What is 74+4/16-2/23 ?

The solution to 74+4/16-2/23 is 74 15/92

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Popular Pre Algebra >

74+4/16-2/23

Solution

74 + \frac{4}{16} - \frac{2}{23}

Solution

74 \frac{15}{92}

Decimal

74.16304 \dots

Solution steps

74 + \frac{4}{16} - \frac{2}{23}

\frac{4}{16} = \frac{1}{4}

Cancel the common factor:

4

\frac{1}{4}

= 74 + \frac{1}{4} - \frac{2}{23}

Follow the PEMDAS order of operations

Add and subtract (left to right)

74 + \frac{1}{4} - \frac{2}{23} : \frac{6823}{92}

74 + \frac{1}{4} - \frac{2}{23}

74 + \frac{1}{4} = \frac{297}{4}

74 + \frac{1}{4}

Convert element to fraction:

74 = \frac{74 \cdot 4}{4}

= \frac{74 \cdot 4}{4} + \frac{1}{4}

Since the denominators are equal, combine the fractions:

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

= \frac{74 \cdot 4 + 1}{4}

74 \cdot 4 + 1 = 297

74 \cdot 4 + 1

Multiply the numbers:

74 \cdot 4 = 296

= 296 + 1

Add the numbers:

296 + 1 = 297

= 297

= \frac{297}{4}

= \frac{297}{4} - \frac{2}{23}

\frac{297}{4} - \frac{2}{23} = \frac{6823}{92}

\frac{297}{4} - \frac{2}{23}

Least Common Multiplier of

4, 23 : 92

4, 23

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

23 : 23

23

23

is a prime number, therefore no factorization is possible

= 23

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

4

23

= 2 \cdot 2 \cdot 23

Multiply the numbers:

2 \cdot 2 \cdot 23 = 92

= 92

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

92

For

\frac{297}{4} :

multiply the denominator and numerator by

23

\frac{297}{4} = \frac{297 \cdot 23}{4 \cdot 23} = \frac{6831}{92}

For

\frac{2}{23} :

multiply the denominator and numerator by

4

\frac{2}{23} = \frac{2 \cdot 4}{23 \cdot 4} = \frac{8}{92}

= \frac{6831}{92} - \frac{8}{92}

Since the denominators are equal, combine the fractions:

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

= \frac{6831 - 8}{92}

Subtract the numbers:

6831 - 8 = 6823

= \frac{6823}{92}

= \frac{6823}{92}

= \frac{6823}{92}

Convert improper fractions to mixed numbers:

\frac{6823}{92} = 74 \frac{15}{92}

\frac{6823}{92} = 74

Remainder

15

\frac{6823}{92}

Write the problem in long division format

92 \overline{∣ 6823}

Divide

682

92

to get

7

Divide

682

92

to get

7

7 92 \overline{∣ 6823}

Multiply the quotient digit

(7)

by the divisor

92

7 92 \overline{∣ 6823} \underline{644}

Subtract

644

from

682

7 92 \overline{∣ 6823} \underline{644} 38

Bring down the next number of the dividend

7 92 \overline{∣ 6823} \underline{644} 383

7 92 \overline{∣ 6823} \underline{644} 383

Divide

383

92

to get

4

Divide

383

92

to get

4

74 92 \overline{∣ 6823} \underline{644} 383

Multiply the quotient digit

(4)

by the divisor

92

74 92 \overline{∣ 6823} \underline{644} 383 \underline{368}

Subtract

368

from

383

74 92 \overline{∣ 6823} \underline{644} 383 \underline{368} 15

74 92 \overline{∣ 6823} \underline{644} 383 \underline{368} 15

The solution for Long Division of

\frac{6823}{92}

74

with remainder of

15

74 Remainder 15

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{6823}{92} = 74 \frac{15}{92}

= 74 \frac{15}{92}

= 74 \frac{15}{92}

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What is 74+4/16-2/23 ?
The solution to 74+4/16-2/23 is 74 15/92

74+4/16-2/23

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What is 74+4/16-2/23 ?

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