Measurement: Background You’ll Need – Page 2

  • Simplify using fractions

Multiply or Divide Fractions

Multiplying and dividing fractions, including mixed numbers, are essential operations in mathematics that extend beyond basic arithmetic into more complex areas like algebra and geometry. Whether you’re combining proportions in a recipe or solving for unknowns in equations, understanding how to manipulate these numbers is key. Before we dive into operations with mixed numbers, remember that they need to be converted into improper fractions. This uniform format makes the multiplication or division process straightforward. Here are the steps to ensure you can tackle these operations with confidence.

How To: Multiply or Divide Mixed Numbers

  1. Convert the mixed numbers to improper fractions.
  2. Follow the rules for fraction multiplication or division.
  3. Simplify if possible.
Multiply the following. Write your answer in simplified form.

[latex]2\Large\frac{4}{5}\left(\normalsize -1\Large\frac{7}{8}\right)[/latex]

Divide the following. Write your answer in simplified form.

[latex]3\Large\frac{4}{7}\normalsize\div 5[/latex]

Simplify Complex Fractions

Our work with fractions so far has included proper fractions, improper fractions, and mixed numbers. Another kind of fraction is called complex fraction, which is a fraction in which the numerator or the denominator contains a fraction.

Some examples of complex fractions are:

[latex]\LARGE\frac{\frac{6}{7}}{ 3}, \frac{\frac{3}{4}}{\frac{5}{8}}, \frac{\frac{x}{2}}{\frac{5}{6}}[/latex]
To simplify a complex fraction, remember that the fraction bar means division. So the complex fraction [latex]\LARGE\frac{\frac{3}{4}}{\frac{5}{8}}[/latex] can be written as: [latex]\Large\frac{3}{4}\normalsize\div\Large\frac{5}{8}[/latex]

How To: Simplify a Complex Fraction

  1. Rewrite the complex fraction as a division problem.
  2. Follow the rules for dividing fractions.
  3. Simplify if possible.
Simplify: [latex]\LARGE\frac{-\frac{6}{7}}{ 3}[/latex]