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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Pre Algebra >

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

Solution

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

Solution

2 \frac{3}{8}

Decimal

2.375

Solution steps

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

Follow the PEMDAS order of operations

Calculate within parentheses

(\frac{5}{2} - 1) : \frac{3}{2}

\frac{5}{2} - 1

\frac{5}{2} - 1 = \frac{3}{2}

\frac{5}{2} - 1

Convert element to fraction:

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

= - \frac{1 \cdot 2}{2} + \frac{5}{2}

Since the denominators are equal, combine the fractions:

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

= \frac{- 1 \cdot 2 + 5}{2}

- 1 \cdot 2 + 5 = 3

- 1 \cdot 2 + 5

Multiply the numbers:

1 \cdot 2 = 2

= - 2 + 5

Add/Subtract the numbers:

- 2 + 5 = 3

= 3

= \frac{3}{2}

= \frac{3}{2}

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

Multiply and divide (left to right)

\frac{3}{4} \cdot \frac{3}{2} : \frac{9}{8}

\frac{3}{4} \cdot \frac{3}{2}

Apply the fraction rule:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{3 \cdot 3}{4 \cdot 2}

Multiply the numbers:

3 \cdot 3 = 9

= \frac{9}{4 \cdot 2}

Multiply the numbers:

4 \cdot 2 = 8

= \frac{9}{8}

= \frac{1}{2} + 3 - \frac{9}{8}

Add and subtract (left to right)

\frac{1}{2} + 3 - \frac{9}{8} : \frac{19}{8}

\frac{1}{2} + 3 - \frac{9}{8}

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

\frac{1}{2} + 3

Convert element to fraction:

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

= \frac{3 \cdot 2}{2} + \frac{1}{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 + 1}{2}

3 \cdot 2 + 1 = 7

3 \cdot 2 + 1

Multiply the numbers:

3 \cdot 2 = 6

= 6 + 1

Add the numbers:

6 + 1 = 7

= 7

= \frac{7}{2}

= \frac{7}{2} - \frac{9}{8}

\frac{7}{2} - \frac{9}{8} = \frac{19}{8}

\frac{7}{2} - \frac{9}{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{7}{2} :

multiply the denominator and numerator by

4

\frac{7}{2} = \frac{7 \cdot 4}{2 \cdot 4} = \frac{28}{8}

= \frac{28}{8} - \frac{9}{8}

Since the denominators are equal, combine the fractions:

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

= \frac{28 - 9}{8}

Subtract the numbers:

28 - 9 = 19

= \frac{19}{8}

= \frac{19}{8}

= \frac{19}{8}

Convert improper fractions to mixed numbers:

\frac{19}{8} = 2 \frac{3}{8}

\frac{19}{8} = 2

Remainder

3

\frac{19}{8}

Write the problem in long division format

8 \overline{∣ 19}

Divide

19

8

to get

2

Divide

19

8

to get

2

2 8 \overline{∣ 19}

Multiply the quotient digit

(2)

by the divisor

8

2 8 \overline{∣ 19} \underline{16}

Subtract

16

from

19

2 8 \overline{∣ 19} \underline{16} 3

2 8 \overline{∣ 19} \underline{16} 3

The solution for Long Division of

\frac{19}{8}

2

with remainder of

3

2 Remainder 3

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{19}{8} = 2 \frac{3}{8}

= 2 \frac{3}{8}

= 2 \frac{3}{8}

Popular Examples

49\div 7+12\div 5-48\div 8

(36\div 3+3)\div 5+4*8-10

47^2-37^2

4-15× 4+7× 8+48× 12-3

-3^2+2^0+27-2/3

Frequently Asked Questions (FAQ)

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

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

Solution

Solution

Popular Examples

Frequently Asked Questions (FAQ)

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

Popular topics