Multiplying a Fraction by a Whole Number

Multiplying a Fraction by a Whole Number exercise

• Which fractions do the shaded shapes represent?

  Hints

  Think about the proportion of the circle that is shaded. For example, this circle is $\frac{3}{4}$ shaded.

  Can you simplify the fractions with the larger denominators to help you?

  Solution

  Here are the fractions that match each shape.

  • The first shape represents $\frac{1}{4}$. $\frac{3}{12}$ can be simplified to $\frac{1}{4}$ by dividing both the numerator and the denominator by 3.

  • The second shape represents $\frac{1}{3}$. $\frac{2}{6}$ can be simplified to $\frac{1}{3}$ by dividing both the numerator and the denominator by 2.

  • The third shape represents $\frac{1}{2}$. $\frac{4}{8}$ can be simplified to $\frac{1}{2}$ by dividing both the numerator and the denominator by 4. $\frac{6}{12}$ can also be simplified to $\frac{1}{2}$ by dividing both the numerator and the denominator by 6.

  • The fourth shape represents $\frac{2}{3}$. $\frac{4}{6}$ can be simplified to $\frac{2}{3}$ by dividing both the numerator and the denominator by 2. $\frac{6}{9}$ can also be simplified to $\frac{2}{3}$ by dividing both the numerator and the denominator by 3.

• Can you help Axel and Tank?

  Hints

  Start by finding the fraction you are multiplying.

  We can write the whole number as a fraction to help us find the answer.

  Are there any words in the text that could help you with ordering?

  Solution

  These are the correctly ordered steps that Axel and Tank should follow:

  1. First, write the fraction.
  2. Write the whole number as a fraction.
  3. Multiply the numerators.
  4. Multiply the denominators.
  5. Finally, re-write the fraction as a mixed number if necessary.

• Find the times for each exercise.

  Hints

  Use the shaded circle to help you e.g. this circle represents $\frac{3}{4}$.

  Remember, you can make the whole number into a fraction like this to help you with the multiplication.

  You could get some paper and a pen to help you if you need to.

  Solution

  This is how long Axel and Tank will do each exercise each week.

  • Cycling = $\frac{3}{6}$ x 5 = $\frac{3}{6}$ x $\frac{5}{1}$ = $\frac{15}{6}$ = 2 $\frac{3}{6}$ = 2 $\mathbf{\frac{1}{2}}$

  • Running = $\frac{7}{8}$ x 3 = $\frac{7}{8}$ x $\frac{3}{1}$ = $\frac{21}{8}$ = 2 $\mathbf{\frac{5}{8}}$

  • Swimming = $\frac{9}{10}$ x 7 = $\frac{9}{10}$ x $\frac{7}{1}$ = $\frac{63}{10}$ = 6 $\mathbf{\frac{3}{10}}$

  • Walking = $\frac{1}{3}$ x 6 = $\frac{1}{3}$ x $\frac{6}{1}$ = $\frac{6}{3}$ = 2

• Solve the multiplication problems

  Hints

  How can you change the whole number to make it easier to multiply?

  Remember to re-write your final fraction at the end as a mixed number if necessary.

  Solution

  Axel and Tank have spent this many hours doing these activities.

  • Watching TV= $\frac{4}{5}$ x 6 = $\frac{4}{5}$ x $\frac{6}{1}$ = $\frac{24}{5}$ = 4 $\mathbf{\frac{4}{5}}$

  • Cooking = $\frac{3}{4}$ x 8 = $\frac{3}{4}$ x $\frac{8}{1}$ = $\frac{24}{4}$ = 6

  • Cleaning = $\frac{4}{7}$ x 3 = $\frac{4}{7}$ x $\frac{3}{1}$ = $\frac{12}{7}$ = 1 $\mathbf{\frac{5}{7}}$

  • Reading = $\frac{6}{9}$ x 4 = $\frac{6}{9}$ x $\frac{4}{1}$ = $\frac{24}{9}$ = 2 $\frac{6}{9}$ = 2 $\mathbf{\frac{2}{3}}$

• Can you work out how long Axel and Tank want to cycle for now?

  Hints

  You are trying to solve $\frac{2}{3}$ x 3.

  When multiplying a fraction by a whole number, what can we do to the whole number to make it easier to solve?

  Can you simplify the fraction you are left with?

  Solution

  Here is the completed expression:

  • We can change 3 into $\frac{3}{1}$
  • $\frac{2}{3}$ x $\frac{3}{1}$ = $\frac{6}{3}$
  • $\frac{6}{3}$ can be simplified to 2.
  • The correct answer is 2 hours.

• Can you check the multiplication equations?

  Hints

  When we make the whole number into a fraction, the denominator is always...?

  Have the answers been simplified correctly?

  Solution

  These are the parts that should have been highlighted.

  The equations written correctly are:

  1. $\frac{6}{7}$ x 5 = $\frac{6}{7}$ x $\mathbf{\frac{5}{1}}$ = $\frac{30}{7}$ = 4 $\frac{2}{7}$
  2. $\frac{5}{8}$ x 9 = $\frac{5}{8}$ x $\frac{9}{1}$ = $\mathbf{\frac{45}{8}}$ = 5 $\frac{5}{8}$
  3. $\frac{4}{6}$ x 8 = $\frac{4}{6}$ x $\frac{8}{1}$ = $\frac{32}{6}$ = 5
  4. $\frac{6}{12}$ x 3 = $\frac{6}{12}$ x $\frac{3}{1}$ = $\mathbf{\frac{18}{12}}$ = 1 $\frac{1}{2}$