Question

Multiply or divide as indicated. Write answers in lowest terms as needed. 314⋅1233\frac{1}{4} \cdot 1\frac{2}{3}

Accepted Answer

First, convert the mixed numbers to improper fractions. For 3\left(\frac{1}{4}ight), multiply the whole number 3 by the denominator 4 and add the numerator 1:

$$3 	imes 4 + 1 = 12 + 1 = 13$$, so the improper fraction is $$\frac{13}{4}. $$Next, convert the second mixed number 1\left(\frac{2}{3}ight) to an improper fraction by multiplying the whole number 1 by the denominator 3 and adding the numerator 2:

$$1 	imes 3 + 2 = 3 + 2 = 5$$, so the improper fraction is $$\frac{5}{3}. $$Now multiply the two improper fractions:

$$\frac{13}{4} 	imes \frac{5}{3} = \frac{13 	imes 5}{4 	imes 3} = \frac{65}{12}. $$After multiplying, check if the fraction $$\frac{65}{12}$$ can be simplified by finding the greatest common divisor (GCD) of 65 and 12. If the GCD is 1, the fraction is already in lowest terms. Finally, if needed, convert the improper fraction back to a mixed number by dividing the numerator by the denominator:

$$65 \div 12$$ gives the whole number part and the remainder forms the numerator of the fractional part.

Multiply or divide as indicated. Write answers in lowest terms as needed. $3 and one fourth times 1 and two thirds$

Verified video answer for a similar problem:

Key Concepts

Multiplication of Mixed Numbers

Simplifying Fractions

Converting Improper Fractions to Mixed Numbers

Multiply or divide as indicated. Write answers in lowest terms as needed. 314⋅1233\(\frac{1}{4}\) \(\cdot\) 1\(\frac{2}{3}\)