What is 6 3/4+(4 2/4+5 1/4) ?

The solution to 6 3/4+(4 2/4+5 1/4) is 16 1/2

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Popular >

6 3/4+(4 2/4+5 1/4)

Solution

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

Solution

16 \frac{1}{2}

Solution steps

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

Convert mixed numbers to improper fractions:

6 \frac{3}{4} = \frac{27}{4}

6 \frac{3}{4}

Convert mixed numbers to improper fraction:

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

6 \frac{3}{4} = \frac{6 \cdot 4 + 3}{4}

= \frac{27}{4}

= \frac{27}{4} + (4 \frac{2}{4} + 5 \frac{1}{4})

Convert mixed numbers to improper fractions:

4 \frac{2}{4} = \frac{18}{4}

4 \frac{2}{4}

Convert mixed numbers to improper fraction:

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

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

= \frac{18}{4}

= \frac{27}{4} + (\frac{18}{4} + 5 \frac{1}{4})

Convert mixed numbers to improper fractions:

5 \frac{1}{4} = \frac{21}{4}

5 \frac{1}{4}

Convert mixed numbers to improper fraction:

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

5 \frac{1}{4} = \frac{5 \cdot 4 + 1}{4}

= \frac{21}{4}

= \frac{27}{4} + (\frac{18}{4} + \frac{21}{4})

\frac{18}{4} = \frac{9}{2}

Cancel the common factor:

2

\frac{9}{2}

= \frac{27}{4} + \frac{9}{2} + \frac{21}{4}

Follow the PEMDAS order of operations

Add and subtract (left to right)

\frac{27}{4} + \frac{9}{2} + \frac{21}{4} : \frac{33}{2}

\frac{27}{4} + \frac{9}{2} + \frac{21}{4}

\frac{27}{4} + \frac{9}{2} = \frac{45}{4}

\frac{27}{4} + \frac{9}{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{9}{2} :

multiply the denominator and numerator by

2

\frac{9}{2} = \frac{9 \cdot 2}{2 \cdot 2} = \frac{18}{4}

= \frac{27}{4} + \frac{18}{4}

Since the denominators are equal, combine the fractions:

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

= \frac{27 + 18}{4}

Add the numbers:

27 + 18 = 45

= \frac{45}{4}

= \frac{45}{4} + \frac{21}{4}

\frac{45}{4} + \frac{21}{4} = \frac{33}{2}

\frac{45}{4} + \frac{21}{4}

Apply rule

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

= \frac{45 + 21}{4}

Add the numbers:

45 + 21 = 66

= \frac{66}{4}

Cancel the common factor:

2

= \frac{33}{2}

= \frac{33}{2}

= \frac{33}{2}

Convert improper fractions to mixed numbers:

\frac{33}{2} = 16 \frac{1}{2}

\frac{33}{2} = 16

Remainder

1

\frac{33}{2}

Write the problem in long division format

2 \overline{∣ 33}

Divide

3

2

to get

1

Divide

3

2

to get

1

1 2 \overline{∣ 33}

Multiply the quotient digit

(1)

by the divisor

2

1 2 \overline{∣ 33} \underline{2}

Subtract

2

from

3

1 2 \overline{∣ 33} \underline{2} 1

Bring down the next number of the dividend

1 2 \overline{∣ 33} \underline{2} 13

1 2 \overline{∣ 33} \underline{2} 13

Divide

13

2

to get

6

Divide

13

2

to get

6

16 2 \overline{∣ 33} \underline{2} 13

Multiply the quotient digit

(6)

by the divisor

2

16 2 \overline{∣ 33} \underline{2} 13 \underline{12}

Subtract

12

from

13

16 2 \overline{∣ 33} \underline{2} 13 \underline{12} 1

16 2 \overline{∣ 33} \underline{2} 13 \underline{12} 1

The solution for Long Division of

\frac{33}{2}

16

with remainder of

1

16 Remainder 1

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{33}{2} = 16 \frac{1}{2}

= 16 \frac{1}{2}

= 16 \frac{1}{2}

Popular Examples

2/27 (3^7-8*7+2)

\frac{2}{27} (3^{7} - 8 \cdot 7 + 2)

16+(-18)-24+45

16 + (- 18) - 24 + 45

2^4*5

2^{4} \cdot 5

2^2-2(2)-8

2^{2} - 2 (2) - 8

-2^2+8+5

- 2^{2} + 8 + 5

Frequently Asked Questions (FAQ)

What is 6 3/4+(4 2/4+5 1/4) ?
The solution to 6 3/4+(4 2/4+5 1/4) is 16 1/2