Basic Math Examples

L = (450 + 150) + 120 + \frac{450 - 150}{240}

$L = (450 + 150) + 120 + \frac{450 - 150}{240}$

Step 1

Remove parentheses.

L = 450 + 150 + 120 + \frac{450 - 150}{240}

$L = 450 + 150 + 120 + \frac{450 - 150}{240}$

Step 2

Simplify

450 + 150 + 120 + \frac{450 - 150}{240}

$450 + 150 + 120 + \frac{450 - 150}{240}$ .

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Step 2.1

Subtract

150

$150$ from

450

$450$ .

L = 450 + 150 + 120 + \frac{300}{240}

$L = 450 + 150 + 120 + \frac{300}{240}$

Step 2.2

Find the common denominator.

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Step 2.2.1

Write

450

$450$ as a fraction with denominator

1

$1$ .

L = \frac{450}{1} + 150 + 120 + \frac{300}{240}

$L = \frac{450}{1} + 150 + 120 + \frac{300}{240}$

Step 2.2.2

Multiply

\frac{450}{1}

$\frac{450}{1}$ by

\frac{240}{240}

$\frac{240}{240}$ .

L = \frac{450}{1} \cdot \frac{240}{240} + 150 + 120 + \frac{300}{240}

$L = \frac{450}{1} \cdot \frac{240}{240} + 150 + 120 + \frac{300}{240}$

Step 2.2.3

Multiply

\frac{450}{1}

$\frac{450}{1}$ by

\frac{240}{240}

$\frac{240}{240}$ .

L = \frac{450 \cdot 240}{240} + 150 + 120 + \frac{300}{240}

$L = \frac{450 \cdot 240}{240} + 150 + 120 + \frac{300}{240}$

Step 2.2.4

Write

150

$150$ as a fraction with denominator

1

$1$ .

L = \frac{450 \cdot 240}{240} + \frac{150}{1} + 120 + \frac{300}{240}

$L = \frac{450 \cdot 240}{240} + \frac{150}{1} + 120 + \frac{300}{240}$

Step 2.2.5

Multiply

\frac{150}{1}

$\frac{150}{1}$ by

\frac{240}{240}

$\frac{240}{240}$ .

L = \frac{450 \cdot 240}{240} + \frac{150}{1} \cdot \frac{240}{240} + 120 + \frac{300}{240}

$L = \frac{450 \cdot 240}{240} + \frac{150}{1} \cdot \frac{240}{240} + 120 + \frac{300}{240}$

Step 2.2.6

Multiply

\frac{150}{1}

$\frac{150}{1}$ by

\frac{240}{240}

$\frac{240}{240}$ .

L = \frac{450 \cdot 240}{240} + \frac{150 \cdot 240}{240} + 120 + \frac{300}{240}

$L = \frac{450 \cdot 240}{240} + \frac{150 \cdot 240}{240} + 120 + \frac{300}{240}$

Step 2.2.7

Write

120

$120$ as a fraction with denominator

1

$1$ .

L = \frac{450 \cdot 240}{240} + \frac{150 \cdot 240}{240} + \frac{120}{1} + \frac{300}{240}

$L = \frac{450 \cdot 240}{240} + \frac{150 \cdot 240}{240} + \frac{120}{1} + \frac{300}{240}$

Step 2.2.8

Multiply

\frac{120}{1}

$\frac{120}{1}$ by

\frac{240}{240}

$\frac{240}{240}$ .

L = \frac{450 \cdot 240}{240} + \frac{150 \cdot 240}{240} + \frac{120}{1} \cdot \frac{240}{240} + \frac{300}{240}

$L = \frac{450 \cdot 240}{240} + \frac{150 \cdot 240}{240} + \frac{120}{1} \cdot \frac{240}{240} + \frac{300}{240}$

Step 2.2.9

Multiply

\frac{120}{1}

$\frac{120}{1}$ by

\frac{240}{240}

$\frac{240}{240}$ .

L = \frac{450 \cdot 240}{240} + \frac{150 \cdot 240}{240} + \frac{120 \cdot 240}{240} + \frac{300}{240}

$L = \frac{450 \cdot 240}{240} + \frac{150 \cdot 240}{240} + \frac{120 \cdot 240}{240} + \frac{300}{240}$

L = \frac{450 \cdot 240}{240} + \frac{150 \cdot 240}{240} + \frac{120 \cdot 240}{240} + \frac{300}{240}

$L = \frac{450 \cdot 240}{240} + \frac{150 \cdot 240}{240} + \frac{120 \cdot 240}{240} + \frac{300}{240}$

Step 2.3

Combine the numerators over the common denominator.

L = \frac{450 \cdot 240 + 150 \cdot 240 + 120 \cdot 240 + 300}{240}

$L = \frac{450 \cdot 240 + 150 \cdot 240 + 120 \cdot 240 + 300}{240}$

Step 2.4

Simplify each term.

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Step 2.4.1

Multiply

450

$450$ by

240

$240$ .

L = \frac{108000 + 150 \cdot 240 + 120 \cdot 240 + 300}{240}

$L = \frac{108000 + 150 \cdot 240 + 120 \cdot 240 + 300}{240}$

Step 2.4.2

Multiply

150

$150$ by

240

$240$ .

L = \frac{108000 + 36000 + 120 \cdot 240 + 300}{240}

$L = \frac{108000 + 36000 + 120 \cdot 240 + 300}{240}$

Step 2.4.3

Multiply

120

$120$ by

240

$240$ .

L = \frac{108000 + 36000 + 28800 + 300}{240}

$L = \frac{108000 + 36000 + 28800 + 300}{240}$

L = \frac{108000 + 36000 + 28800 + 300}{240}

$L = \frac{108000 + 36000 + 28800 + 300}{240}$

Step 2.5

Reduce the expression by cancelling the common factors.

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Step 2.5.1

Add

108000

$108000$ and

36000

$36000$ .

L = \frac{144000 + 28800 + 300}{240}

$L = \frac{144000 + 28800 + 300}{240}$

Step 2.5.2

Simplify by adding numbers.

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Step 2.5.2.1

Add

144000

$144000$ and

28800

$28800$ .

L = \frac{172800 + 300}{240}

$L = \frac{172800 + 300}{240}$

Step 2.5.2.2

Add

172800

$172800$ and

300

$300$ .

L = \frac{173100}{240}

$L = \frac{173100}{240}$

L = \frac{173100}{240}

$L = \frac{173100}{240}$

Step 2.5.3

Cancel the common factor of

173100

$173100$ and

240

$240$ .

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Step 2.5.3.1

Factor

60

$60$ out of

173100

$173100$ .

L = \frac{60 (2885)}{240}

$L = \frac{60 (2885)}{240}$

Step 2.5.3.2

Cancel the common factors.

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Step 2.5.3.2.1

Factor

60

$60$ out of

240

$240$ .

L = \frac{60 \cdot 2885}{60 \cdot 4}

$L = \frac{60 \cdot 2885}{60 \cdot 4}$

Step 2.5.3.2.2

Cancel the common factor.

$L = \frac{60 \cdot 2885}{60 \cdot 4}$

Step 2.5.3.2.3

Rewrite the expression.

$L = \frac{2885}{4}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$L = \frac{2885}{4}$

Decimal Form:

$L = 721.25$

Mixed Number Form:

$L = 721 \frac{1}{4}$