Multiplying Mixed Numbers: Word Problems

Multiplying Mixed Numbers: Word Problems exercise

• Barry needs $3 \frac{3}{4}$​ metres of wood to build one section of a fence.

  Hints

  Convert the mixed number $3 \frac{3}{4}$​​​ into an improper fraction by multiplying the whole number by the denominator of the fraction part and then adding the numerator.

  Multiply the resulting improper fraction by the number of sections to find the total amount of wood needed.

  Solution

  1.) First, we convert $3 \frac{3}{4}$​​ to an improper fraction.

  2.) Convert $3 \frac{3}{4}$​​ to an improper fraction:

  $3 \times 4 + 3 = 15 \rightarrow \frac{15}{4}$​

  3.) Multiply the improper fraction by the number of sections:

  $\frac{15}{4}​ \times 4 = \frac{60}{4}​ = 15$

  4.) We now have the correct answer of $15$ metres.

• Julia is hosting a pizza party and each guest eats $2 \frac{1}{2}$ slices of pizza.

  Hints

  Convert $2 \frac{1}{2}$​ to an improper fraction:

  $2 \times 2 + 1 = 5 \rightarrow \frac{5}{2}$​

  Multiply the improper fraction by the number of guests:

  $\frac{5}{2}​ \times 5 = \frac{25}{2}$​

  Convert $\frac{25}{2}$​​ back to a mixed number.

  Solution

  They eat $12 \frac{1}{2}$ slices of pizza.

• How much paint is used?

  Hints

  Convert the mixed number $1 \frac{3}{5}$​ into an improper fraction by multiplying the whole number part by the denominator of the fractional part and then adding the numerator.

  Multiply the resulting improper fraction by the number of students to find out the total number of tubes needed for the class, and then convert the answer to a mixed number if necessary.

  Solution

  $12\mathbf{\frac{4}{5}}$ tubes of paint are used by all the students.

  1. Convert $1 \frac{3}{5}$ to an improper fraction: $1 \times 5 + 3 = 8 \rightarrow \frac{8}{5}$

  2. $\frac{8}{5} \times 8 = \frac{64}{5} = 12 \frac{4}{5}$

• How many seed packets are used?

  Hints

  Convert both mixed numbers into improper fractions.

  Multiply the numerators and multiply the denominators.

  Convert this answer back to a mixed number.

  Solution

  Sandy will use $7\frac{1}{2}$ packets of seeds.

  Convert $3\frac{1}{3}$ to an improper fraction - $\frac{10}{3}$

  Convert $2\frac{1}{4}$ to an improper fraction - $\frac{9}{4}$

  Multiply $\frac{10}{3} \times \frac{9}{4} = \frac{90}{12}$

  Convert $\frac{90}{12}$ to a mixed number - $7\frac{6}{12}$ which is simplified to $7\frac{1}{2}$.

• A recipe calls for $1 \frac{1}{3}$ cups of sugar to make a batch of cookies.

  Hints

  Convert $1 \frac{1}{3}$ to an improper fraction by multiplying $1 \times 3$ and adding $1$.

  When multiplying the improper fraction by a whole number, multiply the numerator only.

  Solution

  The total amount of sugar needed to make 3 batches of cookies is 4 cups.

  1.) $1 \frac{1}{3}$ = $\frac{4}{3}$

  2.) $\frac{4}{3} \times 3 =$ $\frac{12}{3}$

  3.) $\frac{12}{3}$ = $4$

  4.) The total amount of sugar needed to make $3$ batches of cookies is $4$ cups.

• Solve the multiplication problems.

  Hints

  Convert the mixed numbers to improper fractions before multiplying.

  When multiplying a fraction by a single number, just multiply the numerator.

  When multiplying two fractions, multiply the numerators and multiply the denominators.

  Solution

  $3\frac{1}{10} \times 3 = 9\frac{3}{10}$

  $4\frac{1}{2} \times 2\frac{1}{6} = 9\frac{3}{4}$

  $5\frac{2}{3} \times 2 = 11\frac{1}{3}$

  $1\frac{3}{4} \times 3\frac{1}{4} = 5\frac{11}{16}$