What is 2\div 5-7\div 16 ?

The solution to 2\div 5-7\div 16 is -3/80

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Popular >

2\div 5-7\div 16

Solution

2 \div 5 - 7 \div 16

Solution

- \frac{3}{80}

Solution steps

2 \div 5 - 7 \div 16

Follow the PEMDAS order of operations

Multiply and divide (left to right)

2 \div 5 : \frac{2}{5}

2 \div 5

2 \div 5 = \frac{2}{5}

= \frac{2}{5}

= \frac{2}{5} - 7 \div 16

Multiply and divide (left to right)

7 \div 16 : \frac{7}{16}

7 \div 16

7 \div 16 = \frac{7}{16}

= \frac{7}{16}

= \frac{2}{5} - \frac{7}{16}

Add and subtract (left to right)

\frac{2}{5} - \frac{7}{16} : - \frac{3}{80}

\frac{2}{5} - \frac{7}{16}

\frac{2}{5} - \frac{7}{16} = - \frac{3}{80}

\frac{2}{5} - \frac{7}{16}

Least Common Multiplier of

5, 16 : 80

5, 16

Least Common Multiplier (LCM)

Prime factorization of

5 : 5

5

5

is a prime number, therefore no factorization is possible

= 5

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

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

5

16

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

Multiply the numbers:

5 \cdot 2 \cdot 2 \cdot 2 \cdot 2 = 80

= 80

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

80

For

\frac{2}{5} :

multiply the denominator and numerator by

16

\frac{2}{5} = \frac{2 \cdot 16}{5 \cdot 16} = \frac{32}{80}

For

\frac{7}{16} :

multiply the denominator and numerator by

5

\frac{7}{16} = \frac{7 \cdot 5}{16 \cdot 5} = \frac{35}{80}

= \frac{32}{80} - \frac{35}{80}

Since the denominators are equal, combine the fractions:

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

= \frac{32 - 35}{80}

Subtract the numbers:

32 - 35 = - 3

= \frac{- 3}{80}

Apply the fraction rule:

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

= - \frac{3}{80}

= - \frac{3}{80}

= - \frac{3}{80}

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Frequently Asked Questions (FAQ)

What is 2\div 5-7\div 16 ?
The solution to 2\div 5-7\div 16 is -3/80