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How do you time a fraction by a whole number?

Published in Fraction Multiplication 2 mins read

To multiply a fraction by a whole number, you essentially multiply the numerator (the top number) of the fraction by the whole number, keeping the denominator (the bottom number) the same. Then, simplify the resulting fraction if possible. Here's a breakdown:

Steps to Multiply a Fraction by a Whole Number:

  1. Convert the Whole Number to a Fraction (Optional but Helpful): Think of the whole number as a fraction with a denominator of 1. For example, 5 can be written as 5/1.

  2. Multiply the Numerators: Multiply the numerator of the fraction by the whole number (or the numerator of the whole number fraction).

  3. Keep the Denominator: The denominator of the fraction stays the same.

  4. Simplify (if possible):

    • Improper Fractions: If the numerator is larger than the denominator (an improper fraction), convert it into a mixed number. According to the reference, this involves dividing the numerator by the denominator to get a whole number and a remainder. The whole number becomes the whole number part of the mixed number, the remainder becomes the new numerator, and the denominator stays the same (YouTube Reference).

    • Reduce to Lowest Terms: Find the greatest common factor (GCF) of the numerator and denominator and divide both by it.

Example

Let's say we want to multiply 2/3 by 4.

  1. Write the whole number as a fraction: 4 = 4/1
  2. Multiply the numerators: 2 * 4 = 8
  3. Keep the denominator: The denominator is 3. So, we have 8/3.
  4. Simplify: 8/3 is an improper fraction. Divide 8 by 3. 3 goes into 8 two times (2 x 3 = 6) with a remainder of 2. Therefore, 8/3 = 2 2/3.

Table Summary

Step Description Example (2/3 * 4)
1. Whole # as Fraction Represent the whole number as a fraction with a denominator of 1. 4 = 4/1
2. Multiply Numerators Multiply the top numbers of the fractions. 2 * 4 = 8
3. Keep Denominator Keep the original denominator of the fraction. 3
4. Simplify Convert improper fractions to mixed numbers or reduce to lowest terms. 8/3 = 2 2/3 (Dividing 8 by 3 gives 2 with a remainder of 2.)

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