What is 3 2/5 multiplied by 1 1/2?
Understand the Problem
The question asks us to calculate the product between two mixed numbers: 3 2/5 and 1 1/2. First the mixed numbers need to be converted to improper fractions and then they will be multiplied together.
Answer
$5\frac{1}{10}$
Answer for screen readers
$5\frac{1}{10}$
Steps to Solve
- Convert $3\frac{2}{5}$ to an improper fraction
Multiply the whole number part (3) by the denominator (5) and add the numerator (2). Place the result over the original denominator (5).
$3\frac{2}{5} = \frac{(3 \times 5) + 2}{5} = \frac{15 + 2}{5} = \frac{17}{5}$
- Convert $1\frac{1}{2}$ to an improper fraction
Multiply the whole number part (1) by the denominator (2) and add the numerator (1). Place the result over the original denominator (2).
$1\frac{1}{2} = \frac{(1 \times 2) + 1}{2} = \frac{2 + 1}{2} = \frac{3}{2}$
- Multiply the two improper fractions
Multiply the numerators together and the denominators together.
$\frac{17}{5} \times \frac{3}{2} = \frac{17 \times 3}{5 \times 2} = \frac{51}{10}$
- Convert the improper fraction $\frac{51}{10}$ to a mixed number
Divide the numerator (51) by the denominator (10). The quotient is the whole number part of the mixed number, and the remainder is the numerator of the fractional part. The denominator stays the same.
$51 \div 10 = 5$ with a remainder of $1$. So, $\frac{51}{10}= 5\frac{1}{10}$
$5\frac{1}{10}$
More Information
The result of the multiplication is $5\frac{1}{10}$, which is equivalent to $5.1$ in decimal form.
Tips
A common mistake is adding the whole number and numerator when converting mixed numbers to improper fractions, instead of multiplying the whole number and denominator and then adding the numerator. Another common mistake is forgetting to keep the original denominator.
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