Multiplying Mixed Numbers: Word Problems

Multiplying Mixed Numbers – Word Problems

Understanding how to work with mixed numbers is essential in our daily lives. From cooking recipes to measuring materials for a project, we often encounter situations where mixed numbers come into play. Gaining comfort in multiplying these numbers helps in effectively solving real-world problems.

Mixed Numbers and Improper Fractions

It's really helpful to know about improper fractions and mixed numbers when you're solving math problems, so let's make sure we understand what they are!

Conversion between Mixed Numbers and Improper Fractions

Convert the mixed number $3 \frac{1}{4}$ to an improper fraction.

• Multiply the whole number part by the denominator and add the numerator.
• $3 \times 4 + 1 = 12 + 1 = 13$.
• The mixed number $3 \frac{1}{4}$ is equal to the improper fraction $\frac{13}{4}$.

Convert the improper fraction $\frac{11}{3}$ to a mixed number.

• Divide the numerator by the denominator.
• $11 \div 3 = 3$ remainder $2$.
• The improper fraction $\frac{11}{3}$ is equal to the mixed number $3 \frac{2}{3}$.

Multiplying Mixed Numbers: Word Problems – Step-by-Step Process

Multiplying a fraction by a whole number and dealing with two mixed numbers are common in real-world problems. It's important to understand how these calculations work in practical situations. Let’s practice some examples!

A recipe needs $1 \frac{2}{3}$ cups of sugar for a batch of cookies, and you want to make $2 \frac{1}{2}$ batches.

• Convert Mixed to Improper: Convert $1 \frac{2}{3}$ to $\frac{5}{3}$ and $2 \frac{1}{2}$ to $\frac{5}{2}$.
• Multiply: Multiply $\frac{5}{3}$ by $\frac{5}{2}$.
• Calculate & Convert Back: $\frac{5}{3} \times \frac{5}{2} = \frac{25}{6}$. Convert $\frac{25}{6}$ to mixed number: $4 \frac{1}{6}$. You need $4 \frac{1}{6}$ cups of sugar.

If a garden requires $2 \frac{1}{4}$ cubic meters of soil for each section, and you are landscaping $3$ sections, how much soil is needed in total?

• Convert Mixed to Improper: Convert $2 \frac{1}{4}$ to an improper fraction: $\frac{2 \times 4 + 1}{4} = \frac{9}{4}$.
• Multiply by 3: $\frac{9}{4} \times 3$.
• Calculate & Convert Back: $\frac{27}{4} = 6 \frac{3}{4}$. You need $6 \frac{3}{4}$ cubic meters of soil.

Each shelf needs $2 \frac{1}{2}$ feet of wood, and you are building $4$ shelves. How much wood in total**?

• Convert Mixed to Improper: Convert $2 \frac{1}{2}$ to $\frac{5}{2}$.
• Multiply: Multiply by 4: $\frac{5}{2} \times 4$.
• Calculate & Convert Back: $\frac{20}{2} = 10$. You need $10$ feet of wood.

Multiplying Mixed Numbers: Word Problems – Practice

Practice some on your own!

Multiplying Mixed Numbers: Word Problems – Summary

Multiplying Mixed Numbers: Word Problems – Frequently Asked Questions