Finite Math Examples

$\frac{d}{45} + \frac{d}{50} = 28$

Step 1

Simplify $\frac{d}{45} + \frac{d}{50}$ .

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Step 1.1

To write $\frac{d}{45}$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$\frac{d}{45} \cdot \frac{10}{10} + \frac{d}{50} = 28$

Step 1.2

To write $\frac{d}{50}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{d}{45} \cdot \frac{10}{10} + \frac{d}{50} \cdot \frac{9}{9} = 28$

Step 1.3

Write each expression with a common denominator of $450$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{d}{45}$ by $\frac{10}{10}$ .

$\frac{d \cdot 10}{45 \cdot 10} + \frac{d}{50} \cdot \frac{9}{9} = 28$

Step 1.3.2

Multiply $45$ by $10$ .

$\frac{d \cdot 10}{450} + \frac{d}{50} \cdot \frac{9}{9} = 28$

Step 1.3.3

Multiply $\frac{d}{50}$ by $\frac{9}{9}$ .

$\frac{d \cdot 10}{450} + \frac{d \cdot 9}{50 \cdot 9} = 28$

Step 1.3.4

Multiply $50$ by $9$ .

$\frac{d \cdot 10}{450} + \frac{d \cdot 9}{450} = 28$

Step 1.4

Combine the numerators over the common denominator.

$\frac{d \cdot 10 + d \cdot 9}{450} = 28$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Move $10$ to the left of $d$ .

$\frac{10 \cdot d + d \cdot 9}{450} = 28$

Step 1.5.2

Move $9$ to the left of $d$ .

$\frac{10 d + 9 \cdot d}{450} = 28$

Step 1.5.3

Add $10 d$ and $9 d$ .

$\frac{19 d}{450} = 28$

Step 2

Multiply both sides of the equation by $\frac{450}{19}$ .

$\frac{450}{19} \cdot \frac{19 d}{450} = \frac{450}{19} \cdot 28$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{450}{19} \cdot \frac{19 d}{450}$ .

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Step 3.1.1.1

Cancel the common factor of $450$ .

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Step 3.1.1.1.1

Cancel the common factor.

$\frac{450}{19} \cdot \frac{19 d}{450} = \frac{450}{19} \cdot 28$

Step 3.1.1.1.2

Rewrite the expression.

$\frac{1}{19} (19 d) = \frac{450}{19} \cdot 28$

Step 3.1.1.2

Cancel the common factor of $19$ .

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Step 3.1.1.2.1

Factor $19$ out of $19 d$ .

$\frac{1}{19} (19 (d)) = \frac{450}{19} \cdot 28$

Step 3.1.1.2.2

Cancel the common factor.

$\frac{1}{19} (19 d) = \frac{450}{19} \cdot 28$

Step 3.1.1.2.3

Rewrite the expression.

$d = \frac{450}{19} \cdot 28$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $\frac{450}{19} \cdot 28$ .

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Step 3.2.1.1

Combine $\frac{450}{19}$ and $28$ .

$d = \frac{450 \cdot 28}{19}$

Step 3.2.1.2

Multiply $450$ by $28$ .

$d = \frac{12600}{19}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$d = \frac{12600}{19}$

Decimal Form:

$d = 663.15789473 \dots$

Mixed Number Form:

$d = 663 \frac{3}{19}$