What is 66 2/3 \div 150\times 100 ?

The solution to 66 2/3 \div 150\times 100 is 44 4/9

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66 2/3 \div 150\times 100

Solution

66 \frac{2}{3} \div 150 \times 100

Solution

44 \frac{4}{9}

Solution steps

66 \frac{2}{3} \div 150 \times 100

Convert mixed numbers to improper fractions:

66 \frac{2}{3} = \frac{200}{3}

66 \frac{2}{3}

Convert mixed numbers to improper fraction:

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

66 \frac{2}{3} = \frac{66 \cdot 3 + 2}{3}

= \frac{200}{3}

= \frac{200}{3} \div 150 \times 100

Follow the PEMDAS order of operations

Multiply and divide (left to right)

\frac{200}{3} \div 150 \times 100 : \frac{400}{9}

\frac{200}{3} \div 150 \times 100

\frac{200}{3} \div 150 = \frac{4}{9}

\frac{200}{3} \div 150

Convert element to fraction:

150 = \frac{150}{1}

= \frac{200}{3} \div \frac{150}{1}

Apply the fraction rule:

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

= \frac{200}{3} \cdot \frac{1}{150}

Cross-cancel common factor:

50

200, 150

Greatest Common Divisor (GCD)

Prime factorization of

200 : 2 \cdot 2 \cdot 2 \cdot 5 \cdot 5

200

200

divides by

2200 = 100 \cdot 2

= 2 \cdot 100

100

divides by

2100 = 50 \cdot 2

= 2 \cdot 2 \cdot 50

50

divides by

250 = 25 \cdot 2

= 2 \cdot 2 \cdot 2 \cdot 25

25

divides by

525 = 5 \cdot 5

= 2 \cdot 2 \cdot 2 \cdot 5 \cdot 5

2, 5

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 2 \cdot 2 \cdot 5 \cdot 5

Prime factorization of

150 : 2 \cdot 3 \cdot 5 \cdot 5

150

150

divides by

2150 = 75 \cdot 2

= 2 \cdot 75

75

divides by

375 = 25 \cdot 3

= 2 \cdot 3 \cdot 25

25

divides by

525 = 5 \cdot 5

= 2 \cdot 3 \cdot 5 \cdot 5

2, 3, 5

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 3 \cdot 5 \cdot 5

The prime factors common to

200, 150

are

= 2 \cdot 5 \cdot 5

Multiply the numbers:

2 \cdot 5 \cdot 5 = 50

= 50

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

Multiply fractions:

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

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

Multiply the numbers:

4 \cdot 1 = 4

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

Multiply the numbers:

3 \cdot 3 = 9

= \frac{4}{9}

= \frac{4}{9} \times 100

\frac{4}{9} \times 100 = \frac{400}{9}

\frac{4}{9} \cdot 100

Convert element to fraction:

100 = \frac{100}{1}

= \frac{4}{9} \cdot \frac{100}{1}

Apply the fraction rule:

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

= \frac{4 \cdot 100}{9 \cdot 1}

Multiply the numbers:

4 \cdot 100 = 400

= \frac{400}{9 \cdot 1}

Multiply the numbers:

9 \cdot 1 = 9

= \frac{400}{9}

= \frac{400}{9}

= \frac{400}{9}

Convert improper fractions to mixed numbers:

\frac{400}{9} = 44 \frac{4}{9}

\frac{400}{9} = 44

Remainder

4

\frac{400}{9}

Write the problem in long division format

9 \overline{∣ 400}

Divide

40

9

to get

4

Divide

40

9

to get

4

4 9 \overline{∣ 400}

Multiply the quotient digit

(4)

by the divisor

9

4 9 \overline{∣ 400} \underline{36}

Subtract

36

from

40

4 9 \overline{∣ 400} \underline{36} 4

Bring down the next number of the dividend

4 9 \overline{∣ 400} \underline{36} 40

4 9 \overline{∣ 400} \underline{36} 40

Divide

40

9

to get

4

Divide

40

9

to get

4

44 9 \overline{∣ 400} \underline{36} 40

Multiply the quotient digit

(4)

by the divisor

9

44 9 \overline{∣ 400} \underline{36} 40 \underline{36}

Subtract

36

from

40

44 9 \overline{∣ 400} \underline{36} 40 \underline{36} 4

44 9 \overline{∣ 400} \underline{36} 40 \underline{36} 4

The solution for Long Division of

\frac{400}{9}

44

with remainder of

4

44 Remainder 4

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{400}{9} = 44 \frac{4}{9}

= 44 \frac{4}{9}

= 44 \frac{4}{9}

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Frequently Asked Questions (FAQ)

What is 66 2/3 \div 150\times 100 ?
The solution to 66 2/3 \div 150\times 100 is 44 4/9