Pre-Algebra Examples

$\frac{5}{2} + \frac{3}{\frac{4}{\frac{7}{5} - \frac{7}{10}}}$

Step 1

Simplify each term.

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Step 1.1

Multiply the numerator by the reciprocal of the denominator.

$\frac{5}{2} + 3 \frac{\frac{7}{5} - \frac{7}{10}}{4}$

Step 1.2

Simplify the numerator.

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Step 1.2.1

To write $\frac{7}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{5}{2} + 3 \frac{\frac{7}{5} \cdot \frac{2}{2} - \frac{7}{10}}{4}$

Step 1.2.2

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.2.2.1

Multiply $\frac{7}{5}$ by $\frac{2}{2}$ .

$\frac{5}{2} + 3 \frac{\frac{7 \cdot 2}{5 \cdot 2} - \frac{7}{10}}{4}$

Step 1.2.2.2

Multiply $5$ by $2$ .

$\frac{5}{2} + 3 \frac{\frac{7 \cdot 2}{10} - \frac{7}{10}}{4}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{5}{2} + 3 \frac{\frac{7 \cdot 2 - 7}{10}}{4}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $7$ by $2$ .

$\frac{5}{2} + 3 \frac{\frac{14 - 7}{10}}{4}$

Step 1.2.4.2

Subtract $7$ from $14$ .

$\frac{5}{2} + 3 \frac{\frac{7}{10}}{4}$

Step 1.3

Multiply the numerator by the reciprocal of the denominator.

$\frac{5}{2} + 3 (\frac{7}{10} \cdot \frac{1}{4})$

Step 1.4

Multiply $\frac{7}{10} \cdot \frac{1}{4}$ .

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Step 1.4.1

Multiply $\frac{7}{10}$ by $\frac{1}{4}$ .

$\frac{5}{2} + 3 \frac{7}{10 \cdot 4}$

Step 1.4.2

Multiply $10$ by $4$ .

$\frac{5}{2} + 3 (\frac{7}{40})$

Step 1.5

Multiply $3 (\frac{7}{40})$ .

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Step 1.5.1

Combine $3$ and $\frac{7}{40}$ .

$\frac{5}{2} + \frac{3 \cdot 7}{40}$

Step 1.5.2

Multiply $3$ by $7$ .

$\frac{5}{2} + \frac{21}{40}$

Step 2

To write $\frac{5}{2}$ as a fraction with a common denominator, multiply by $\frac{20}{20}$ .

$\frac{5}{2} \cdot \frac{20}{20} + \frac{21}{40}$

Step 3

Write each expression with a common denominator of $40$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{5}{2}$ by $\frac{20}{20}$ .

$\frac{5 \cdot 20}{2 \cdot 20} + \frac{21}{40}$

Step 3.2

Multiply $2$ by $20$ .

$\frac{5 \cdot 20}{40} + \frac{21}{40}$

Step 4

Combine the numerators over the common denominator.

$\frac{5 \cdot 20 + 21}{40}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $5$ by $20$ .

$\frac{100 + 21}{40}$

Step 5.2

Add $100$ and $21$ .

$\frac{121}{40}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{121}{40}$

Decimal Form:

$3.025$

Mixed Number Form:

$3 \frac{1}{40}$