Properties of Multiplication of Fractional Numbers

The properties of multiplication of fractional numbers are discussed here.

Property 1: If two fractional numbers are multiplied in either order, the product remains the same.

For Example:

(i) \(\frac{2}{3}\) × \(\frac{7}{5}\)

= \(\frac{2 × 7}{3 × 5}\)

= \(\frac{14}{15}\)

And now if you interchange the place of the fractional numbers the product does not change.

\(\frac{7}{5}\) × \(\frac{2}{3}\)

= \(\frac{7 × 2}{5 × 3}\)

= \(\frac{14}{15}\)

We observe that the product in both the cases are same.

So, \(\frac{2}{3}\) × \(\frac{7}{5}\) = \(\frac{7}{5}\) × \(\frac{2}{3}\).

Note: From the above example we understand that, changing the order of fractional numbers does not change the product.

(ii) (4\(\frac{2}{3}\) × 5\(\frac{1}{3}\)) × \(\frac{1}{5}\) = 4\(\frac{2}{3}\) (5\(\frac{1}{3}\) × \(\frac{1}{5}\))

Properties of Multiplication of Fractional Numbers

Property 2: If a fractional number is multiplied by one, the product is the fractional number itself.

For Example:

(i) \(\frac{7}{9}\) × 1 

= \(\frac{7}{9}\) × \(\frac{1}{1}\)

= \(\frac{7 × 1}{9 × 1}\)

= \(\frac{7}{9}\)

So, we observe that a fraction multiplied by 1 is the fraction itself.

(ii) \(\frac{5}{8}\) × 1

= \(\frac{5}{8}\) × \(\frac{1}{1}\)

= \(\frac{5 × 1}{(8 × 1}\)

= \(\frac{5}{8}\)

(iii) \(\frac{15}{19}\) × 1

= \(\frac{15}{19}\) × \(\frac{1}{1}\)

= \(\frac{15 × 1}{(19 × 1}\)

= \(\frac{15}{19}\)

Property 3: If a fractional number is multiplied by zero, the product is zero.

For Example:

(i) \(\frac{3}{11}\) × 0

= \(\frac{3 × 0}{11}\)

= 0

(ii) \(\frac{7}{15}\) × 0

= \(\frac{7 × 0}{15}\)

= 0

 Multiplication is Repeated Addition.

● Multiplication of Fractional Number by a Whole Number.

● Multiplication of a Fraction by Fraction.

● Properties of Multiplication of Fractional Numbers.

● Multiplicative Inverse.

● Worksheet on Multiplication on Fraction.

● Division of a Fraction by a Whole Number.

● Division of a Fractional Number.

● Division of a Whole Number by a Fraction.

● Properties of Fractional Division.

● Worksheet on Division of Fractions.

● Simplification of Fractions.

● Worksheet on Simplification of Fractions.

● Word Problems on Fraction.

● Worksheet on Word Problems on Fractions.

5th Grade Numbers Page 

5th Grade Math Problems 

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