What is 1 1/2 multiplied by 2 1/4?
Understand the Problem
The question requires us to perform multiplication with two mixed number fractions. First we will convert the mixed numbers to improper fractions, then multiply the numerators and denominators.
Answer
$3 \frac{3}{8}$
Answer for screen readers
$3 \frac{3}{8}$
Steps to Solve
- Convert $1 \frac{1}{2}$ to an improper fraction
Multiply the whole number (1) by the denominator (2) and add the numerator (1) to get the new numerator. Keep the same denominator. $1 \frac{1}{2} = \frac{(1 \times 2) + 1}{2} = \frac{2 + 1}{2} = \frac{3}{2}$
- Convert $2 \frac{1}{4}$ to an improper fraction
Multiply the whole number (2) by the denominator (4) and add the numerator (1) to get the new numerator. Keep the same denominator. $2 \frac{1}{4} = \frac{(2 \times 4) + 1}{4} = \frac{8 + 1}{4} = \frac{9}{4}$
- Multiply the two improper fractions
Multiply the numerators together and the denominators together. $\frac{3}{2} \times \frac{9}{4} = \frac{3 \times 9}{2 \times 4} = \frac{27}{8}$
- Convert the resulting improper fraction to a mixed number
Divide the numerator (27) by the denominator (8). The quotient is the whole number part of the mixed number. The remainder is the numerator of the fractional part, and the denominator stays the same. $27 \div 8 = 3$ with a remainder of $3$. Therefore, $\frac{27}{8} = 3 \frac{3}{8}$
$3 \frac{3}{8}$
More Information
The result of multiplying $1 \frac{1}{2}$ and $2 \frac{1}{4}$ is $3 \frac{3}{8}$. This is equivalent to 3.375 in decimal form.
Tips
A common mistake is to add the fractions instead of multiplying them. Another common mistake is forgetting to convert the mixed numbers to improper fractions before multiplying.
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