Multiplication of a Fraction by a Fraction

We will discuss here about the multiplication of a fraction by a fraction.

\(\frac{1}{2}\) is multiplied by \(\frac{1}{3}\) or, \(\frac{1}{3}\) of \(\frac{1}{2}\)

Whole Part

Suppose this is whole (1)

Whole Figure

The whole figure has been divided into two halves.

Fractional Number Image

For showing \(\frac{1}{3}\) of \(\frac{1}{2}\), it is further sub divided half of the figure into 3 equal parts.

Whole figure is divided into 6 equal parts.

Here the double shaded portion is \(\frac{1}{3}\) of \(\frac{1}{2}\) parts.

Now \(\frac{1}{3}\) of \(\frac{1}{2}\) is \(\frac{1}{6}\) of the whole figure

Therefore, \(\frac{1}{3}\) × \(\frac{1}{2}\) = \(\frac{1}{6}\)

or, \(\frac{1}{3}\) × \(\frac{1}{2}\) = \(\frac{1 × 1}{3 × 2}\) =  \(\frac{1}{6}\)

Hence we conclude that, when we multiply a fractional number, multiply the numerator of the first fraction by the numerator of the second fraction and the denominator of the first fraction by the denominator of the second fraction. The first product is the numerator and the second product is the denominator of the required product.

The following rules are given below for the multiplication of a fractional number by a fractional number:

(a) Change mixed fraction into improper fraction.

(b) Product of two fractions = (Product of numerators)/(Product of denominators).

(c) Reduce numerator and denominator to the lowest terms.

(d) The answer should be a whole number, a mixed fraction or a proper fraction and never an improper fraction.

[The same rule can be applied for multiplying any number or fraction].

Solved examples on multiplication of a fraction by a fraction:

1. \(\frac{1}{2}\) × \(\frac{1}{3}\)

= \(\frac{1 × 1}{2 × 3}\)

= \(\frac{1}{6}\)

2. 2\(\frac{1}{2}\) × \(\frac{1}{3}\)

= \(\frac{2 × 2 + 1}{2}\) × \(\frac{1}{3}\)

= \(\frac{5}{2}\) × \(\frac{1}{3}\)

= \(\frac{5 × 1}{2 × 3}\)

= \(\frac{5}{6}\)

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

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

= \(\frac{13}{3}\) × \(\frac{11}{5}\)

= \(\frac{13 × 11}{3 × 5}\)

= \(\frac{143}{15}\)

Multiplication of a Fraction by a Fraction

= 9\(\frac{8}{15}\)

4. \(\frac{11}{3}\) × \(\frac{12}{55}\)

= \(\frac{11 × 12}{3 × 55}\)

Multiplication of a Fraction by a Fraction

[Reducing numerator and denominator to the lowest terms]

= \(\frac{4}{5}\)

5. Find the product:

(a) \(\frac{4}{3}\) × \(\frac{7}{9}\)

 \(\frac{4 × 7}{3 × 9}\)

= \(\frac{28}{27}\)

(b) 5\(\frac{1}{3}\) × \(\frac{2}{5}\)

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

= \(\frac{16}{3}\) × \(\frac{2}{5}\)

= \(\frac{16 × 2}{3 × 5}\)

= \(\frac{32}{15}\)

Multiplication of a Fraction by a Fraction

= 2\(\frac{2}{15}\)

 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 

5th Grade Math Problems 

From Multiplication of a Fraction by a Fraction to HOME PAGE

Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.

Share this page: What’s this?

Recent Articles

  1. Shifting of Digits in a Number |Exchanging the Digits to Another Place

    May 19, 24 05:43 PM

    What is the Effect of shifting of digits in a number? Let us observe two numbers 1528 and 5182. We see that the digits are the same, but places are different in these two numbers. Thus, if the digits…

    Read More

  2. Formation of Greatest and Smallest Numbers | Arranging the Numbers

    May 19, 24 03:36 PM

    Formation of Greatest and Smallest Numbers
    the greatest number is formed by arranging the given digits in descending order and the smallest number by arranging them in ascending order. The position of the digit at the extreme left of a number…

    Read More

  3. Formation of Numbers with the Given Digits |Making Numbers with Digits

    May 19, 24 03:19 PM

    In formation of numbers with the given digits we may say that a number is an arranged group of digits. Numbers may be formed with or without the repetition of digits.

    Read More

  4. Arranging Numbers | Ascending Order | Descending Order |Compare Digits

    May 19, 24 02:23 PM

    Arranging Numbers
    We know, while arranging numbers from the smallest number to the largest number, then the numbers are arranged in ascending order. Vice-versa while arranging numbers from the largest number to the sma…

    Read More

  5. Comparison of Numbers | Compare Numbers Rules | Examples of Comparison

    May 19, 24 01:26 PM

    Rules for Comparison of Numbers
    Rule I: We know that a number with more digits is always greater than the number with less number of digits. Rule II: When the two numbers have the same number of digits, we start comparing the digits…

    Read More