What is 4/5\times 11/6 ?

The solution to 4/5\times 11/6 is 1 7/15

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4/5\times 11/6

Solution

4/5 \times 11/6

Solution

1 \frac{7}{15}

Solution steps

4/5 \times 11/6

Follow the PEMDAS order of operations

Multiply and divide (left to right)

4/5 = \frac{4}{5}

= \frac{4}{5} \times 11/6

\frac{4}{5} \times 11 = \frac{44}{5}

\frac{4}{5} \cdot 11

Convert element to fraction:

11 = \frac{11}{1}

= \frac{4}{5} \cdot \frac{11}{1}

Apply the fraction rule:

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

= \frac{4 \cdot 11}{5 \cdot 1}

Multiply the numbers:

4 \cdot 11 = 44

= \frac{44}{5 \cdot 1}

Multiply the numbers:

5 \cdot 1 = 5

= \frac{44}{5}

= \frac{44}{5} /6

\frac{44}{5} /6 = \frac{22}{15}

\frac{44}{5} /6

Convert element to fraction:

6 = \frac{6}{1}

= \frac{44}{5} \div \frac{6}{1}

Apply the fraction rule:

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

= \frac{44}{5} \cdot \frac{1}{6}

Cross-cancel common factor:

2

44, 6

Greatest Common Divisor (GCD)

Prime factorization of

44 : 2 \cdot 2 \cdot 11

44

44

divides by

244 = 22 \cdot 2

= 2 \cdot 22

22

divides by

222 = 11 \cdot 2

= 2 \cdot 2 \cdot 11

2, 11

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 2 \cdot 11

Prime factorization of

6 : 2 \cdot 3

6

6

divides by

26 = 3 \cdot 2

= 2 \cdot 3

2, 3

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 3

The prime factors common to

44, 6

are

= 2

= \frac{22}{5} \cdot \frac{1}{3}

Multiply fractions:

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

= \frac{22 \cdot 1}{5 \cdot 3}

Multiply the numbers:

22 \cdot 1 = 22

= \frac{22}{5 \cdot 3}

Multiply the numbers:

5 \cdot 3 = 15

= \frac{22}{15}

= \frac{22}{15}

Convert improper fractions to mixed numbers:

\frac{22}{15} = 1 \frac{7}{15}

\frac{22}{15} = 1

Remainder

7

\frac{22}{15}

Write the problem in long division format

15 \overline{∣ 22}

Divide

22

15

to get

1

Divide

22

15

to get

1

1 15 \overline{∣ 22}

Multiply the quotient digit

(1)

by the divisor

15

1 15 \overline{∣ 22} \underline{15}

Subtract

15

from

22

1 15 \overline{∣ 22} \underline{15} 7

1 15 \overline{∣ 22} \underline{15} 7

The solution for Long Division of

\frac{22}{15}

1

with remainder of

7

1 Remainder 7

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{22}{15} = 1 \frac{7}{15}

= 1 \frac{7}{15}

= 1 \frac{7}{15}

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Frequently Asked Questions (FAQ)

What is 4/5\times 11/6 ?
The solution to 4/5\times 11/6 is 1 7/15