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

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

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(2+1 1/2)-2 1/2

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

1

Solution steps

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

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}

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

Convert mixed numbers to improper fractions:

1 \frac{1}{2} = \frac{3}{2}

1 \frac{1}{2}

Convert mixed numbers to improper fraction:

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

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

= \frac{3}{2}

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

Follow the PEMDAS order of operations

Calculate within parentheses

(2 + \frac{3}{2}) : \frac{7}{2}

2 + \frac{3}{2}

2 + \frac{3}{2} = \frac{7}{2}

2 + \frac{3}{2}

Convert element to fraction:

2 = \frac{2 \cdot 2}{2}

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

Since the denominators are equal, combine the fractions:

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

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

2 \cdot 2 + 3 = 7

2 \cdot 2 + 3

Multiply the numbers:

2 \cdot 2 = 4

= 4 + 3

Add the numbers:

4 + 3 = 7

= 7

= \frac{7}{2}

= \frac{7}{2}

= \frac{7}{2} - \frac{5}{2}

Add and subtract (left to right)

\frac{7}{2} - \frac{5}{2} : 1

\frac{7}{2} - \frac{5}{2}

\frac{7}{2} - \frac{5}{2} = 1

\frac{7}{2} - \frac{5}{2}

Apply rule

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

= \frac{7 - 5}{2}

Subtract the numbers:

7 - 5 = 2

= \frac{2}{2}

Apply rule

\frac{a}{a} = 1

= 1

= 1

= 1

(1 + 2 \times 3)^{2} \div 7

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\frac{1}{2} (4)^{1}

(\frac{3}{9} \div \frac{3}{1}) \frac{4}{1}

5 (\frac{1}{3}) - (- 2)