What is (3-7/2)-(5/4-1) ?

The solution to (3-7/2)-(5/4-1) is -3/4

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Popular >

(3-7/2)-(5/4-1)

Solution

(3 - \frac{7}{2}) - (\frac{5}{4} - 1)

Solution

- \frac{3}{4}

Solution steps

(3 - \frac{7}{2}) - (\frac{5}{4} - 1)

Follow the PEMDAS order of operations

Calculate within parentheses

(3 - \frac{7}{2}) : - \frac{1}{2}

3 - \frac{7}{2}

3 - \frac{7}{2} = - \frac{1}{2}

3 - \frac{7}{2}

Convert element to fraction:

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

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

Since the denominators are equal, combine the fractions:

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

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

3 \cdot 2 - 7 = - 1

3 \cdot 2 - 7

Multiply the numbers:

3 \cdot 2 = 6

= 6 - 7

Subtract the numbers:

6 - 7 = - 1

= - 1

= \frac{- 1}{2}

Apply the fraction rule:

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

= - \frac{1}{2}

= - \frac{1}{2}

= - \frac{1}{2} - (\frac{5}{4} - 1)

Calculate within parentheses

(\frac{5}{4} - 1) : \frac{1}{4}

\frac{5}{4} - 1

\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{1}{2} - \frac{1}{4}

Add and subtract (left to right)

- \frac{1}{2} - \frac{1}{4} : - \frac{3}{4}

- \frac{1}{2} - \frac{1}{4}

- \frac{1}{2} - \frac{1}{4} = - \frac{3}{4}

- \frac{1}{2} - \frac{1}{4}

Least Common Multiplier of

2, 4 : 4

2, 4

Least Common Multiplier (LCM)

Prime factorization of

2 : 2

2

2

is a prime number, therefore no factorization is possible

= 2

Prime factorization of

4 : 2 \cdot 2

4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 2

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

2

4

= 2 \cdot 2

Multiply the numbers:

2 \cdot 2 = 4

= 4

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

4

For

\frac{1}{2} :

multiply the denominator and numerator by

2

\frac{1}{2} = \frac{1 \cdot 2}{2 \cdot 2} = \frac{2}{4}

= - \frac{2}{4} - \frac{1}{4}

Since the denominators are equal, combine the fractions:

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

= \frac{- 2 - 1}{4}

Subtract the numbers:

- 2 - 1 = - 3

= \frac{- 3}{4}

Apply the fraction rule:

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

= - \frac{3}{4}

= - \frac{3}{4}

= - \frac{3}{4}

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Frequently Asked Questions (FAQ)

What is (3-7/2)-(5/4-1) ?
The solution to (3-7/2)-(5/4-1) is -3/4