Basic Math Examples

$1 \frac{1}{2} + \frac{1}{3} + \frac{1}{4} = \frac{π}{12}$

Step 1

Simplify the left side.

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Step 1.1

Simplify

$1 \frac{1}{2} + \frac{1}{3} + \frac{1}{4}$ .

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Step 1.1.1

Convert

$1 \frac{1}{2}$ to an improper fraction.

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Step 1.1.1.1

A mixed number is an addition of its whole and fractional parts.

$1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} = \frac{π}{12}$

Step 1.1.1.2

Add

$1$ and

$\frac{1}{2}$ .

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Step 1.1.1.2.1

Write

$1$ as a fraction with a common denominator.

$\frac{2}{2} + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} = \frac{π}{12}$

Step 1.1.1.2.2

Combine the numerators over the common denominator.

$\frac{2 + 1}{2} + \frac{1}{3} + \frac{1}{4} = \frac{π}{12}$

Step 1.1.1.2.3

Add

$2$ and

$1$ .

$\frac{3}{2} + \frac{1}{3} + \frac{1}{4} = \frac{π}{12}$

Step 1.1.2

Find the common denominator.

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Step 1.1.2.1

Multiply

$\frac{3}{2}$ by

$\frac{6}{6}$ .

$\frac{3}{2} \cdot \frac{6}{6} + \frac{1}{3} + \frac{1}{4} = \frac{π}{12}$

Step 1.1.2.2

Multiply

$\frac{3}{2}$ by

$\frac{6}{6}$ .

$\frac{3 \cdot 6}{2 \cdot 6} + \frac{1}{3} + \frac{1}{4} = \frac{π}{12}$

Step 1.1.2.3

Multiply

$\frac{1}{3}$ by

$\frac{4}{4}$ .

$\frac{3 \cdot 6}{2 \cdot 6} + \frac{1}{3} \cdot \frac{4}{4} + \frac{1}{4} = \frac{π}{12}$

Step 1.1.2.4

Multiply

$\frac{1}{3}$ by

$\frac{4}{4}$ .

$\frac{3 \cdot 6}{2 \cdot 6} + \frac{4}{3 \cdot 4} + \frac{1}{4} = \frac{π}{12}$

Step 1.1.2.5

Multiply

$\frac{1}{4}$ by

$\frac{3}{3}$ .

$\frac{3 \cdot 6}{2 \cdot 6} + \frac{4}{3 \cdot 4} + \frac{1}{4} \cdot \frac{3}{3} = \frac{π}{12}$

Step 1.1.2.6

Multiply

$\frac{1}{4}$ by

$\frac{3}{3}$ .

$\frac{3 \cdot 6}{2 \cdot 6} + \frac{4}{3 \cdot 4} + \frac{3}{4 \cdot 3} = \frac{π}{12}$

Step 1.1.2.7

Multiply

$2$ by

$6$ .

$\frac{3 \cdot 6}{12} + \frac{4}{3 \cdot 4} + \frac{3}{4 \cdot 3} = \frac{π}{12}$

Step 1.1.2.8

Multiply

$3$ by

$4$ .

$\frac{3 \cdot 6}{12} + \frac{4}{12} + \frac{3}{4 \cdot 3} = \frac{π}{12}$

Step 1.1.2.9

Reorder the factors of

$4 \cdot 3$ .

$\frac{3 \cdot 6}{12} + \frac{4}{12} + \frac{3}{3 \cdot 4} = \frac{π}{12}$

Step 1.1.2.10

Multiply

$3$ by

$4$ .

$\frac{3 \cdot 6}{12} + \frac{4}{12} + \frac{3}{12} = \frac{π}{12}$

Step 1.1.3

Combine the numerators over the common denominator.

$\frac{3 \cdot 6 + 4 + 3}{12} = \frac{π}{12}$

Step 1.1.4

Simplify the expression.

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Step 1.1.4.1

Multiply

$3$ by

$6$ .

$\frac{18 + 4 + 3}{12} = \frac{π}{12}$

Step 1.1.4.2

Add

$18$ and

$4$ .

$\frac{22 + 3}{12} = \frac{π}{12}$

Step 1.1.4.3

Add

$22$ and

$3$ .

$\frac{25}{12} = \frac{π}{12}$

Step 2

Divide

$3.14159265$ by

$12$ .

$\frac{25}{12} = 0.26179938$

Step 3

Since

$\frac{25}{12} \neq 0.26179938$ , there are no solutions.

No solution