Basic Math Examples

$100 \cdot \frac{13}{57} + 200 \cdot \frac{6}{57} + 300 \cdot \frac{12}{57} + 400 \cdot \frac{8}{57} + 500 \cdot \frac{8}{57} + 600 \cdot \frac{10}{57}$

Step 1

Simplify each term.

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Step 1.1

Multiply $100 (\frac{13}{57})$ .

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Step 1.1.1

Combine $100$ and $\frac{13}{57}$ .

$\frac{100 \cdot 13}{57} + 200 \cdot \frac{6}{57} + 300 \cdot \frac{12}{57} + 400 \cdot \frac{8}{57} + 500 \cdot \frac{8}{57} + 600 \cdot \frac{10}{57}$

Step 1.1.2

Multiply $100$ by $13$ .

$\frac{1300}{57} + 200 \cdot \frac{6}{57} + 300 \cdot \frac{12}{57} + 400 \cdot \frac{8}{57} + 500 \cdot \frac{8}{57} + 600 \cdot \frac{10}{57}$

Step 1.2

Cancel the common factor of $6$ and $57$ .

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Step 1.2.1

Factor $3$ out of $6$ .

$\frac{1300}{57} + 200 \cdot \frac{3 (2)}{57} + 300 \cdot \frac{12}{57} + 400 \cdot \frac{8}{57} + 500 \cdot \frac{8}{57} + 600 \cdot \frac{10}{57}$

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Factor $3$ out of $57$ .

$\frac{1300}{57} + 200 \cdot \frac{3 \cdot 2}{3 \cdot 19} + 300 \cdot \frac{12}{57} + 400 \cdot \frac{8}{57} + 500 \cdot \frac{8}{57} + 600 \cdot \frac{10}{57}$

Step 1.2.2.2

Cancel the common factor.

$\frac{1300}{57} + 200 \cdot \frac{3 \cdot 2}{3 \cdot 19} + 300 \cdot \frac{12}{57} + 400 \cdot \frac{8}{57} + 500 \cdot \frac{8}{57} + 600 \cdot \frac{10}{57}$

Step 1.2.2.3

Rewrite the expression.

$\frac{1300}{57} + 200 \cdot \frac{2}{19} + 300 \cdot \frac{12}{57} + 400 \cdot \frac{8}{57} + 500 \cdot \frac{8}{57} + 600 \cdot \frac{10}{57}$

Step 1.3

Multiply $200 (\frac{2}{19})$ .

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Step 1.3.1

Combine $200$ and $\frac{2}{19}$ .

$\frac{1300}{57} + \frac{200 \cdot 2}{19} + 300 \cdot \frac{12}{57} + 400 \cdot \frac{8}{57} + 500 \cdot \frac{8}{57} + 600 \cdot \frac{10}{57}$

Step 1.3.2

Multiply $200$ by $2$ .

$\frac{1300}{57} + \frac{400}{19} + 300 \cdot \frac{12}{57} + 400 \cdot \frac{8}{57} + 500 \cdot \frac{8}{57} + 600 \cdot \frac{10}{57}$

Step 1.4

Cancel the common factor of $3$ .

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Step 1.4.1

Factor $3$ out of $300$ .

$\frac{1300}{57} + \frac{400}{19} + 3 (100) \cdot \frac{12}{57} + 400 \cdot \frac{8}{57} + 500 \cdot \frac{8}{57} + 600 \cdot \frac{10}{57}$

Step 1.4.2

Factor $3$ out of $57$ .

$\frac{1300}{57} + \frac{400}{19} + 3 \cdot 100 \cdot \frac{12}{3 \cdot 19} + 400 \cdot \frac{8}{57} + 500 \cdot \frac{8}{57} + 600 \cdot \frac{10}{57}$

Step 1.4.3

Cancel the common factor.

$\frac{1300}{57} + \frac{400}{19} + 3 \cdot 100 \cdot \frac{12}{3 \cdot 19} + 400 \cdot \frac{8}{57} + 500 \cdot \frac{8}{57} + 600 \cdot \frac{10}{57}$

Step 1.4.4

Rewrite the expression.

$\frac{1300}{57} + \frac{400}{19} + 100 \cdot \frac{12}{19} + 400 \cdot \frac{8}{57} + 500 \cdot \frac{8}{57} + 600 \cdot \frac{10}{57}$

Step 1.5

Combine $100$ and $\frac{12}{19}$ .

$\frac{1300}{57} + \frac{400}{19} + \frac{100 \cdot 12}{19} + 400 \cdot \frac{8}{57} + 500 \cdot \frac{8}{57} + 600 \cdot \frac{10}{57}$

Step 1.6

Multiply $100$ by $12$ .

$\frac{1300}{57} + \frac{400}{19} + \frac{1200}{19} + 400 \cdot \frac{8}{57} + 500 \cdot \frac{8}{57} + 600 \cdot \frac{10}{57}$

Step 1.7

Multiply $400 (\frac{8}{57})$ .

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Step 1.7.1

Combine $400$ and $\frac{8}{57}$ .

$\frac{1300}{57} + \frac{400}{19} + \frac{1200}{19} + \frac{400 \cdot 8}{57} + 500 \cdot \frac{8}{57} + 600 \cdot \frac{10}{57}$

Step 1.7.2

Multiply $400$ by $8$ .

$\frac{1300}{57} + \frac{400}{19} + \frac{1200}{19} + \frac{3200}{57} + 500 \cdot \frac{8}{57} + 600 \cdot \frac{10}{57}$

Step 1.8

Multiply $500 (\frac{8}{57})$ .

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Step 1.8.1

Combine $500$ and $\frac{8}{57}$ .

$\frac{1300}{57} + \frac{400}{19} + \frac{1200}{19} + \frac{3200}{57} + \frac{500 \cdot 8}{57} + 600 \cdot \frac{10}{57}$

Step 1.8.2

Multiply $500$ by $8$ .

$\frac{1300}{57} + \frac{400}{19} + \frac{1200}{19} + \frac{3200}{57} + \frac{4000}{57} + 600 \cdot \frac{10}{57}$

Step 1.9

Cancel the common factor of $3$ .

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Step 1.9.1

Factor $3$ out of $600$ .

$\frac{1300}{57} + \frac{400}{19} + \frac{1200}{19} + \frac{3200}{57} + \frac{4000}{57} + 3 (200) \cdot \frac{10}{57}$

Step 1.9.2

Factor $3$ out of $57$ .

$\frac{1300}{57} + \frac{400}{19} + \frac{1200}{19} + \frac{3200}{57} + \frac{4000}{57} + 3 \cdot 200 \cdot \frac{10}{3 \cdot 19}$

Step 1.9.3

Cancel the common factor.

$\frac{1300}{57} + \frac{400}{19} + \frac{1200}{19} + \frac{3200}{57} + \frac{4000}{57} + 3 \cdot 200 \cdot \frac{10}{3 \cdot 19}$

Step 1.9.4

Rewrite the expression.

$\frac{1300}{57} + \frac{400}{19} + \frac{1200}{19} + \frac{3200}{57} + \frac{4000}{57} + 200 \cdot \frac{10}{19}$

Step 1.10

Combine $200$ and $\frac{10}{19}$ .

$\frac{1300}{57} + \frac{400}{19} + \frac{1200}{19} + \frac{3200}{57} + \frac{4000}{57} + \frac{200 \cdot 10}{19}$

Step 1.11

Multiply $200$ by $10$ .

$\frac{1300}{57} + \frac{400}{19} + \frac{1200}{19} + \frac{3200}{57} + \frac{4000}{57} + \frac{2000}{19}$

Step 2

Combine fractions.

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Step 2.1

Combine the numerators over the common denominator.

$\frac{1300 + 3200 + 4000}{57} + \frac{400 + 1200 + 2000}{19}$

Step 2.2

Simplify by adding numbers.

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Step 2.2.1

Add $1300$ and $3200$ .

$\frac{4500 + 4000}{57} + \frac{400 + 1200 + 2000}{19}$

Step 2.2.2

Add $4500$ and $4000$ .

$\frac{8500}{57} + \frac{400 + 1200 + 2000}{19}$

Step 2.2.3

Add $400$ and $1200$ .

$\frac{8500}{57} + \frac{1600 + 2000}{19}$

Step 2.2.4

Add $1600$ and $2000$ .

$\frac{8500}{57} + \frac{3600}{19}$

Step 3

To write $\frac{3600}{19}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{8500}{57} + \frac{3600}{19} \cdot \frac{3}{3}$

Step 4

Write each expression with a common denominator of $57$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{3600}{19}$ by $\frac{3}{3}$ .

$\frac{8500}{57} + \frac{3600 \cdot 3}{19 \cdot 3}$

Step 4.2

Multiply $19$ by $3$ .

$\frac{8500}{57} + \frac{3600 \cdot 3}{57}$

Step 5

Combine the numerators over the common denominator.

$\frac{8500 + 3600 \cdot 3}{57}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $3600$ by $3$ .

$\frac{8500 + 10800}{57}$

Step 6.2

Add $8500$ and $10800$ .

$\frac{19300}{57}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{19300}{57}$

Decimal Form:

$338.59649122 \dots$

Mixed Number Form:

$338 \frac{34}{57}$