What is (1 11/16-3 7/8)\times 4 ?

The solution to (1 11/16-3 7/8)\times 4 is -35/4

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Popular >

(1 11/16-3 7/8)\times 4

Solution

(1 \frac{11}{16} - 3 \frac{7}{8}) \cdot 4

Solution

- \frac{35}{4}

Solution steps

(1 \frac{11}{16} - 3 \frac{7}{8}) \cdot 4

Convert mixed numbers to improper fractions:

1 \frac{11}{16} = \frac{27}{16}

1 \frac{11}{16}

Convert mixed numbers to improper fraction:

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

1 \frac{11}{16} = \frac{1 \cdot 16 + 11}{16}

= \frac{27}{16}

= (\frac{27}{16} - 3 \frac{7}{8}) \cdot 4

Convert mixed numbers to improper fractions:

3 \frac{7}{8} = \frac{31}{8}

3 \frac{7}{8}

Convert mixed numbers to improper fraction:

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

3 \frac{7}{8} = \frac{3 \cdot 8 + 7}{8}

= \frac{31}{8}

= (\frac{27}{16} - \frac{31}{8}) \cdot 4

Follow the PEMDAS order of operations

Calculate within parentheses

(\frac{27}{16} - \frac{31}{8}) : - \frac{35}{16}

\frac{27}{16} - \frac{31}{8}

\frac{27}{16} - \frac{31}{8} = - \frac{35}{16}

\frac{27}{16} - \frac{31}{8}

Least Common Multiplier of

16, 8 : 16

16, 8

Least Common Multiplier (LCM)

Prime factorization of

16 : 2 \cdot 2 \cdot 2 \cdot 2

16

16

divides by

216 = 8 \cdot 2

= 2 \cdot 8

8

divides by

28 = 4 \cdot 2

= 2 \cdot 2 \cdot 4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 2 \cdot 2 \cdot 2

Prime factorization of

8 : 2 \cdot 2 \cdot 2

8

8

divides by

28 = 4 \cdot 2

= 2 \cdot 4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 2 \cdot 2

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

16

8

= 2 \cdot 2 \cdot 2 \cdot 2

Multiply the numbers:

2 \cdot 2 \cdot 2 \cdot 2 = 16

= 16

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

16

For

\frac{31}{8} :

multiply the denominator and numerator by

2

\frac{31}{8} = \frac{31 \cdot 2}{8 \cdot 2} = \frac{62}{16}

= \frac{27}{16} - \frac{62}{16}

Since the denominators are equal, combine the fractions:

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

= \frac{27 - 62}{16}

Subtract the numbers:

27 - 62 = - 35

= \frac{- 35}{16}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{35}{16}

= - \frac{35}{16}

= - \frac{35}{16} \cdot 4

Multiply and divide (left to right)

- \frac{35}{16} \cdot 4 : - \frac{35}{4}

- \frac{35}{16} \cdot 4

Convert element to fraction:

4 = \frac{4}{1}

= - \frac{35}{16} \cdot \frac{4}{1}

Apply the fraction rule:

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

\frac{35}{16} \cdot \frac{4}{1} = \frac{35 \cdot 4}{16 \cdot 1}

= - \frac{35 \cdot 4}{16 \cdot 1}

\frac{35 \cdot 4}{16 \cdot 1} = \frac{35}{4}

\frac{35 \cdot 4}{16 \cdot 1}

Multiply the numbers:

16 \cdot 1 = 16

= \frac{35 \cdot 4}{16}

Factor the number:

16 = 4 \cdot 4

= \frac{35 \cdot 4}{4 \cdot 4}

Cancel the common factor:

4

= \frac{35}{4}

= - \frac{35}{4}

= - \frac{35}{4}

Popular Examples

9\times 8\div 2

9 \times 8 \div 2

2*2+2

2 \cdot 2 + 2

2*2+8

2 \cdot 2 + 8

1+4-9-3+11

1 + 4 - 9 - 3 + 11

-8-18+(-2)^3

- 8 - 18 + (- 2)^{3}

Frequently Asked Questions (FAQ)

What is (1 11/16-3 7/8)\times 4 ?
The solution to (1 11/16-3 7/8)\times 4 is -35/4