Simplifying Fractions —Let's Practice!

Simplifying Fractions —Let's Practice! exercise

• True or False?

  Hints

  How do we make fractions from the blocks shown in the image?

  • Count the number of highlighted blocks in the group on the left. Write this number on the top of the fraction.

  • Count the total number of highlighted and non-highlighted blocks on the left. Write this number on the bottom.

  Repeat these steps to get the fraction for the blocks on the right.

  Equivalent means equal.

  To answer question #2, find out if the two fractions in the image are equal.

  The greatest common factor is the largest number that both 4 and 12 are divisible by.

  Solution

  1. True. Left fraction: $\frac{4}{12}$, right fraction: $\frac{1}{3}$
  2. True. The two fractions are equivalent.
  3. False. The greatest common factor of 4 and 12 is not 2.

  • To find the greatest common factor, list the numbers that both 4 and 12 are divisible by. They are: 1, 2 and 4. Therefore, the greatest common factor is 4.

• Simplify the fraction.

  Hints

  List all common factors that the numerator and denominator share. Which is greatest?

  Divide the numerator and denominator by the greatest common factor to get the simplified fraction.

  Solution

  The greatest common factor is 5.

  In the simplified fraction, the numerator is 1 and the denominator is 4.

  The simplified fraction is $\frac{1}{4}$.

• Find the greatest common factor of each fraction.

  Hints

  List all common factors that the numerator and denominator share.

  Choose the largest factor from the list to find the greatest common factor.

  The factors of 28 and 35 are:

  28: 1, 2, 4, 7, 14

  35: 1, 5, 7

  What is the largest factor they both share?

  Solution

  1) $\frac{12}{16}$: The greatest common factor is 4.

  2) $\frac{15}{18}$: The greatest common factor is 3.

  3) $\frac{28}{35}$: The greatest common factor is 7.

  4) $\frac{24}{39}$: The greatest common factor is 3.

• Simplify all fractions. Answer the questions.

  Hints

  Divide the numerator and denominator by the greatest common factor.

  List all factors for 35 and 56:

  35: 1, 5, 7

  56: 1, 2, 4, 7, 8, 14, 28

  Divide both numbers by the greatest factor they both share to simplify the fraction.

  Solution

  $\frac{27}{36}$: The greatest common factor is 9. The simplified fraction is 3 over 4 or $\frac{3}{4}$.

  $\frac{20}{28}$: The greatest common factor is 4. The simplified fraction is 5 over 7 or $\frac{5}{7}$.

  $\frac{35}{56}$: The greatest common factor is 7. The simplified fraction is 5 over 8 or $\frac{5}{8}$.

• Simplify the fraction.

  Hints

  To find the unsimplified fraction shown by the blocks:

  • Count the number of highlighted blocks. Write this number on the top of the fraction.

  • Count the total number of highlighted and non-highlighted blocks. Write this number on the bottom.

  To find the greatest common factor:

  • Count the number of highlighted blocks in the numerator.

  • Count the number of highlighted blocks in the denominator.

  Which numbers can both the numerator and denominator be divided by?

  Divide 4 and 6 by their greatest common factor to find the simplified fraction.

  Solution

  1. The unsimplified fraction is $\frac{4}{6}$.
  2. The greatest common factor is 2.
  3. The numerator of the simplified fraction is 2.
  4. the denominator of the simplified fraction is 3.
  5. The simplified fraction is $\frac{2}{3}$.

• Solve the word problem.

  Hints

  Shown below is a daisy.

  Start by writing out the unsimplified fraction.

  The number of daisies is the numerator.

  The total number of all flowers is the denominator.

  Count out the number of daisies and total number of flowers in the photo if you need to.

  Next, simplify the fraction.

  Divide both the numerator and denominator by the greatest common factor.

  Solution

  The fraction of daisies in the total bouquet is 3 over 8 or $\frac{3}{8}$.

  The unsimplified fraction is $\frac{12}{32}$. Divide each number by 4 to get the simplified fraction, $\frac{3}{8}$.