RadfordMathematics.com

Multiplying with Fractions

(how to multiply fractions with fractions & fractions with whole numbers)

In this section we learn how to multiply with fractions. In particular we learn how to multiply two fractions together as well as how to multiply fractions with whole numbers.

By the end of this section we should be comfortable calculating either of the following: \[\frac{3}{7} \times \frac{2}{5} \quad \text{or} \quad 5\times \frac{3}{10}\]

Tutorial 1: How to Multiply Two Fractions

In the following tutorial we learn how to multiply fractions by working through the example: \[\frac{2}{3}\times \frac{4}{5}\]

The method for multiplying fractions we've just seen is written here; make a note of it.

Formula: Multiplying with Fractions

Given two fractions \(\frac{a}{b}\) and \(\frac{c}{d}\), we can multiply them using the formula: \[\frac{a}{b} \times \frac{c}{d} = \frac{a\times c }{b \times d}\] in words: we multiply the two numerators toegther and multiply the two denominators together.

Exercise 1

Calculate each of the following, writing your answer in its simplest form:

  1. \(\frac{3}{4}\times \frac{1}{5}\)
  2. \(\frac{3}{5}\times \frac{2}{3}\)
  3. \(\frac{2}{7}\times \frac{3}{5}\)
  4. \(\frac{3}{10}\times \frac{4}{7}\)
  5. \(\frac{2}{3}\times \frac{12}{13}\)
  6. \(\frac{2}{3}\times \frac{6}{8}\)
  7. \(\frac{4}{7}\times \frac{2}{3}\)
  8. \(\frac{4}{11}\times \frac{5}{8}\)

Answers Without Working

We find the following results:

  1. \(\frac{3}{4}\times \frac{1}{5} = \frac{3}{20}\)
  2. \(\frac{3}{5}\times \frac{2}{3} = \frac{2}{5}\)
  3. \(\frac{2}{7}\times \frac{3}{5} = \frac{6}{35}\)
  4. \(\frac{3}{10}\times \frac{4}{7} = \frac{6}{35}\)
  5. \(\frac{2}{3}\times \frac{12}{13} = \frac{24}{39}\)
  6. \(\frac{2}{3}\times \frac{6}{8} = \frac{1}{2}\)
  7. \(\frac{4}{7}\times \frac{2}{3} = \frac{8}{21}\)
  8. \(\frac{4}{11}\times \frac{5}{8} = \frac{5}{22}\)

Multiplying Fractions with Whole Numbers

Now that we know how to multiply two fractions, we learn how to multiply a fraction with a whole number. In other words we learn how to calculate expressions such as: \[5\times \frac{3}{7}\]

Tutorial 2: How to Multiply Fractions by Whole Numbers

In the following tutorial we learn how to multiply fractions by whole numbers by working through the example: \[\frac{2}{3}\times 5\]

Formula: Multiplying Fractions and Whole Numbers

Given a fraction \(\frac{a}{b}\) and a whole number \(c\) they can be multipled using the following formula: \[c \times \frac{a}{b} = \frac{a\times c}{b}\] which can also be written in inverse order: \[\frac{a}{b}\times c = \frac{c \times a}{b}\]

Exercise 2

Calculate each of the following, writing your answer in its simplest form:

  1. \(5\times \frac{3}{4}\)
  2. \(\frac{5}{8}\times 4\)
  3. \(2\times \frac{6}{7}\)
  4. \(3\times \frac{7}{12}\)
  5. \(\frac{6}{11}\times 8\)

Answers Without Working

We find the following results:

  1. \(5\times \frac{3}{4} = \frac{15}{4}\)
  2. \(\frac{5}{8}\times 4 = \frac{5}{2}\)
  3. \(2\times \frac{6}{7} = \frac{12}{7}\)
  4. \(3\times \frac{7}{12} = \frac{21}{12}\)
  5. \(\frac{6}{11}\times 8 = \frac{48}{11}\)


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