Simplify (2 1/4)(10 2/3)

$(2 \frac{1}{4}) (10 \frac{2}{3})$

Step 1

Convert

$2 \frac{1}{4}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

$(2 + \frac{1}{4}) (10 \frac{2}{3})$

Add

$2$ and

$\frac{1}{4}$ .

To write

$2$ as a fraction with a common denominator, multiply by

$\frac{4}{4}$ .

$(2 \cdot \frac{4}{4} + \frac{1}{4}) (10 \frac{2}{3})$

Combine

$2$ and

$\frac{4}{4}$ .

$(\frac{2 \cdot 4}{4} + \frac{1}{4}) (10 \frac{2}{3})$

Combine the numerators over the common denominator.

$\frac{2 \cdot 4 + 1}{4} (10 \frac{2}{3})$

Simplify the numerator.

Multiply

$2$ by

$4$ .

$\frac{8 + 1}{4} (10 \frac{2}{3})$

Add

$8$ and

$1$ .

$\frac{9}{4} (10 \frac{2}{3})$

Step 2

Convert

$10 \frac{2}{3}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

$\frac{9}{4} (10 + \frac{2}{3})$

Add

$10$ and

$\frac{2}{3}$ .

To write

$10$ as a fraction with a common denominator, multiply by

$\frac{3}{3}$ .

$\frac{9}{4} (10 \cdot \frac{3}{3} + \frac{2}{3})$

Combine

$10$ and

$\frac{3}{3}$ .

$\frac{9}{4} (\frac{10 \cdot 3}{3} + \frac{2}{3})$

Combine the numerators over the common denominator.

$\frac{9}{4} \cdot \frac{10 \cdot 3 + 2}{3}$

Simplify the numerator.

Multiply

$10$ by

$3$ .

$\frac{9}{4} \cdot \frac{30 + 2}{3}$

Add

$30$ and

$2$ .

$\frac{9}{4} \cdot \frac{32}{3}$

Step 3

Cancel the common factor of

$3$ .

Factor

$3$ out of

$9$ .

$\frac{3 (3)}{4} \cdot \frac{32}{3}$

Cancel the common factor.

$\frac{3 \cdot 3}{4} \cdot \frac{32}{3}$

Rewrite the expression.

$\frac{3}{4} \cdot 32$

Step 4

Cancel the common factor of

$4$ .

Factor

$4$ out of

$32$ .

$\frac{3}{4} \cdot (4 (8))$

Cancel the common factor.

$\frac{3}{4} \cdot (4 \cdot 8)$

Rewrite the expression.

$3 \cdot 8$

Step 5

Multiply

$3$ by

$8$ .

$24$

Simplify (2 1/4)(10 2/3)

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