What is 5/4-(1/2+3/8) ?

The solution to 5/4-(1/2+3/8) is 3/8

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5/4-(1/2+3/8)

Solution

\frac{5}{4} - (\frac{1}{2} + \frac{3}{8})

Solution

\frac{3}{8}

Solution steps

\frac{5}{4} - (\frac{1}{2} + \frac{3}{8})

Follow the PEMDAS order of operations

Calculate within parentheses

(\frac{1}{2} + \frac{3}{8}) : \frac{7}{8}

\frac{1}{2} + \frac{3}{8}

\frac{1}{2} + \frac{3}{8} = \frac{7}{8}

\frac{1}{2} + \frac{3}{8}

Least Common Multiplier of

2, 8 : 8

2, 8

Least Common Multiplier (LCM)

Prime factorization of

2 : 2

2

2

is a prime number, therefore no factorization is possible

= 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

2

8

= 2 \cdot 2 \cdot 2

Multiply the numbers:

2 \cdot 2 \cdot 2 = 8

= 8

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

8

For

\frac{1}{2} :

multiply the denominator and numerator by

4

\frac{1}{2} = \frac{1 \cdot 4}{2 \cdot 4} = \frac{4}{8}

= \frac{4}{8} + \frac{3}{8}

Since the denominators are equal, combine the fractions:

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

= \frac{4 + 3}{8}

Add the numbers:

4 + 3 = 7

= \frac{7}{8}

= \frac{7}{8}

= \frac{5}{4} - \frac{7}{8}

Add and subtract (left to right)

\frac{5}{4} - \frac{7}{8} : \frac{3}{8}

\frac{5}{4} - \frac{7}{8}

\frac{5}{4} - \frac{7}{8} = \frac{3}{8}

\frac{5}{4} - \frac{7}{8}

Least Common Multiplier of

4, 8 : 8

4, 8

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

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

4

8

= 2 \cdot 2 \cdot 2

Multiply the numbers:

2 \cdot 2 \cdot 2 = 8

= 8

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

8

For

\frac{5}{4} :

multiply the denominator and numerator by

2

\frac{5}{4} = \frac{5 \cdot 2}{4 \cdot 2} = \frac{10}{8}

= \frac{10}{8} - \frac{7}{8}

Since the denominators are equal, combine the fractions:

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

= \frac{10 - 7}{8}

Subtract the numbers:

10 - 7 = 3

= \frac{3}{8}

= \frac{3}{8}

= \frac{3}{8}

Popular Examples

(8-25)-(8+5)+(13+11)

(8 - 25) - (8 + 5) + (13 + 11)

2^2+5

2^{2} + 5

(1-1)^2

(1 - 1)^{2}

-2(3)^2

- 2 (3)^{2}

8^2+5^2

8^{2} + 5^{2}

Frequently Asked Questions (FAQ)

What is 5/4-(1/2+3/8) ?
The solution to 5/4-(1/2+3/8) is 3/8