Finite Math Examples

$121 (\frac{29}{60}) + 13 (\frac{9}{60}) = x$

Step 1

Rewrite the equation as $x = 121 (\frac{29}{60}) + 13 (\frac{9}{60})$ .

$x = 121 (\frac{29}{60}) + 13 (\frac{9}{60})$

Step 2

Simplify $121 (\frac{29}{60}) + 13 (\frac{9}{60})$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $121 (\frac{29}{60})$ .

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Step 2.1.1.1

Combine $121$ and $\frac{29}{60}$ .

$x = \frac{121 \cdot 29}{60} + 13 (\frac{9}{60})$

Step 2.1.1.2

Multiply $121$ by $29$ .

$x = \frac{3509}{60} + 13 (\frac{9}{60})$

Step 2.1.2

Cancel the common factor of $9$ and $60$ .

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Step 2.1.2.1

Factor $3$ out of $9$ .

$x = \frac{3509}{60} + 13 \frac{3 (3)}{60}$

Step 2.1.2.2

Cancel the common factors.

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Step 2.1.2.2.1

Factor $3$ out of $60$ .

$x = \frac{3509}{60} + 13 \frac{3 \cdot 3}{3 \cdot 20}$

Step 2.1.2.2.2

Cancel the common factor.

$x = \frac{3509}{60} + 13 \frac{3 \cdot 3}{3 \cdot 20}$

Step 2.1.2.2.3

Rewrite the expression.

$x = \frac{3509}{60} + 13 (\frac{3}{20})$

Step 2.1.3

Multiply $13 (\frac{3}{20})$ .

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Step 2.1.3.1

Combine $13$ and $\frac{3}{20}$ .

$x = \frac{3509}{60} + \frac{13 \cdot 3}{20}$

Step 2.1.3.2

Multiply $13$ by $3$ .

$x = \frac{3509}{60} + \frac{39}{20}$

Step 2.2

To write $\frac{39}{20}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$x = \frac{3509}{60} + \frac{39}{20} \cdot \frac{3}{3}$

Step 2.3

Write each expression with a common denominator of $60$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.3.1

Multiply $\frac{39}{20}$ by $\frac{3}{3}$ .

$x = \frac{3509}{60} + \frac{39 \cdot 3}{20 \cdot 3}$

Step 2.3.2

Multiply $20$ by $3$ .

$x = \frac{3509}{60} + \frac{39 \cdot 3}{60}$

Step 2.4

Combine the numerators over the common denominator.

$x = \frac{3509 + 39 \cdot 3}{60}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $39$ by $3$ .

$x = \frac{3509 + 117}{60}$

Step 2.5.2

Add $3509$ and $117$ .

$x = \frac{3626}{60}$

Step 2.6

Cancel the common factor of $3626$ and $60$ .

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Step 2.6.1

Factor $2$ out of $3626$ .

$x = \frac{2 (1813)}{60}$

Step 2.6.2

Cancel the common factors.

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Step 2.6.2.1

Factor $2$ out of $60$ .

$x = \frac{2 \cdot 1813}{2 \cdot 30}$

Step 2.6.2.2

Cancel the common factor.

$x = \frac{2 \cdot 1813}{2 \cdot 30}$

Step 2.6.2.3

Rewrite the expression.

$x = \frac{1813}{30}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1813}{30}$

Decimal Form:

$x = 60.4\overline{3}$

Mixed Number Form:

$x = 60 \frac{13}{30}$