole number results in another whole number. For example, 20 x 3/4 = 15.

- Apply the knowledge of comparing fractions in deciding if the product of a fraction and a whole number is greater or smaller than a given number.

Real-World Applications

We come across many situations where we end up multiplying fractions by a whole number. When each person eats half a pizza and we have to order for six, we multiply a fraction by a whole (in this case, 1/2 by 6). Similarly, we do realize that buying eight quarter-sized chocolate pastries is equivalent to buying two whole yummy cakes. Needless to say, this skill helps children be ready for all this and more.

What’s next?

With their knowledge of multiplying fractions by a whole number, children can now learn multiplication of fractions by fractions.

Cool Fact

The whole number factor 'c' in the product of ‘a/b’ and ‘c’ doesn't change the denominator, except in the case where 'c' and 'b' have a common factor. Consider this example: 2/5 x 3 = 6/5 but 5/6 x 3 = 15/6 or 5/2.

Common Core Alignment

5.NF.5.aComparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.

5.NF.5.bExplaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n×a)/(n×b) to the effect of multiplying a/b by 1.

5.NF.4.aInterpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b.