What is 30+15 1/4-10 15/16 ?

The solution to 30+15 1/4-10 15/16 is 34 5/16

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Popular Pre Algebra >

30+15 1/4-10 15/16

Solution

30 + 15 \frac{1}{4} - 10 \frac{15}{16}

Solution

34 \frac{5}{16}

Decimal

34.3125

Solution steps

30 + 15 \frac{1}{4} - 10 \frac{15}{16}

Convert mixed numbers to improper fractions:

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

15 \frac{1}{4}

Convert mixed numbers to improper fraction:

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

15 \frac{1}{4} = \frac{15 \cdot 4 + 1}{4}

= \frac{61}{4}

= 30 + \frac{61}{4} - 10 \frac{15}{16}

Convert mixed numbers to improper fractions:

10 \frac{15}{16} = \frac{175}{16}

10 \frac{15}{16}

Convert mixed numbers to improper fraction:

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

10 \frac{15}{16} = \frac{10 \cdot 16 + 15}{16}

= \frac{175}{16}

= 30 + \frac{61}{4} - \frac{175}{16}

Follow the PEMDAS order of operations

Add and subtract (left to right)

30 + \frac{61}{4} - \frac{175}{16} : \frac{549}{16}

30 + \frac{61}{4} - \frac{175}{16}

30 + \frac{61}{4} = \frac{181}{4}

30 + \frac{61}{4}

Convert element to fraction:

30 = \frac{30 \cdot 4}{4}

= \frac{30 \cdot 4}{4} + \frac{61}{4}

Since the denominators are equal, combine the fractions:

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

= \frac{30 \cdot 4 + 61}{4}

30 \cdot 4 + 61 = 181

30 \cdot 4 + 61

Multiply the numbers:

30 \cdot 4 = 120

= 120 + 61

Add the numbers:

120 + 61 = 181

= 181

= \frac{181}{4}

= \frac{181}{4} - \frac{175}{16}

\frac{181}{4} - \frac{175}{16} = \frac{549}{16}

\frac{181}{4} - \frac{175}{16}

Least Common Multiplier of

4, 16 : 16

4, 16

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

16 : 2 \cdot 2 \cdot 2 \cdot 2

16

16

divides by

216 = 8 \cdot 2

= 2 \cdot 8

8

divides by

28 = 4 \cdot 2

= 2 \cdot 2 \cdot 4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 2 \cdot 2 \cdot 2

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

4

16

= 2 \cdot 2 \cdot 2 \cdot 2

Multiply the numbers:

2 \cdot 2 \cdot 2 \cdot 2 = 16

= 16

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

16

For

\frac{181}{4} :

multiply the denominator and numerator by

4

\frac{181}{4} = \frac{181 \cdot 4}{4 \cdot 4} = \frac{724}{16}

= \frac{724}{16} - \frac{175}{16}

Since the denominators are equal, combine the fractions:

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

= \frac{724 - 175}{16}

Subtract the numbers:

724 - 175 = 549

= \frac{549}{16}

= \frac{549}{16}

= \frac{549}{16}

Convert improper fractions to mixed numbers:

\frac{549}{16} = 34 \frac{5}{16}

\frac{549}{16} = 34

Remainder

5

\frac{549}{16}

Write the problem in long division format

16 \overline{∣ 549}

Divide

54

16

to get

3

Divide

54

16

to get

3

3 16 \overline{∣ 549}

Multiply the quotient digit

(3)

by the divisor

16

3 16 \overline{∣ 549} \underline{48}

Subtract

48

from

54

3 16 \overline{∣ 549} \underline{48} 6

Bring down the next number of the dividend

3 16 \overline{∣ 549} \underline{48} 69

3 16 \overline{∣ 549} \underline{48} 69

Divide

69

16

to get

4

Divide

69

16

to get

4

34 16 \overline{∣ 549} \underline{48} 69

Multiply the quotient digit

(4)

by the divisor

16

34 16 \overline{∣ 549} \underline{48} 69 \underline{64}

Subtract

64

from

69

34 16 \overline{∣ 549} \underline{48} 69 \underline{64} 5

34 16 \overline{∣ 549} \underline{48} 69 \underline{64} 5

The solution for Long Division of

\frac{549}{16}

34

with remainder of

5

34 Remainder 5

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{549}{16} = 34 \frac{5}{16}

= 34 \frac{5}{16}

= 34 \frac{5}{16}

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Frequently Asked Questions (FAQ)

What is 30+15 1/4-10 15/16 ?
The solution to 30+15 1/4-10 15/16 is 34 5/16

30+15 1/4-10 15/16

Solution

Solution

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Frequently Asked Questions (FAQ)

What is 30+15 1/4-10 15/16 ?

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