What is 3 3/4-(2 3/8-1 3/4) ?

The solution to 3 3/4-(2 3/8-1 3/4) is 3 1/8

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3 3/4-(2 3/8-1 3/4)

Solution

3 \frac{3}{4} - (2 \frac{3}{8} - 1 \frac{3}{4})

Solution

3 \frac{1}{8}

Solution steps

3 \frac{3}{4} - (2 \frac{3}{8} - 1 \frac{3}{4})

Convert mixed numbers to improper fractions:

3 \frac{3}{4} = \frac{15}{4}

3 \frac{3}{4}

Convert mixed numbers to improper fraction:

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

3 \frac{3}{4} = \frac{3 \cdot 4 + 3}{4}

= \frac{15}{4}

= \frac{15}{4} - (2 \frac{3}{8} - 1 \frac{3}{4})

Convert mixed numbers to improper fractions:

2 \frac{3}{8} = \frac{19}{8}

2 \frac{3}{8}

Convert mixed numbers to improper fraction:

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

2 \frac{3}{8} = \frac{2 \cdot 8 + 3}{8}

= \frac{19}{8}

= \frac{15}{4} - (\frac{19}{8} - 1 \frac{3}{4})

Convert mixed numbers to improper fractions:

1 \frac{3}{4} = \frac{7}{4}

1 \frac{3}{4}

Convert mixed numbers to improper fraction:

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

1 \frac{3}{4} = \frac{1 \cdot 4 + 3}{4}

= \frac{7}{4}

= \frac{15}{4} - (\frac{19}{8} - \frac{7}{4})

Follow the PEMDAS order of operations

Calculate within parentheses

(\frac{19}{8} - \frac{7}{4}) : \frac{5}{8}

\frac{19}{8} - \frac{7}{4}

\frac{19}{8} - \frac{7}{4} = \frac{5}{8}

\frac{19}{8} - \frac{7}{4}

Least Common Multiplier of

8, 4 : 8

8, 4

Least Common Multiplier (LCM)

Prime factorization of

8 : 2 \cdot 2 \cdot 2

8

8

divides by

28 = 4 \cdot 2

= 2 \cdot 4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 2 \cdot 2

Prime factorization of

4 : 2 \cdot 2

4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 2

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

8

4

= 2 \cdot 2 \cdot 2

Multiply the numbers:

2 \cdot 2 \cdot 2 = 8

= 8

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

8

For

\frac{7}{4} :

multiply the denominator and numerator by

2

\frac{7}{4} = \frac{7 \cdot 2}{4 \cdot 2} = \frac{14}{8}

= \frac{19}{8} - \frac{14}{8}

Since the denominators are equal, combine the fractions:

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

= \frac{19 - 14}{8}

Subtract the numbers:

19 - 14 = 5

= \frac{5}{8}

= \frac{5}{8}

= \frac{15}{4} - \frac{5}{8}

Add and subtract (left to right)

\frac{15}{4} - \frac{5}{8} : \frac{25}{8}

\frac{15}{4} - \frac{5}{8}

\frac{15}{4} - \frac{5}{8} = \frac{25}{8}

\frac{15}{4} - \frac{5}{8}

Least Common Multiplier of

4, 8 : 8

4, 8

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

8 : 2 \cdot 2 \cdot 2

8

8

divides by

28 = 4 \cdot 2

= 2 \cdot 4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 2 \cdot 2

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

4

8

= 2 \cdot 2 \cdot 2

Multiply the numbers:

2 \cdot 2 \cdot 2 = 8

= 8

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

8

For

\frac{15}{4} :

multiply the denominator and numerator by

2

\frac{15}{4} = \frac{15 \cdot 2}{4 \cdot 2} = \frac{30}{8}

= \frac{30}{8} - \frac{5}{8}

Since the denominators are equal, combine the fractions:

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

= \frac{30 - 5}{8}

Subtract the numbers:

30 - 5 = 25

= \frac{25}{8}

= \frac{25}{8}

= \frac{25}{8}

Convert improper fractions to mixed numbers:

\frac{25}{8} = 3 \frac{1}{8}

\frac{25}{8} = 3

Remainder

1

\frac{25}{8}

Write the problem in long division format

8 \overline{∣ 25}

Divide

25

8

to get

3

Divide

25

8

to get

3

3 8 \overline{∣ 25}

Multiply the quotient digit

(3)

by the divisor

8

3 8 \overline{∣ 25} \underline{24}

Subtract

24

from

25

3 8 \overline{∣ 25} \underline{24} 1

3 8 \overline{∣ 25} \underline{24} 1

The solution for Long Division of

\frac{25}{8}

3

with remainder of

1

3 Remainder 1

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{25}{8} = 3 \frac{1}{8}

= 3 \frac{1}{8}

= 3 \frac{1}{8}

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2 (2 + 5)

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9+(-2)^3-2(-6^2)

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Frequently Asked Questions (FAQ)

What is 3 3/4-(2 3/8-1 3/4) ?
The solution to 3 3/4-(2 3/8-1 3/4) is 3 1/8