What is 18-1 7/16-7/12 ?

The solution to 18-1 7/16-7/12 is 15 47/48

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Popular Pre Algebra >

18-1 7/16-7/12

Solution

18 - 1 \frac{7}{16} - \frac{7}{12}

Solution

15 \frac{47}{48}

Decimal

15.97916 \dots

Solution steps

18 - 1 \frac{7}{16} - \frac{7}{12}

Convert mixed numbers to improper fractions:

1 \frac{7}{16} = \frac{23}{16}

1 \frac{7}{16}

Convert mixed numbers to improper fraction:

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

1 \frac{7}{16} = \frac{1 \cdot 16 + 7}{16}

= \frac{23}{16}

= 18 - \frac{23}{16} - \frac{7}{12}

Follow the PEMDAS order of operations

Add and subtract (left to right)

18 - \frac{23}{16} - \frac{7}{12} : \frac{767}{48}

18 - \frac{23}{16} - \frac{7}{12}

18 - \frac{23}{16} = \frac{265}{16}

18 - \frac{23}{16}

Convert element to fraction:

18 = \frac{18 \cdot 16}{16}

= \frac{18 \cdot 16}{16} - \frac{23}{16}

Since the denominators are equal, combine the fractions:

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

= \frac{18 \cdot 16 - 23}{16}

18 \cdot 16 - 23 = 265

18 \cdot 16 - 23

Multiply the numbers:

18 \cdot 16 = 288

= 288 - 23

Subtract the numbers:

288 - 23 = 265

= 265

= \frac{265}{16}

= \frac{265}{16} - \frac{7}{12}

\frac{265}{16} - \frac{7}{12} = \frac{767}{48}

\frac{265}{16} - \frac{7}{12}

Least Common Multiplier of

16, 12 : 48

16, 12

Least Common Multiplier (LCM)

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

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

16

12

= 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3

Multiply the numbers:

2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 = 48

= 48

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

48

For

\frac{265}{16} :

multiply the denominator and numerator by

3

\frac{265}{16} = \frac{265 \cdot 3}{16 \cdot 3} = \frac{795}{48}

For

\frac{7}{12} :

multiply the denominator and numerator by

4

\frac{7}{12} = \frac{7 \cdot 4}{12 \cdot 4} = \frac{28}{48}

= \frac{795}{48} - \frac{28}{48}

Since the denominators are equal, combine the fractions:

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

= \frac{795 - 28}{48}

Subtract the numbers:

795 - 28 = 767

= \frac{767}{48}

= \frac{767}{48}

= \frac{767}{48}

Convert improper fractions to mixed numbers:

\frac{767}{48} = 15 \frac{47}{48}

\frac{767}{48} = 15

Remainder

47

\frac{767}{48}

Write the problem in long division format

48 \overline{∣ 767}

Divide

76

48

to get

1

Divide

76

48

to get

1

1 48 \overline{∣ 767}

Multiply the quotient digit

(1)

by the divisor

48

1 48 \overline{∣ 767} \underline{48}

Subtract

48

from

76

1 48 \overline{∣ 767} \underline{48} 28

Bring down the next number of the dividend

1 48 \overline{∣ 767} \underline{48} 287

1 48 \overline{∣ 767} \underline{48} 287

Divide

287

48

to get

5

Divide

287

48

to get

5

15 48 \overline{∣ 767} \underline{48} 287

Multiply the quotient digit

(5)

by the divisor

48

15 48 \overline{∣ 767} \underline{48} 287 \underline{240}

Subtract

240

from

287

15 48 \overline{∣ 767} \underline{48} 287 \underline{240} 47

15 48 \overline{∣ 767} \underline{48} 287 \underline{240} 47

The solution for Long Division of

\frac{767}{48}

15

with remainder of

47

15 Remainder 47

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{767}{48} = 15 \frac{47}{48}

= 15 \frac{47}{48}

= 15 \frac{47}{48}

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What is 18-1 7/16-7/12 ?
The solution to 18-1 7/16-7/12 is 15 47/48

18-1 7/16-7/12

Solution

Solution

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Frequently Asked Questions (FAQ)

What is 18-1 7/16-7/12 ?

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