Multiplying A Mixed Number By A Whole Number

Review how to multiply mixed numbers. This example shows 2 different methods.

Here are the steps to multiply a mixed number by a whole number.

1. Convert the mixed number to an improper fraction.
2. Multiply the improper fraction by the other number.
3. If needed, simplify the resulting fraction.
4. Convert the resulting improper fraction back to a mixed number, if necessary.

Let's demonstrate these steps with an example:

Example:
Multiply \( \frac{2}{3} \) by \( 1 \frac{1}{4} \).

1. Convert the mixed number to an improper fraction:
   \( 1 \frac{1}{4} = \frac{(1 \times 4) + 1}{4} = \frac{5}{4} \)

2. Multiply the improper fraction by \( \frac{2}{3} \):
   \( \frac{2}{3} \times \frac{5}{4} = \frac{(2 \times 5)}{(3 \times 4)} = \frac{10}{12} \)

3. Simplify the resulting fraction:
   \( \frac{10}{12} \) simplifies to \( \frac{5}{6} \) by dividing both numerator and denominator by their greatest common divisor, which is 2.

4. Convert the resulting improper fraction back to a mixed number:
   \( \frac{5}{6} \) is equivalent to \( 0 \frac{5}{6} \).

So, \( \frac{2}{3} \) multiplied by \( 1 \frac{1}{4} \) equals \( 0 \frac{5}{6} \).

Related Articles