Comparing Fractions Using Cross Multiplication

Comparing Fractions Using Cross Multiplication exercise

• Label the picture.

  Hints

  2 x 5 = ? 3 x 3 = ?
  Which answer is greater?

  The symbol < means the left is less than the right.
  The symbol > means the left is greater than the right.
  The symbol = means both the left and right are equal to each other.

  Solution

  • To find which fraction is greater, use cross multiplication with the numerators and denominators.
  • 2 x 5 = 10, and 3 x 3 = 9.
  • 10 is greater than 9, so $\mathbf{\frac{2}{3}}$ is greater than $\mathbf{\frac{3}{5}}$.

• Complete the steps to compare fractions.

  Hints

  Cross multiply the numerator and denominator before comparing.

  Here is an example.

  $\frac{9}{10}$ ? $\frac{4}{5}$

  In order to find which is greater, first solve for 9 x 5 and 10 x 4, as this cross multiplys the numerators and denominators. Once we have the answers we can compare those numbers.

  The symbol < means the left is less than the right.
  The symbol > means the left is greater than the right.
  The symbol = means both the left and right are equal to each other.

  Solution

  • To find which number is greater, first multiply the numerator of the left fraction with the denominator of the right fraction.
  • Next, multiply the denominator of the left fraction with the numerator of the right fraction.
  • Compare the products of the multiplication equations to find which answer is greater.
  • 45 is greater than 40, so $\frac{9}{10}$ is greater than $\frac{4}{5}$.

• Match the fractions and expressions.

  Hints

  We cross multiply the numerator and denominator to find which fraction is greater than, less than or equal to. We use the answers of the multiplication to do so.

  In this example, 2 x 5 = 10 and 3 x 3 = 9, therefore 10 > 9 is would pair with $\frac{2}{3}$ > $\frac{3}{5}$.

  Example:

  • $\frac{4}{9}$ and $\frac{3}{5}$
  • 4 x 5 = 20, 9 x 3 = 18
  • 20 > 18
  • So, $\frac{4}{9}$ > $\frac{3}{5}$

  Solution

  $\frac{9}{10}$ and $\frac{4}{5}$
  9 x 5 = 45
  10 x 4 = 40
  45 > 40

  $\frac{6}{3}$ and $\frac{4}{9}$
  6 x 9 = 54
  3 x 4 = 12
  54 > 12

  $\frac{2}{5}$ and $\frac{7}{9}$
  2 x 9 = 18
  7 x 5 = 35
  18 < 35

  $\frac{2}{10}$ and $\frac{8}{14}$
  2 x 14 = 28
  10 x 8 = 80
  28 < 80

• Highlight the correct expressions.

  Hints

  Cross multiply the numerator and denominator to find which fraction is greater than, less than or equal to.

  Here is an example.

  The symbol < means the left is less than the right.
  The symbol > means the left is greater than the right.
  The symbol = means both the left and right are equal to each other.

  To compare $\frac{4}{6}$ and $\frac{3}{5}$, multiply:

  • 4 x 5 = 20
  • 3 x 6 = 18

  Which is greater, 20 or 18? Is the comparison symbol the correct way round?

  Solution

  1) 4 x 5 = 20, 6 x 3 = 18. 20 is greater than 18, so $\mathbf{\frac{4}{6}}$ is greater than $\mathbf{\frac{3}{5}}$.
  2) 7 x 10 = 70, 9 x 6 = 54. 70 is greater than 54, so $\mathbf{\frac{7}{9}}$ is greater than $\mathbf{\frac{6}{10}}$.
  3) 2 x 10 = 20, 3 x 8 = 24. 20 is less than 24, so $\mathbf{\frac{2}{3}}$ is less than $\mathbf{\frac{8}{10}}$.
  4) 2 x 10 = 20, 6 x 5 = 30. 20 is less than 30, so $\mathbf{\frac{2}{6}}$ is less than $\mathbf{\frac{5}{10}}$.

• Compare the fractions.

  Hints

  The symbol < means the left is less than the right.
  The symbol > means the left is greater than the right.
  The symbol = means both the left and right are equal to each other.

  In order to find which fraction is greater than, less than or equal to, cross multiply the numerator and denominator. Then compare the products.
  In this example, 10 is greater than 9. So, $\mathbf{\frac{2}{3}}$ is greater than $\mathbf{\frac{3}{5}}$.

  Solution

  • $\mathbf{\frac{7}{9}}$ and $\mathbf{\frac{8}{12}}$
  • 7 x 12 = 84
  • 9 x 8 = 72
  • 84 > 72
  • $\mathbf{\frac{7}{9}}$ > $\mathbf{\frac{8}{12}}$

• Compare the fractions.

  Hints

  Cross multiply the numerator and denominator to compare the fractions.

  Example:

  • $\frac{4}{9}$ and $\frac{3}{5}$
  • 4 x 5 = 20, 9 x 3 = 18
  • 20 > 18
  • So, $\frac{4}{9}$ > $\frac{3}{5}$

  Solution

  1) $\frac{5}{11}$ and $\frac{2}{3}$
  5 x 3 = 15
  11 x 2 = 22
  15 < 22
  $\frac{5}{11}$ < $\frac{2}{3}$

  2) $\frac{7}{12}$ and $\frac{6}{7}$
  7 x 7 = 49
  12 x 6 = 72
  49 < 72
  $\frac{7}{12}$ < $\frac{6}{7}$

  3) $\frac{16}{20}$ < $\frac{8}{10}$
  16 x 10 = 160
  20 x 8 = 160
  160 = 160
  $\frac{16}{20}$ = $\frac{8}{10}$

  4) $\frac{13}{15}$ < $\frac{8}{9}$
  13 x 9 = 117
  15 x 8 = 120
  117 < 120
  $\frac{13}{25}$ < $\frac{8}{9}$