What is 21/4+31/2-11/2 ?

The solution to 21/4+31/2-11/2 is 15 1/4

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Popular Pre Algebra >

21/4+31/2-11/2

Solution

21/4 + 31/2 - 11/2

Solution

15 \frac{1}{4}

Decimal

15.25

Solution steps

21/4 + 31/2 - 11/2

Follow the PEMDAS order of operations

Multiply and divide (left to right)

21/4 : \frac{21}{4}

21/4

21/4 = \frac{21}{4}

= \frac{21}{4}

= \frac{21}{4} + 31/2 - 11/2

Multiply and divide (left to right)

31/2 : \frac{31}{2}

31/2

31/2 = \frac{31}{2}

= \frac{31}{2}

= \frac{21}{4} + \frac{31}{2} - 11/2

Multiply and divide (left to right)

11/2 : \frac{11}{2}

11/2

11/2 = \frac{11}{2}

= \frac{11}{2}

= \frac{21}{4} + \frac{31}{2} - \frac{11}{2}

Add and subtract (left to right)

\frac{21}{4} + \frac{31}{2} - \frac{11}{2} : \frac{61}{4}

\frac{21}{4} + \frac{31}{2} - \frac{11}{2}

\frac{21}{4} + \frac{31}{2} = \frac{83}{4}

\frac{21}{4} + \frac{31}{2}

Least Common Multiplier of

4, 2 : 4

4, 2

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

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

4

2

= 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{31}{2} :

multiply the denominator and numerator by

2

\frac{31}{2} = \frac{31 \cdot 2}{2 \cdot 2} = \frac{62}{4}

= \frac{21}{4} + \frac{62}{4}

Since the denominators are equal, combine the fractions:

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

= \frac{21 + 62}{4}

Add the numbers:

21 + 62 = 83

= \frac{83}{4}

= \frac{83}{4} - \frac{11}{2}

\frac{83}{4} - \frac{11}{2} = \frac{61}{4}

\frac{83}{4} - \frac{11}{2}

Least Common Multiplier of

4, 2 : 4

4, 2

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

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

4

2

= 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{11}{2} :

multiply the denominator and numerator by

2

\frac{11}{2} = \frac{11 \cdot 2}{2 \cdot 2} = \frac{22}{4}

= \frac{83}{4} - \frac{22}{4}

Since the denominators are equal, combine the fractions:

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

= \frac{83 - 22}{4}

Subtract the numbers:

83 - 22 = 61

= \frac{61}{4}

= \frac{61}{4}

= \frac{61}{4}

Convert improper fractions to mixed numbers:

\frac{61}{4} = 15 \frac{1}{4}

\frac{61}{4} = 15

Remainder

1

\frac{61}{4}

Write the problem in long division format

4 \overline{∣ 61}

Divide

6

4

to get

1

Divide

6

4

to get

1

1 4 \overline{∣ 61}

Multiply the quotient digit

(1)

by the divisor

4

1 4 \overline{∣ 61} \underline{4}

Subtract

4

from

6

1 4 \overline{∣ 61} \underline{4} 2

Bring down the next number of the dividend

1 4 \overline{∣ 61} \underline{4} 21

1 4 \overline{∣ 61} \underline{4} 21

Divide

21

4

to get

5

Divide

21

4

to get

5

15 4 \overline{∣ 61} \underline{4} 21

Multiply the quotient digit

(5)

by the divisor

4

15 4 \overline{∣ 61} \underline{4} 21 \underline{20}

Subtract

20

from

21

15 4 \overline{∣ 61} \underline{4} 21 \underline{20} 1

15 4 \overline{∣ 61} \underline{4} 21 \underline{20} 1

The solution for Long Division of

\frac{61}{4}

15

with remainder of

1

15 Remainder 1

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{61}{4} = 15 \frac{1}{4}

= 15 \frac{1}{4}

= 15 \frac{1}{4}

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What is 21/4+31/2-11/2 ?
The solution to 21/4+31/2-11/2 is 15 1/4

21/4+31/2-11/2

Solution

Solution

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Frequently Asked Questions (FAQ)

What is 21/4+31/2-11/2 ?

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