What is 21\div (1 3/4 \times 2/9) ?

The solution to 21\div (1 3/4 \times 2/9) is 54

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Popular >

21\div (1 3/4 \times 2/9)

Solution

21 \div (1 \frac{3}{4} \times \frac{2}{9})

Solution

54

Solution steps

21 \div (1 \frac{3}{4} \times \frac{2}{9})

Convert mixed numbers to improper fractions:

1 \frac{3}{4} = \frac{7}{4}

1 \frac{3}{4}

Convert mixed numbers to improper fraction:

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

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

= \frac{7}{4}

= 21 \div (\frac{7}{4} \times \frac{2}{9})

Follow the PEMDAS order of operations

Calculate within parentheses

(\frac{7}{4} \times \frac{2}{9}) : \frac{7}{18}

\frac{7}{4} \times \frac{2}{9}

\frac{7}{4} \cdot \frac{2}{9} = \frac{7}{18}

\frac{7}{4} \cdot \frac{2}{9}

Cross-cancel common factor:

2

2, 4

Greatest Common Divisor (GCD)

Prime factorization of

2 : 2

2

2

is a prime number, therefore no factorization is possible

= 2

Prime factorization of

4 : 2 \cdot 2

4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 2

The prime factors common to

2, 4

are

= 2

= \frac{7}{2} \cdot \frac{1}{9}

Multiply fractions:

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

= \frac{7 \cdot 1}{2 \cdot 9}

Multiply the numbers:

7 \cdot 1 = 7

= \frac{7}{2 \cdot 9}

Multiply the numbers:

2 \cdot 9 = 18

= \frac{7}{18}

= \frac{7}{18}

= 21 \div \frac{7}{18}

Multiply and divide (left to right)

21 \div \frac{7}{18} : 54

21 \div \frac{7}{18}

Convert element to fraction:

21 = \frac{21}{1}

= \frac{21}{1} \div \frac{7}{18}

Apply the fraction rule:

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

= \frac{21}{1} \cdot \frac{18}{7}

Cross-cancel common factor:

7

= \frac{3}{1} \cdot \frac{18}{1}

Multiply fractions:

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

= \frac{3 \cdot 18}{1 \cdot 1}

Multiply the numbers:

3 \cdot 18 = 54

= \frac{54}{1 \cdot 1}

Multiply the numbers:

1 \cdot 1 = 1

= \frac{54}{1}

Apply rule

\frac{a}{1} = a

= 54

= 54

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Frequently Asked Questions (FAQ)

What is 21\div (1 3/4 \times 2/9) ?
The solution to 21\div (1 3/4 \times 2/9) is 54