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N.2 Multipy fractions by whole numbers

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

Multiplying a fraction by a whole number means taking that fraction part several times. You are adding the same fraction repeatedly.

Example:
  • 12 × 3 means you have three halves: 12 + 12 + 12 = 32.
Note

When you multiply a fraction by a whole number, you are scaling the fraction—making it larger by repeating it several times.

How to multiply a fraction by a whole number

To multiply a fraction by a whole number, multiply the numerator (top number) by the whole number and keep the denominator (bottom number) the same.

Steps:
  • Example: 4 × 25
  • Multiply the numerator: 4 × 2 = 8
  • Keep the denominator: 5
  • Result: 85
Note

Always multiply only the numerator by the whole number. The denominator stays the same because the size of each part does not change.

Improper fractions and mixed numbers

Sometimes your answer will be an improper fraction, which means the numerator is greater than the denominator. You can change it to a mixed number to make it easier to understand.

Example:
  • 3 × 34 = 94
  • Change 94 to a mixed number: 2 14
Note

An improper fraction can be turned into a mixed number by dividing the numerator by the denominator. The quotient is the whole number, and the remainder becomes the new numerator.

Real-world example

Multiplying fractions by whole numbers helps in real-life situations, such as recipes, measurements, or sharing equal parts.

Example:
  • If one serving of juice is 23 of a cup, how much juice do 5 servings need?
  • Multiply: 5 × 23 = 103 = 3 13 cups.
Note

Always check if your answer makes sense in the problem’s context. Estimating first can help you see if your result is reasonable.

Tips to remember

Multiplying fractions by whole numbers follows the same pattern every time: multiply the numerator by the whole number and simplify if possible.

Example:
  • 6 × 16 = 66 = 1
Note

Simplify your final answer whenever possible. A fraction like 66 can be reduced to 1.