Basic Math Examples

$\frac{10}{1} - (\frac{5}{3} + \frac{11}{4} + \frac{23}{6})$

Step 1

Simplify each term.

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Step 1.1

Divide $10$ by $1$ .

$10 - (\frac{5}{3} + \frac{11}{4} + \frac{23}{6})$

Step 1.2

Find the common denominator.

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Step 1.2.1

Multiply $\frac{5}{3}$ by $\frac{4}{4}$ .

$10 - (\frac{5}{3} \cdot \frac{4}{4} + \frac{11}{4} + \frac{23}{6})$

Step 1.2.2

Multiply $\frac{5}{3}$ by $\frac{4}{4}$ .

$10 - (\frac{5 \cdot 4}{3 \cdot 4} + \frac{11}{4} + \frac{23}{6})$

Step 1.2.3

Multiply $\frac{11}{4}$ by $\frac{3}{3}$ .

$10 - (\frac{5 \cdot 4}{3 \cdot 4} + \frac{11}{4} \cdot \frac{3}{3} + \frac{23}{6})$

Step 1.2.4

Multiply $\frac{11}{4}$ by $\frac{3}{3}$ .

$10 - (\frac{5 \cdot 4}{3 \cdot 4} + \frac{11 \cdot 3}{4 \cdot 3} + \frac{23}{6})$

Step 1.2.5

Multiply $\frac{23}{6}$ by $\frac{2}{2}$ .

$10 - (\frac{5 \cdot 4}{3 \cdot 4} + \frac{11 \cdot 3}{4 \cdot 3} + \frac{23}{6} \cdot \frac{2}{2})$

Step 1.2.6

Multiply $\frac{23}{6}$ by $\frac{2}{2}$ .

$10 - (\frac{5 \cdot 4}{3 \cdot 4} + \frac{11 \cdot 3}{4 \cdot 3} + \frac{23 \cdot 2}{6 \cdot 2})$

Step 1.2.7

Multiply $3$ by $4$ .

$10 - (\frac{5 \cdot 4}{12} + \frac{11 \cdot 3}{4 \cdot 3} + \frac{23 \cdot 2}{6 \cdot 2})$

Step 1.2.8

Reorder the factors of $4 \cdot 3$ .

$10 - (\frac{5 \cdot 4}{12} + \frac{11 \cdot 3}{3 \cdot 4} + \frac{23 \cdot 2}{6 \cdot 2})$

Step 1.2.9

Multiply $3$ by $4$ .

$10 - (\frac{5 \cdot 4}{12} + \frac{11 \cdot 3}{12} + \frac{23 \cdot 2}{6 \cdot 2})$

Step 1.2.10

Reorder the factors of $6 \cdot 2$ .

$10 - (\frac{5 \cdot 4}{12} + \frac{11 \cdot 3}{12} + \frac{23 \cdot 2}{2 \cdot 6})$

Step 1.2.11

Multiply $2$ by $6$ .

$10 - (\frac{5 \cdot 4}{12} + \frac{11 \cdot 3}{12} + \frac{23 \cdot 2}{12})$

Step 1.3

Combine the numerators over the common denominator.

$10 - \frac{5 \cdot 4 + 11 \cdot 3 + 23 \cdot 2}{12}$

Step 1.4

Simplify each term.

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Step 1.4.1

Multiply $5$ by $4$ .

$10 - \frac{20 + 11 \cdot 3 + 23 \cdot 2}{12}$

Step 1.4.2

Multiply $11$ by $3$ .

$10 - \frac{20 + 33 + 23 \cdot 2}{12}$

Step 1.4.3

Multiply $23$ by $2$ .

$10 - \frac{20 + 33 + 46}{12}$

Step 1.5

Add $20$ and $33$ .

$10 - \frac{53 + 46}{12}$

Step 1.6

Add $53$ and $46$ .

$10 - \frac{99}{12}$

Step 1.7

Cancel the common factor of $99$ and $12$ .

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Step 1.7.1

Factor $3$ out of $99$ .

$10 - \frac{3 (33)}{12}$

Step 1.7.2

Cancel the common factors.

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Step 1.7.2.1

Factor $3$ out of $12$ .

$10 - \frac{3 \cdot 33}{3 \cdot 4}$

Step 1.7.2.2

Cancel the common factor.

$10 - \frac{3 \cdot 33}{3 \cdot 4}$

Step 1.7.2.3

Rewrite the expression.

$10 - \frac{33}{4}$

Step 2

To write $10$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$10 \cdot \frac{4}{4} - \frac{33}{4}$

Step 3

Combine $10$ and $\frac{4}{4}$ .

$\frac{10 \cdot 4}{4} - \frac{33}{4}$

Step 4

Combine the numerators over the common denominator.

$\frac{10 \cdot 4 - 33}{4}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $10$ by $4$ .

$\frac{40 - 33}{4}$

Step 5.2

Subtract $33$ from $40$ .

$\frac{7}{4}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{7}{4}$

Decimal Form:

$1.75$

Mixed Number Form:

$1 \frac{3}{4}$