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

The solution to 21\div (1 3/4 \times 2 2/9) is 5 2/5

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

Solution

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

Solution

5 \frac{2}{5}

Solution steps

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

Convert mixed numbers to improper fractions:

2 \frac{2}{9} = \frac{20}{9}

2 \frac{2}{9}

Convert mixed numbers to improper fraction:

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

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

= \frac{20}{9}

= 21 \div (\frac{7}{4} \times \frac{20}{9})

Follow the PEMDAS order of operations

Calculate within parentheses

(\frac{7}{4} \times \frac{20}{9}) : \frac{35}{9}

\frac{7}{4} \times \frac{20}{9}

\frac{7}{4} \cdot \frac{20}{9} = \frac{35}{9}

\frac{7}{4} \cdot \frac{20}{9}

Cross-cancel common factor:

4

= \frac{7}{1} \cdot \frac{5}{9}

Multiply fractions:

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

= \frac{7 \cdot 5}{1 \cdot 9}

Multiply the numbers:

7 \cdot 5 = 35

= \frac{35}{1 \cdot 9}

Multiply the numbers:

1 \cdot 9 = 9

= \frac{35}{9}

= \frac{35}{9}

= 21 \div \frac{35}{9}

Multiply and divide (left to right)

21 \div \frac{35}{9} : \frac{27}{5}

21 \div \frac{35}{9}

Convert element to fraction:

21 = \frac{21}{1}

= \frac{21}{1} \div \frac{35}{9}

Apply the fraction rule:

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

= \frac{21}{1} \cdot \frac{9}{35}

Cross-cancel common factor:

7

21, 35

Greatest Common Divisor (GCD)

Prime factorization of

21 : 3 \cdot 7

21

21

divides by

321 = 7 \cdot 3

= 3 \cdot 7

3, 7

are all prime numbers, therefore no further factorization is possible

= 3 \cdot 7

Prime factorization of

35 : 5 \cdot 7

35

35

divides by

535 = 7 \cdot 5

= 5 \cdot 7

5, 7

are all prime numbers, therefore no further factorization is possible

= 5 \cdot 7

The prime factors common to

21, 35

are

= 7

= \frac{3}{1} \cdot \frac{9}{5}

Multiply fractions:

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

= \frac{3 \cdot 9}{1 \cdot 5}

Multiply the numbers:

3 \cdot 9 = 27

= \frac{27}{1 \cdot 5}

Multiply the numbers:

1 \cdot 5 = 5

= \frac{27}{5}

= \frac{27}{5}

Convert improper fractions to mixed numbers:

\frac{27}{5} = 5 \frac{2}{5}

\frac{27}{5} = 5

Remainder

2

\frac{27}{5}

Write the problem in long division format

5 \overline{∣ 27}

Divide

27

5

to get

5

Divide

27

5

to get

5

5 5 \overline{∣ 27}

Multiply the quotient digit

(5)

by the divisor

5

5 5 \overline{∣ 27} \underline{25}

Subtract

25

from

27

5 5 \overline{∣ 27} \underline{25} 2

5 5 \overline{∣ 27} \underline{25} 2

The solution for Long Division of

\frac{27}{5}

5

with remainder of

2

5 Remainder 2

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{27}{5} = 5 \frac{2}{5}

= 5 \frac{2}{5}

= 5 \frac{2}{5}

Popular Examples

10^5\div 2^4

1 0^{5} \div 2^{4}

(2*(-2)+1)/2

\frac{2 \cdot ( - 2 ) + 1}{2}

((104-38)\div 104)\times 290

((104 - 38) \div 104) \times 290

8\div 2^2

8 \div 2^{2}

-0^2+3

- 0^{2} + 3

Frequently Asked Questions (FAQ)

What is 21\div (1 3/4 \times 2 2/9) ?
The solution to 21\div (1 3/4 \times 2 2/9) is 5 2/5