What is 21/8+3\div 2 ?

The solution to 21/8+3\div 2 is 4 1/8

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Popular Pre Algebra >

21/8+3\div 2

Solution

\frac{21}{8} + 3 \div 2

Solution

4 \frac{1}{8}

Decimal

4.125

Solution steps

\frac{21}{8} + 3 \div 2

Follow the PEMDAS order of operations

Multiply and divide (left to right)

3 \div 2 : \frac{3}{2}

3 \div 2

3 \div 2 = \frac{3}{2}

= \frac{3}{2}

= \frac{21}{8} + \frac{3}{2}

Add and subtract (left to right)

\frac{21}{8} + \frac{3}{2} : \frac{33}{8}

\frac{21}{8} + \frac{3}{2}

\frac{21}{8} + \frac{3}{2} = \frac{33}{8}

\frac{21}{8} + \frac{3}{2}

Least Common Multiplier of

8, 2 : 8

8, 2

Least Common Multiplier (LCM)

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

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

8

2

= 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{3}{2} :

multiply the denominator and numerator by

4

\frac{3}{2} = \frac{3 \cdot 4}{2 \cdot 4} = \frac{12}{8}

= \frac{21}{8} + \frac{12}{8}

Since the denominators are equal, combine the fractions:

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

= \frac{21 + 12}{8}

Add the numbers:

21 + 12 = 33

= \frac{33}{8}

= \frac{33}{8}

= \frac{33}{8}

Convert improper fractions to mixed numbers:

\frac{33}{8} = 4 \frac{1}{8}

\frac{33}{8} = 4

Remainder

1

\frac{33}{8}

Write the problem in long division format

8 \overline{∣ 33}

Divide

33

8

to get

4

Divide

33

8

to get

4

4 8 \overline{∣ 33}

Multiply the quotient digit

(4)

by the divisor

8

4 8 \overline{∣ 33} \underline{32}

Subtract

32

from

33

4 8 \overline{∣ 33} \underline{32} 1

4 8 \overline{∣ 33} \underline{32} 1

The solution for Long Division of

\frac{33}{8}

4

with remainder of

1

4 Remainder 1

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{33}{8} = 4 \frac{1}{8}

= 4 \frac{1}{8}

= 4 \frac{1}{8}

Popular Examples

(9(8-2)-3(15-7))/(6(7-1)-3(17-9))

Frequently Asked Questions (FAQ)

What is 21/8+3\div 2 ?
The solution to 21/8+3\div 2 is 4 1/8

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