Multiplying Mixed Numbers: Word Problems

Multiplying Mixed Numbers: Word Problems exercise

• A contractor needs $3 \frac{3}{4}$​ meters 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

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

  Then, convert $3 \frac{3}{4}$​​ to an improper fraction:

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

  Next, multiply the improper fraction by the number of sections:

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

  Finally, the correct answer is $15$ meters.

• 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.

• 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:

  $1 \times 3 + 1 = 4 \rightarrow \frac{4}{3}$

  Multiply the improper fraction by the number of batches:

  $\frac{4}{3} \times 3$

  Solution

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

  1. Convert $1 \frac{1}{3}$ to an improper fraction: $1 \times 3 + 1 = 4 \rightarrow \frac{4}{3}$

  2. Multiply the improper fraction by the number of batches: $\frac{4}{3} \times 3 = \frac{12}{3} = 4$

• In an art class, each student uses $1 \frac{3}{5}$ tubes of paint for their project.

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

• During a relay race, each runner covers $2 \frac{3}{4}$​ kilometers.

  Hints

  Convert the mixed number $2 \frac{3}{4}$​ ​into an improper fraction by multiplying the whole number by the denominator of the fraction part and then adding the numerator.

  After converting, multiply the resulting improper fraction by the number of runners to find the total distance covered by the team.

  Solution

  Convert $2 \frac{3}{4}$​ to an improper fraction and then multiply the fraction by the number of runners.

  The total distance covered by the team is $\bf{11}$ kilometers.

  1.Convert $2 \frac{3}{4}$​ to an improper fraction: $2 \times 4 + 3 = 11 \rightarrow \frac{11}{4}$​

  2. Multiply the improper fraction by the number of runners: $\frac{11}{4}​ \times 4 = \frac{44}{4} = 11$

• How many liters of water are needed to fill the pool?

  Hints

  Convert the mixed number $5 \frac{3}{8}$​ 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 buckets to find out the total amount of water needed to fill the pool, and then convert the answer to a mixed number if necessary.

  Solution

  The total amount of water needed to fill the pool is $32 \frac{1}{4}$ liters.

  1. Convert $5 \frac{3}{8}$​ to an improper fraction: $5 \times 8 + 3 = 43 \rightarrow \frac{43}{8}$

  2. Multiply the improper fraction by the number of buckets: $\frac{43}{8} \times 6 = \frac{258}{8} = 32 \frac{2}{8} = 32 \frac{1}{4}$