1/15
00:00

Learn more about this topic →

N.1 Use models to multiply fractions by whole numbers

Loading questions...

Go to the practice →

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

Multiplying a fraction by a whole number means finding a part of a set or quantity repeatedly. It shows how many times the fraction is being added together.

Example:
  • 12 × 3 means you have three halves, or 32.
  • That can also be shown as 112.
Note

Think of multiplication as repeated addition. Multiplying a fraction by a whole number is the same as adding that fraction the number of times shown by the whole number.

How to use models to multiply fractions by whole numbers

Models help visualize fraction multiplication. You can use area models, number lines, or sets of objects to represent the repeated parts.

Example:
  • To find 4 × 13, draw 4 equal rectangles divided into thirds.
  • Shade 1 part out of 3 in each rectangle.
  • Altogether, 4 parts are shaded out of 3 parts per whole, giving 43 or 113.
Note

Models make it easier to see why multiplying a fraction by a whole number can result in a number greater than 1 when the parts are added together.

Steps for multiplying a fraction by a whole number

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

Steps:
  • Step 1: Write the whole number as a fraction (for example, 5 = 51).
  • Step 2: Multiply the numerators (top numbers).
  • Step 3: Keep the denominator (bottom number) the same.
  • Step 4: Simplify if possible.
Note

Always check that your fraction is in simplest form and that your answer makes sense in the context of the problem.

Example problems

Here are some examples to help you understand how to multiply fractions by whole numbers.

Examples:
  • 3 × 25 = 65 = 115
  • 5 × 34 = 154 = 334
  • 2 × 56 = 106 = 126 = 113
Note

Remember: multiplying increases the number of parts. Simplify your answers to mixed numbers when appropriate.

Connecting to real-life examples

Fraction multiplication helps solve real-world problems involving parts of sets or repeated portions.

Example:
  • If one cookie recipe uses 23 cup of sugar and you bake 3 batches, you will need 3 × 23 = 63 = 2 cups of sugar.
Note

Using fraction multiplication helps you make accurate calculations in cooking, building, and measuring situations.

Go to the practice →