What is 80/9+20/3+1/2 ?

The solution to 80/9+20/3+1/2 is 16 1/18

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Popular Pre Algebra >

80/9+20/3+1/2

Solution

80/9 + 20/3 + 1/2

Solution

16 \frac{1}{18}

Decimal

16.05555 \dots

Solution steps

80/9 + 20/3 + 1/2

Follow the PEMDAS order of operations

Multiply and divide (left to right)

80/9 : \frac{80}{9}

80/9

80/9 = \frac{80}{9}

= \frac{80}{9}

= \frac{80}{9} + 20/3 + 1/2

Multiply and divide (left to right)

20/3 : \frac{20}{3}

20/3

20/3 = \frac{20}{3}

= \frac{20}{3}

= \frac{80}{9} + \frac{20}{3} + 1/2

Multiply and divide (left to right)

1/2 : \frac{1}{2}

1/2

1/2 = \frac{1}{2}

= \frac{1}{2}

= \frac{80}{9} + \frac{20}{3} + \frac{1}{2}

Add and subtract (left to right)

\frac{80}{9} + \frac{20}{3} + \frac{1}{2} : \frac{289}{18}

\frac{80}{9} + \frac{20}{3} + \frac{1}{2}

\frac{80}{9} + \frac{20}{3} = \frac{140}{9}

\frac{80}{9} + \frac{20}{3}

Least Common Multiplier of

9, 3 : 9

9, 3

Least Common Multiplier (LCM)

Prime factorization of

9 : 3 \cdot 3

9

9

divides by

39 = 3 \cdot 3

= 3 \cdot 3

Prime factorization of

3 : 3

3

3

is a prime number, therefore no factorization is possible

= 3

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

9

3

= 3 \cdot 3

Multiply the numbers:

3 \cdot 3 = 9

= 9

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

9

For

\frac{20}{3} :

multiply the denominator and numerator by

3

\frac{20}{3} = \frac{20 \cdot 3}{3 \cdot 3} = \frac{60}{9}

= \frac{80}{9} + \frac{60}{9}

Since the denominators are equal, combine the fractions:

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

= \frac{80 + 60}{9}

Add the numbers:

80 + 60 = 140

= \frac{140}{9}

= \frac{140}{9} + \frac{1}{2}

\frac{140}{9} + \frac{1}{2} = \frac{289}{18}

\frac{140}{9} + \frac{1}{2}

Least Common Multiplier of

9, 2 : 18

9, 2

Least Common Multiplier (LCM)

Prime factorization of

9 : 3 \cdot 3

9

9

divides by

39 = 3 \cdot 3

= 3 \cdot 3

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

9

2

= 3 \cdot 3 \cdot 2

Multiply the numbers:

3 \cdot 3 \cdot 2 = 18

= 18

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

18

For

\frac{140}{9} :

multiply the denominator and numerator by

2

\frac{140}{9} = \frac{140 \cdot 2}{9 \cdot 2} = \frac{280}{18}

For

\frac{1}{2} :

multiply the denominator and numerator by

9

\frac{1}{2} = \frac{1 \cdot 9}{2 \cdot 9} = \frac{9}{18}

= \frac{280}{18} + \frac{9}{18}

Since the denominators are equal, combine the fractions:

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

= \frac{280 + 9}{18}

Add the numbers:

280 + 9 = 289

= \frac{289}{18}

= \frac{289}{18}

= \frac{289}{18}

Convert improper fractions to mixed numbers:

\frac{289}{18} = 16 \frac{1}{18}

\frac{289}{18} = 16

Remainder

1

\frac{289}{18}

Write the problem in long division format

18 \overline{∣ 289}

Divide

28

18

to get

1

Divide

28

18

to get

1

1 18 \overline{∣ 289}

Multiply the quotient digit

(1)

by the divisor

18

1 18 \overline{∣ 289} \underline{18}

Subtract

18

from

28

1 18 \overline{∣ 289} \underline{18} 10

Bring down the next number of the dividend

1 18 \overline{∣ 289} \underline{18} 109

1 18 \overline{∣ 289} \underline{18} 109

Divide

109

18

to get

6

Divide

109

18

to get

6

16 18 \overline{∣ 289} \underline{18} 109

Multiply the quotient digit

(6)

by the divisor

18

16 18 \overline{∣ 289} \underline{18} 109 \underline{108}

Subtract

108

from

109

16 18 \overline{∣ 289} \underline{18} 109 \underline{108} 1

16 18 \overline{∣ 289} \underline{18} 109 \underline{108} 1

The solution for Long Division of

\frac{289}{18}

16

with remainder of

1

16 Remainder 1

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{289}{18} = 16 \frac{1}{18}

= 16 \frac{1}{18}

= 16 \frac{1}{18}

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What is 80/9+20/3+1/2 ?
The solution to 80/9+20/3+1/2 is 16 1/18

80/9+20/3+1/2

Solution

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Frequently Asked Questions (FAQ)

What is 80/9+20/3+1/2 ?

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