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

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

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Popular >

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

Solution

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

Solution

4 \frac{1}{2}

Solution steps

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

Convert mixed numbers to improper fractions:

1 \frac{1}{4} = \frac{5}{4}

1 \frac{1}{4}

Convert mixed numbers to improper fraction:

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

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

= \frac{5}{4}

= (2 \frac{1}{2} + 3 \frac{1}{4}) - \frac{5}{4}

Convert mixed numbers to improper fractions:

2 \frac{1}{2} = \frac{5}{2}

2 \frac{1}{2}

Convert mixed numbers to improper fraction:

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

2 \frac{1}{2} = \frac{2 \cdot 2 + 1}{2}

= \frac{5}{2}

= (\frac{5}{2} + 3 \frac{1}{4}) - \frac{5}{4}

Convert mixed numbers to improper fractions:

3 \frac{1}{4} = \frac{13}{4}

3 \frac{1}{4}

Convert mixed numbers to improper fraction:

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

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

= \frac{13}{4}

= (\frac{5}{2} + \frac{13}{4}) - \frac{5}{4}

Follow the PEMDAS order of operations

Calculate within parentheses

(\frac{5}{2} + \frac{13}{4}) : \frac{23}{4}

\frac{5}{2} + \frac{13}{4}

\frac{5}{2} + \frac{13}{4} = \frac{23}{4}

\frac{5}{2} + \frac{13}{4}

Least Common Multiplier of

2, 4 : 4

2, 4

Least Common Multiplier (LCM)

Prime factorization of

2 : 2

2

2

is a prime number, therefore no factorization is possible

= 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

2

4

= 2 \cdot 2

Multiply the numbers:

2 \cdot 2 = 4

= 4

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

4

For

\frac{5}{2} :

multiply the denominator and numerator by

2

\frac{5}{2} = \frac{5 \cdot 2}{2 \cdot 2} = \frac{10}{4}

= \frac{10}{4} + \frac{13}{4}

Since the denominators are equal, combine the fractions:

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

= \frac{10 + 13}{4}

Add the numbers:

10 + 13 = 23

= \frac{23}{4}

= \frac{23}{4}

= \frac{23}{4} - \frac{5}{4}

Add and subtract (left to right)

\frac{23}{4} - \frac{5}{4} : \frac{9}{2}

\frac{23}{4} - \frac{5}{4}

\frac{23}{4} - \frac{5}{4} = \frac{9}{2}

\frac{23}{4} - \frac{5}{4}

Apply rule

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

= \frac{23 - 5}{4}

Subtract the numbers:

23 - 5 = 18

= \frac{18}{4}

Cancel the common factor:

2

= \frac{9}{2}

= \frac{9}{2}

= \frac{9}{2}

Convert improper fractions to mixed numbers:

\frac{9}{2} = 4 \frac{1}{2}

\frac{9}{2} = 4

Remainder

1

\frac{9}{2}

Write the problem in long division format

2 \overline{∣ 9}

Divide

9

2

to get

4

Divide

9

2

to get

4

4 2 \overline{∣ 9}

Multiply the quotient digit

(4)

by the divisor

2

4 2 \overline{∣ 9} \underline{8}

Subtract

8

from

9

4 2 \overline{∣ 9} \underline{8} 1

4 2 \overline{∣ 9} \underline{8} 1

The solution for Long Division of

\frac{9}{2}

4

with remainder of

1

4 Remainder 1

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{9}{2} = 4 \frac{1}{2}

= 4 \frac{1}{2}

= 4 \frac{1}{2}

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2 + 3 \cdot \frac{3}{5}

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8 (- 2)^{3} - 8 (- 2)

Frequently Asked Questions (FAQ)

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