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P.1 Use models to multiply mixed numbers by whole numbers

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What are mixed numbers?

Mixed numbers are numbers that include both a whole number and a fraction. They show quantities greater than one whole.

Examples:
  • 112 means 1 whole and 12 of another whole.
  • 234 means 2 wholes and 34 of another whole.
Note

A mixed number can also be written as an improper fraction (for example, 112 = 32).

What does it mean to multiply a mixed number by a whole number?

Multiplying a mixed number by a whole number means taking that amount several times. It shows repeated addition of the same mixed number.

Example:
  • 3 × 112 means 112 + 112 + 112.
  • Altogether, that equals 412.
Note

Multiplying a mixed number by a whole number is like adding that mixed number repeatedly. You can use models to make this clear.

Using models to multiply mixed numbers by whole numbers

Models, such as area models or visual fraction bars, help you see how the whole and fractional parts are multiplied separately and then combined.

Example:
  • To find 2 × 113, draw two models showing one whole and one-third in each.
  • Together, you have 2 wholes and 2 thirds, or 223.
Note

Models help students understand that both the whole number and the fraction parts are multiplied, then added together to form the total product.

Steps to multiply a mixed number by a whole number

Follow these steps to multiply a mixed number by a whole number correctly.

Steps:
  • Step 1: Convert the mixed number to an improper fraction.
  • Step 2: Multiply the numerator by the whole number.
  • Step 3: Keep the denominator the same.
  • Step 4: Simplify the fraction or convert back to a mixed number if needed.
Note

Always check that your final answer is simplified and written in the correct form. Use estimation to be sure your result makes sense.

Example problems

Here are some examples that show how to multiply mixed numbers by whole numbers.

Examples:
  • 2 × 112 = 2 × 32 = 62 = 3
  • 3 × 214 = 3 × 94 = 274 = 634
  • 4 × 125 = 4 × 75 = 285 = 535
Note

Mixed numbers are easier to work with when converted to improper fractions. Always simplify your final answer for clarity.

Real-world connections

Multiplying mixed numbers by whole numbers is useful for solving real-world problems that involve repeated mixed quantities.

Example:
  • If one board is 212 feet long and you need 3 boards, you can find the total length: 3 × 212 = 712 feet.
Note

This skill helps when working with measurements, recipes, or any situation involving repeated mixed quantities.

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