What is 3/2 (11/3-2/7) ?

The solution to 3/2 (11/3-2/7) is 5 1/14

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3/2 (11/3-2/7)

Solution

\frac{3}{2} (\frac{11}{3} - \frac{2}{7})

Solution

5 \frac{1}{14}

Solution steps

\frac{3}{2} (\frac{11}{3} - \frac{2}{7})

Follow the PEMDAS order of operations

Calculate within parentheses

(\frac{11}{3} - \frac{2}{7}) : \frac{71}{21}

\frac{11}{3} - \frac{2}{7}

\frac{11}{3} - \frac{2}{7} = \frac{71}{21}

\frac{11}{3} - \frac{2}{7}

Least Common Multiplier of

3, 7 : 21

3, 7

Least Common Multiplier (LCM)

Prime factorization of

3 : 3

3

3

is a prime number, therefore no factorization is possible

= 3

Prime factorization of

7 : 7

7

7

is a prime number, therefore no factorization is possible

= 7

Multiply each factor the greatest number of times it occurs in either

3

7

= 3 \cdot 7

Multiply the numbers:

3 \cdot 7 = 21

= 21

Adjust Fractions based on the LCM

Multiply each numerator by the same amount needed to multiply its

corresponding denominator to turn it into the LCM

21

For

\frac{11}{3} :

multiply the denominator and numerator by

7

\frac{11}{3} = \frac{11 \cdot 7}{3 \cdot 7} = \frac{77}{21}

For

\frac{2}{7} :

multiply the denominator and numerator by

3

\frac{2}{7} = \frac{2 \cdot 3}{7 \cdot 3} = \frac{6}{21}

= \frac{77}{21} - \frac{6}{21}

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{77 - 6}{21}

Subtract the numbers:

77 - 6 = 71

= \frac{71}{21}

= \frac{71}{21}

= \frac{3}{2} \cdot \frac{71}{21}

Multiply and divide (left to right)

\frac{3}{2} \cdot \frac{71}{21} : \frac{71}{14}

\frac{3}{2} \cdot \frac{71}{21}

Apply the fraction rule:

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

= \frac{3 \cdot 71}{2 \cdot 21}

Cancel

\frac{3 \cdot 71}{2 \cdot 21} : \frac{71}{14}

\frac{3 \cdot 71}{2 \cdot 21}

Factor the number:

21 = 3 \cdot 7

= \frac{3 \cdot 71}{2 \cdot 3 \cdot 7}

Cancel the common factor:

3

= \frac{71}{2 \cdot 7}

Multiply the numbers:

2 \cdot 7 = 14

= \frac{71}{14}

= \frac{71}{14}

= \frac{71}{14}

Convert improper fractions to mixed numbers:

\frac{71}{14} = 5 \frac{1}{14}

\frac{71}{14} = 5

Remainder

1

\frac{71}{14}

Write the problem in long division format

14 \overline{∣ 71}

Divide

71

14

to get

5

Divide

71

14

to get

5

5 14 \overline{∣ 71}

Multiply the quotient digit

(5)

by the divisor

14

5 14 \overline{∣ 71} \underline{70}

Subtract

70

from

71

5 14 \overline{∣ 71} \underline{70} 1

5 14 \overline{∣ 71} \underline{70} 1

The solution for Long Division of

\frac{71}{14}

5

with remainder of

1

5 Remainder 1

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{71}{14} = 5 \frac{1}{14}

= 5 \frac{1}{14}

= 5 \frac{1}{14}

Popular Examples

2\times [(-12+36)\div 6+(8-5)\div (-3)]-6

2 \times [(- 12 + 36) \div 6 + (8 - 5) \div (- 3)] - 6

14+18\div 2*18-7

14 + 18 \div 2 \cdot 18 - 7

2-2/3 (3)

2 - \frac{2}{3} (3)

10-1\times 5^3+9\div 18+3

10 - 1 \times 5^{3} + 9 \div 18 + 3

(-25)*8*(-1)

(- 25) \cdot 8 \cdot (- 1)

Frequently Asked Questions (FAQ)

What is 3/2 (11/3-2/7) ?
The solution to 3/2 (11/3-2/7) is 5 1/14