How Do You Multiply a Fraction by a Mixed Number?

To multiply a fraction by a mixed number, first convert the mixed number into an improper fraction, and then multiply the two fractions together.

Here's a step-by-step explanation:

Steps to Multiply a Fraction by a Mixed Number

Convert the mixed number to an improper fraction: Multiply the whole number part of the mixed number by the denominator of the fractional part. Then, add the numerator of the fractional part to that result. This sum becomes the new numerator, and the denominator stays the same.
- For example, if you have the mixed number 3 1/4, multiply 3 (the whole number) by 4 (the denominator), which equals 12. Add 1 (the numerator) to 12, which equals 13. The improper fraction is 13/4.
Multiply the two fractions: Multiply the numerators together to get the new numerator, and multiply the denominators together to get the new denominator.
- For example, if you want to multiply 1/2 by 3 1/4 (which we converted to 13/4), multiply 1 (the numerator of the first fraction) by 13 (the numerator of the improper fraction), which equals 13. Then, multiply 2 (the denominator of the first fraction) by 4 (the denominator of the improper fraction), which equals 8. The result is 13/8.
Simplify the resulting fraction (if possible): Reduce the fraction to its simplest form. Also, convert the improper fraction back to a mixed number, if desired.
- In our example, 13/8 is an improper fraction. To convert it to a mixed number, divide 13 by 8. The quotient (1) becomes the whole number part of the mixed number, the remainder (5) becomes the numerator, and the denominator (8) stays the same. So, 13/8 is equal to 1 5/8.

Let's multiply 2/3 by 2 1/2:

Convert 2 1/2 to an improper fraction: (2 * 2) + 1 = 5. So, 2 1/2 becomes 5/2.
Multiply the fractions: (2/3) (5/2) = (2 5) / (3 * 2) = 10/6.
Simplify the fraction: 10/6 can be simplified to 5/3. Then, 5/3 can be written as a mixed number: 1 2/3.

Therefore, 2/3 multiplied by 2 1/2 is 1 2/3.