What is 5/4-1-7/5+13/20 ?

The solution to 5/4-1-7/5+13/20 is -1/2

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Popular >

5/4-1-7/5+13/20

Solution

\frac{5}{4} - 1 - \frac{7}{5} + \frac{13}{20}

Solution

- \frac{1}{2}

Solution steps

\frac{5}{4} - 1 - \frac{7}{5} + \frac{13}{20}

Follow the PEMDAS order of operations

Add and subtract (left to right)

\frac{5}{4} - 1 = \frac{1}{4}

\frac{5}{4} - 1

Convert element to fraction:

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

= - \frac{1 \cdot 4}{4} + \frac{5}{4}

Since the denominators are equal, combine the fractions:

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

= \frac{- 1 \cdot 4 + 5}{4}

- 1 \cdot 4 + 5 = 1

- 1 \cdot 4 + 5

Multiply the numbers:

1 \cdot 4 = 4

= - 4 + 5

Add/Subtract the numbers:

- 4 + 5 = 1

= 1

= \frac{1}{4}

= \frac{1}{4} - \frac{7}{5} + \frac{13}{20}

\frac{1}{4} - \frac{7}{5} = - \frac{23}{20}

\frac{1}{4} - \frac{7}{5}

Least Common Multiplier of

4, 5 : 20

4, 5

Least Common Multiplier (LCM)

Prime factorization of

4 : 2 \cdot 2

4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 2

Prime factorization of

5 : 5

5

5

is a prime number, therefore no factorization is possible

= 5

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

4

5

= 2 \cdot 2 \cdot 5

Multiply the numbers:

2 \cdot 2 \cdot 5 = 20

= 20

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

20

For

\frac{1}{4} :

multiply the denominator and numerator by

5

\frac{1}{4} = \frac{1 \cdot 5}{4 \cdot 5} = \frac{5}{20}

For

\frac{7}{5} :

multiply the denominator and numerator by

4

\frac{7}{5} = \frac{7 \cdot 4}{5 \cdot 4} = \frac{28}{20}

= \frac{5}{20} - \frac{28}{20}

Since the denominators are equal, combine the fractions:

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

= \frac{5 - 28}{20}

Subtract the numbers:

5 - 28 = - 23

= \frac{- 23}{20}

Apply the fraction rule:

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

= - \frac{23}{20}

= - \frac{23}{20} + \frac{13}{20}

- \frac{23}{20} + \frac{13}{20} = - \frac{1}{2}

- \frac{23}{20} + \frac{13}{20}

Apply rule

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

= \frac{- 23 + 13}{20}

Add/Subtract the numbers:

- 23 + 13 = - 10

= \frac{- 10}{20}

Apply the fraction rule:

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

= - \frac{10}{20}

Cancel the common factor:

10

= - \frac{1}{2}

= - \frac{1}{2}

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Frequently Asked Questions (FAQ)

What is 5/4-1-7/5+13/20 ?
The solution to 5/4-1-7/5+13/20 is -1/2