The solution to 9/2*9+1/4 is 40 3/4

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Popular Pre Algebra >

9/2*9+1/4

Solution

\frac{9}{2} \cdot 9 + \frac{1}{4}

Solution

40 \frac{3}{4}

Decimal

40.75

Solution steps

\frac{9}{2} \cdot 9 + \frac{1}{4}

Follow the PEMDAS order of operations

Multiply and divide (left to right)

\frac{9}{2} \cdot 9 : \frac{81}{2}

\frac{9}{2} \cdot 9

Convert element to fraction:

9 = \frac{9}{1}

= \frac{9}{2} \cdot \frac{9}{1}

Apply the fraction rule:

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

= \frac{9 \cdot 9}{2 \cdot 1}

Multiply the numbers:

9 \cdot 9 = 81

= \frac{81}{2 \cdot 1}

Multiply the numbers:

2 \cdot 1 = 2

= \frac{81}{2}

= \frac{81}{2} + \frac{1}{4}

Add and subtract (left to right)

\frac{81}{2} + \frac{1}{4} : \frac{163}{4}

\frac{81}{2} + \frac{1}{4}

\frac{81}{2} + \frac{1}{4} = \frac{163}{4}

\frac{81}{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{81}{2} :

multiply the denominator and numerator by

2

\frac{81}{2} = \frac{81 \cdot 2}{2 \cdot 2} = \frac{162}{4}

= \frac{162}{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{162 + 1}{4}

Add the numbers:

162 + 1 = 163

= \frac{163}{4}

= \frac{163}{4}

= \frac{163}{4}

Convert improper fractions to mixed numbers:

\frac{163}{4} = 40 \frac{3}{4}

\frac{163}{4} = 40

Remainder

3

\frac{163}{4}

Write the problem in long division format

4 \overline{∣ 163}

Divide

16

4

to get

4

Divide

16

4

to get

4

4 4 \overline{∣ 163}

Multiply the quotient digit

(4)

by the divisor

4

4 4 \overline{∣ 163} \underline{16}

Subtract

16

from

16

4 4 \overline{∣ 163} \underline{16} 0

Bring down the next number of the dividend

4 4 \overline{∣ 163} \underline{16} 03

4 4 \overline{∣ 163} \underline{16} 03

Divide

3

4

to get

0

Divide

3

4

to get

0

40 4 \overline{∣ 163} \underline{16} 03

Multiply the quotient digit

(0)

by the divisor

4

40 4 \overline{∣ 163} \underline{16} 03 \underline{0}

Subtract

0

from

3

40 4 \overline{∣ 163} \underline{16} 03 \underline{0} 3

40 4 \overline{∣ 163} \underline{16} 03 \underline{0} 3

The solution for Long Division of

\frac{163}{4}

40

with remainder of

3

40 Remainder 3

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{163}{4} = 40 \frac{3}{4}

= 40 \frac{3}{4}

= 40 \frac{3}{4}

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What is 9/2*9+1/4 ?
The solution to 9/2*9+1/4 is 40 3/4

9/2*9+1/4

Solution

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What is 9/2*9+1/4 ?

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