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6.

# Multiply Fractions by Whole Number

- 5th Grade MathAfter 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.a**Comparing 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.b**Explaining 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.a**Interpret 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.