The solution to 45/7-2+7/2 is 7 13/14

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Popular Pre Algebra >

45/7-2+7/2

Solution

\frac{45}{7} - 2 + \frac{7}{2}

Solution

7 \frac{13}{14}

Decimal

7.92857 \dots

Solution steps

\frac{45}{7} - 2 + \frac{7}{2}

Follow the PEMDAS order of operations

Add and subtract (left to right)

\frac{45}{7} - 2 = \frac{31}{7}

\frac{45}{7} - 2

Convert element to fraction:

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

= - \frac{2 \cdot 7}{7} + \frac{45}{7}

Since the denominators are equal, combine the fractions:

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

= \frac{- 2 \cdot 7 + 45}{7}

- 2 \cdot 7 + 45 = 31

- 2 \cdot 7 + 45

Multiply the numbers:

2 \cdot 7 = 14

= - 14 + 45

Add/Subtract the numbers:

- 14 + 45 = 31

= 31

= \frac{31}{7}

= \frac{31}{7} + \frac{7}{2}

\frac{31}{7} + \frac{7}{2} = \frac{111}{14}

\frac{31}{7} + \frac{7}{2}

Least Common Multiplier of

7, 2 : 14

7, 2

Least Common Multiplier (LCM)

Prime factorization of

7 : 7

7

7

is a prime number, therefore no factorization is possible

= 7

Prime factorization of

2 : 2

2

2

is a prime number, therefore no factorization is possible

= 2

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

7

2

= 7 \cdot 2

Multiply the numbers:

7 \cdot 2 = 14

= 14

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

14

For

\frac{31}{7} :

multiply the denominator and numerator by

2

\frac{31}{7} = \frac{31 \cdot 2}{7 \cdot 2} = \frac{62}{14}

For

\frac{7}{2} :

multiply the denominator and numerator by

7

\frac{7}{2} = \frac{7 \cdot 7}{2 \cdot 7} = \frac{49}{14}

= \frac{62}{14} + \frac{49}{14}

Since the denominators are equal, combine the fractions:

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

= \frac{62 + 49}{14}

Add the numbers:

62 + 49 = 111

= \frac{111}{14}

= \frac{111}{14}

Convert improper fractions to mixed numbers:

\frac{111}{14} = 7 \frac{13}{14}

\frac{111}{14} = 7

Remainder

13

\frac{111}{14}

Write the problem in long division format

14 \overline{∣ 111}

Divide

111

14

to get

7

Divide

111

14

to get

7

7 14 \overline{∣ 111}

Multiply the quotient digit

(7)

by the divisor

14

7 14 \overline{∣ 111} \underline{98}

Subtract

98

from

111

7 14 \overline{∣ 111} \underline{98} 13

7 14 \overline{∣ 111} \underline{98} 13

The solution for Long Division of

\frac{111}{14}

7

with remainder of

13

7 Remainder 13

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{111}{14} = 7 \frac{13}{14}

= 7 \frac{13}{14}

= 7 \frac{13}{14}

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What is 45/7-2+7/2 ?
The solution to 45/7-2+7/2 is 7 13/14

45/7-2+7/2

Solution

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What is 45/7-2+7/2 ?

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