What is 5 1/3*(3\div 1 1/3) ?

The solution to 5 1/3*(3\div 1 1/3) is 12

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5 1/3*(3\div 1 1/3)

5 \frac{1}{3} \cdot (3 \div 1 \frac{1}{3})

12

Solution steps

5 \frac{1}{3} \cdot (3 \div 1 \frac{1}{3})

Convert mixed numbers to improper fractions:

5 \frac{1}{3} = \frac{16}{3}

5 \frac{1}{3}

Convert mixed numbers to improper fraction:

a \frac{b}{c} = \frac{a \cdot c + b}{c}

5 \frac{1}{3} = \frac{5 \cdot 3 + 1}{3}

= \frac{16}{3}

= \frac{16}{3} \cdot (3 \div 1 \frac{1}{3})

Convert mixed numbers to improper fractions:

1 \frac{1}{3} = \frac{4}{3}

1 \frac{1}{3}

Convert mixed numbers to improper fraction:

a \frac{b}{c} = \frac{a \cdot c + b}{c}

1 \frac{1}{3} = \frac{1 \cdot 3 + 1}{3}

= \frac{4}{3}

= \frac{16}{3} \cdot (3 \div \frac{4}{3})

Follow the PEMDAS order of operations

Calculate within parentheses

(3 \div \frac{4}{3}) : \frac{9}{4}

3 \div \frac{4}{3}

Multiply and divide (left to right)

Convert element to fraction:

3 = \frac{3}{1}

= \frac{3}{1} \div \frac{4}{3}

Apply the fraction rule:

\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}

= \frac{3}{1} \cdot \frac{3}{4}

Multiply fractions:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{3 \cdot 3}{1 \cdot 4}

Multiply the numbers:

3 \cdot 3 = 9

= \frac{9}{1 \cdot 4}

Multiply the numbers:

1 \cdot 4 = 4

= \frac{9}{4}

= \frac{16}{3} \cdot \frac{9}{4}

Multiply and divide (left to right)

\frac{16}{3} \cdot \frac{9}{4} : 12

\frac{16}{3} \cdot \frac{9}{4}

Apply the fraction rule:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{16 \cdot 9}{3 \cdot 4}

Cancel

\frac{16 \cdot 9}{3 \cdot 4} : 12

\frac{16 \cdot 9}{3 \cdot 4}

Factor the number:

16 = 4 \cdot 4

= \frac{4 \cdot 4 \cdot 9}{3 \cdot 4}

Cancel the common factor:

4

= \frac{4 \cdot 9}{3}

Divide the numbers:

\frac{9}{3} = 3

= 4 \cdot 3

Multiply the numbers:

4 \cdot 3 = 12

= 12

= 12

= 12

(- 1)^{4} + 2 (- 1) + 1

4 (- 2 + 3)

- 7 + 11 + 2 \cdot (2 - 1 + 3) - 4

(11 - 1) (3 - 1)

3^{4} \times 12