What is -4+16/3-(-11/12) ?

The solution to -4+16/3-(-11/12) is 2 1/4

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Popular >

-4+16/3-(-11/12)

Solution

- 4 + \frac{16}{3} - (- \frac{11}{12})

Solution

2 \frac{1}{4}

Solution steps

- 4 + \frac{16}{3} - (- \frac{11}{12})

Follow the PEMDAS order of operations

Add and subtract (left to right)

- 4 + \frac{16}{3} = \frac{4}{3}

= \frac{4}{3} - (- \frac{11}{12})

Apply rule

- (- a) = + a

- (- \frac{11}{12}) = + \frac{11}{12}

= \frac{4}{3} + \frac{11}{12}

\frac{4}{3} + \frac{11}{12} = \frac{9}{4}

\frac{4}{3} + \frac{11}{12}

Least Common Multiplier of

3, 12 : 12

3, 12

Least Common Multiplier (LCM)

Prime factorization of

3 : 3

3

3

is a prime number, therefore no factorization is possible

= 3

Prime factorization of

12 : 2 \cdot 2 \cdot 3

12

12

divides by

212 = 6 \cdot 2

= 2 \cdot 6

6

divides by

26 = 3 \cdot 2

= 2 \cdot 2 \cdot 3

2, 3

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 2 \cdot 3

Multiply each factor the greatest number of times it occurs in either

3

12

= 3 \cdot 2 \cdot 2

Multiply the numbers:

3 \cdot 2 \cdot 2 = 12

= 12

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

12

For

\frac{4}{3} :

multiply the denominator and numerator by

4

\frac{4}{3} = \frac{4 \cdot 4}{3 \cdot 4} = \frac{16}{12}

= \frac{16}{12} + \frac{11}{12}

Since the denominators are equal, combine the fractions:

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

= \frac{16 + 11}{12}

Add the numbers:

16 + 11 = 27

= \frac{27}{12}

Cancel the common factor:

3

= \frac{9}{4}

= \frac{9}{4}

Convert improper fractions to mixed numbers:

\frac{9}{4} = 2 \frac{1}{4}

\frac{9}{4} = 2

Remainder

1

\frac{9}{4}

Write the problem in long division format

4 \overline{∣ 9}

Divide

9

4

to get

2

Divide

9

4

to get

2

2 4 \overline{∣ 9}

Multiply the quotient digit

(2)

by the divisor

4

2 4 \overline{∣ 9} \underline{8}

Subtract

8

from

9

2 4 \overline{∣ 9} \underline{8} 1

2 4 \overline{∣ 9} \underline{8} 1

The solution for Long Division of

\frac{9}{4}

2

with remainder of

1

2 Remainder 1

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{9}{4} = 2 \frac{1}{4}

= 2 \frac{1}{4}

= 2 \frac{1}{4}

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65^2+2\times 65\times 35+35^2

6 5^{2} + 2 \times 65 \times 35 + 3 5^{2}

-1^2+(2\times (-1))-1

- 1^{2} + (2 \times (- 1)) - 1

5+2(-1)

5 + 2 (- 1)

-4(0)^2+6

- 4 (0)^{2} + 6

5*30^2

5 \cdot 3 0^{2}

Frequently Asked Questions (FAQ)

What is -4+16/3-(-11/12) ?
The solution to -4+16/3-(-11/12) is 2 1/4