Finite Math Examples

$100 (\frac{14}{75}) + 200 (\frac{11}{75}) + 300 (\frac{9}{75}) + 400 (\frac{21}{75}) + 500 (\frac{12}{75}) + 600 (\frac{8}{75})$

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $25$ .

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Step 1.1.1

Factor $25$ out of $100$ .

$25 (4) \frac{14}{75} + 200 (\frac{11}{75}) + 300 (\frac{9}{75}) + 400 (\frac{21}{75}) + 500 (\frac{12}{75}) + 600 (\frac{8}{75})$

Step 1.1.2

Factor $25$ out of $75$ .

$25 \cdot 4 \frac{14}{25 \cdot 3} + 200 (\frac{11}{75}) + 300 (\frac{9}{75}) + 400 (\frac{21}{75}) + 500 (\frac{12}{75}) + 600 (\frac{8}{75})$

Step 1.1.3

Cancel the common factor.

$25 \cdot 4 \frac{14}{25 \cdot 3} + 200 (\frac{11}{75}) + 300 (\frac{9}{75}) + 400 (\frac{21}{75}) + 500 (\frac{12}{75}) + 600 (\frac{8}{75})$

Step 1.1.4

Rewrite the expression.

$4 (\frac{14}{3}) + 200 (\frac{11}{75}) + 300 (\frac{9}{75}) + 400 (\frac{21}{75}) + 500 (\frac{12}{75}) + 600 (\frac{8}{75})$

Step 1.2

Combine $4$ and $\frac{14}{3}$ .

$\frac{4 \cdot 14}{3} + 200 (\frac{11}{75}) + 300 (\frac{9}{75}) + 400 (\frac{21}{75}) + 500 (\frac{12}{75}) + 600 (\frac{8}{75})$

Step 1.3

Multiply $4$ by $14$ .

$\frac{56}{3} + 200 (\frac{11}{75}) + 300 (\frac{9}{75}) + 400 (\frac{21}{75}) + 500 (\frac{12}{75}) + 600 (\frac{8}{75})$

Step 1.4

Cancel the common factor of $25$ .

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Step 1.4.1

Factor $25$ out of $200$ .

$\frac{56}{3} + 25 (8) \frac{11}{75} + 300 (\frac{9}{75}) + 400 (\frac{21}{75}) + 500 (\frac{12}{75}) + 600 (\frac{8}{75})$

Step 1.4.2

Factor $25$ out of $75$ .

$\frac{56}{3} + 25 \cdot 8 \frac{11}{25 \cdot 3} + 300 (\frac{9}{75}) + 400 (\frac{21}{75}) + 500 (\frac{12}{75}) + 600 (\frac{8}{75})$

Step 1.4.3

Cancel the common factor.

$\frac{56}{3} + 25 \cdot 8 \frac{11}{25 \cdot 3} + 300 (\frac{9}{75}) + 400 (\frac{21}{75}) + 500 (\frac{12}{75}) + 600 (\frac{8}{75})$

Step 1.4.4

Rewrite the expression.

$\frac{56}{3} + 8 (\frac{11}{3}) + 300 (\frac{9}{75}) + 400 (\frac{21}{75}) + 500 (\frac{12}{75}) + 600 (\frac{8}{75})$

Step 1.5

Combine $8$ and $\frac{11}{3}$ .

$\frac{56}{3} + \frac{8 \cdot 11}{3} + 300 (\frac{9}{75}) + 400 (\frac{21}{75}) + 500 (\frac{12}{75}) + 600 (\frac{8}{75})$

Step 1.6

Multiply $8$ by $11$ .

$\frac{56}{3} + \frac{88}{3} + 300 (\frac{9}{75}) + 400 (\frac{21}{75}) + 500 (\frac{12}{75}) + 600 (\frac{8}{75})$

Step 1.7

Cancel the common factor of $75$ .

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Step 1.7.1

Factor $75$ out of $300$ .

$\frac{56}{3} + \frac{88}{3} + 75 (4) \frac{9}{75} + 400 (\frac{21}{75}) + 500 (\frac{12}{75}) + 600 (\frac{8}{75})$

Step 1.7.2

Cancel the common factor.

$\frac{56}{3} + \frac{88}{3} + 75 \cdot 4 \frac{9}{75} + 400 (\frac{21}{75}) + 500 (\frac{12}{75}) + 600 (\frac{8}{75})$

Step 1.7.3

Rewrite the expression.

$\frac{56}{3} + \frac{88}{3} + 4 \cdot 9 + 400 (\frac{21}{75}) + 500 (\frac{12}{75}) + 600 (\frac{8}{75})$

Step 1.8

Multiply $4$ by $9$ .

$\frac{56}{3} + \frac{88}{3} + 36 + 400 (\frac{21}{75}) + 500 (\frac{12}{75}) + 600 (\frac{8}{75})$

Step 1.9

Cancel the common factor of $25$ .

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Step 1.9.1

Factor $25$ out of $400$ .

$\frac{56}{3} + \frac{88}{3} + 36 + 25 (16) \frac{21}{75} + 500 (\frac{12}{75}) + 600 (\frac{8}{75})$

Step 1.9.2

Factor $25$ out of $75$ .

$\frac{56}{3} + \frac{88}{3} + 36 + 25 \cdot 16 \frac{21}{25 \cdot 3} + 500 (\frac{12}{75}) + 600 (\frac{8}{75})$

Step 1.9.3

Cancel the common factor.

$\frac{56}{3} + \frac{88}{3} + 36 + 25 \cdot 16 \frac{21}{25 \cdot 3} + 500 (\frac{12}{75}) + 600 (\frac{8}{75})$

Step 1.9.4

Rewrite the expression.

$\frac{56}{3} + \frac{88}{3} + 36 + 16 (\frac{21}{3}) + 500 (\frac{12}{75}) + 600 (\frac{8}{75})$

Step 1.10

Combine $16$ and $\frac{21}{3}$ .

$\frac{56}{3} + \frac{88}{3} + 36 + \frac{16 \cdot 21}{3} + 500 (\frac{12}{75}) + 600 (\frac{8}{75})$

Step 1.11

Multiply $16$ by $21$ .

$\frac{56}{3} + \frac{88}{3} + 36 + \frac{336}{3} + 500 (\frac{12}{75}) + 600 (\frac{8}{75})$

Step 1.12

Divide $336$ by $3$ .

$\frac{56}{3} + \frac{88}{3} + 36 + 112 + 500 (\frac{12}{75}) + 600 (\frac{8}{75})$

Step 1.13

Cancel the common factor of $25$ .

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Step 1.13.1

Factor $25$ out of $500$ .

$\frac{56}{3} + \frac{88}{3} + 36 + 112 + 25 (20) \frac{12}{75} + 600 (\frac{8}{75})$

Step 1.13.2

Factor $25$ out of $75$ .

$\frac{56}{3} + \frac{88}{3} + 36 + 112 + 25 \cdot 20 \frac{12}{25 \cdot 3} + 600 (\frac{8}{75})$

Step 1.13.3

Cancel the common factor.

$\frac{56}{3} + \frac{88}{3} + 36 + 112 + 25 \cdot 20 \frac{12}{25 \cdot 3} + 600 (\frac{8}{75})$

Step 1.13.4

Rewrite the expression.

$\frac{56}{3} + \frac{88}{3} + 36 + 112 + 20 (\frac{12}{3}) + 600 (\frac{8}{75})$

Step 1.14

Combine $20$ and $\frac{12}{3}$ .

$\frac{56}{3} + \frac{88}{3} + 36 + 112 + \frac{20 \cdot 12}{3} + 600 (\frac{8}{75})$

Step 1.15

Multiply $20$ by $12$ .

$\frac{56}{3} + \frac{88}{3} + 36 + 112 + \frac{240}{3} + 600 (\frac{8}{75})$

Step 1.16

Divide $240$ by $3$ .

$\frac{56}{3} + \frac{88}{3} + 36 + 112 + 80 + 600 (\frac{8}{75})$

Step 1.17

Cancel the common factor of $75$ .

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Step 1.17.1

Factor $75$ out of $600$ .

$\frac{56}{3} + \frac{88}{3} + 36 + 112 + 80 + 75 (8) \frac{8}{75}$

Step 1.17.2

Cancel the common factor.

$\frac{56}{3} + \frac{88}{3} + 36 + 112 + 80 + 75 \cdot 8 \frac{8}{75}$

Step 1.17.3

Rewrite the expression.

$\frac{56}{3} + \frac{88}{3} + 36 + 112 + 80 + 8 \cdot 8$

Step 1.18

Multiply $8$ by $8$ .

$\frac{56}{3} + \frac{88}{3} + 36 + 112 + 80 + 64$

Step 2

Combine fractions.

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Step 2.1

Combine the numerators over the common denominator.

$36 + 112 + 80 + 64 + \frac{56 + 88}{3}$

Step 2.2

Add $56$ and $88$ .

$36 + 112 + 80 + 64 + \frac{144}{3}$

Step 3

Find the common denominator.

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Step 3.1

Write $36$ as a fraction with denominator $1$ .

$\frac{36}{1} + 112 + 80 + 64 + \frac{144}{3}$

Step 3.2

Multiply $\frac{36}{1}$ by $\frac{3}{3}$ .

$\frac{36}{1} \cdot \frac{3}{3} + 112 + 80 + 64 + \frac{144}{3}$

Step 3.3

Multiply $\frac{36}{1}$ by $\frac{3}{3}$ .

$\frac{36 \cdot 3}{3} + 112 + 80 + 64 + \frac{144}{3}$

Step 3.4

Write $112$ as a fraction with denominator $1$ .

$\frac{36 \cdot 3}{3} + \frac{112}{1} + 80 + 64 + \frac{144}{3}$

Step 3.5

Multiply $\frac{112}{1}$ by $\frac{3}{3}$ .

$\frac{36 \cdot 3}{3} + \frac{112}{1} \cdot \frac{3}{3} + 80 + 64 + \frac{144}{3}$

Step 3.6

Multiply $\frac{112}{1}$ by $\frac{3}{3}$ .

$\frac{36 \cdot 3}{3} + \frac{112 \cdot 3}{3} + 80 + 64 + \frac{144}{3}$

Step 3.7

Write $80$ as a fraction with denominator $1$ .

$\frac{36 \cdot 3}{3} + \frac{112 \cdot 3}{3} + \frac{80}{1} + 64 + \frac{144}{3}$

Step 3.8

Multiply $\frac{80}{1}$ by $\frac{3}{3}$ .

$\frac{36 \cdot 3}{3} + \frac{112 \cdot 3}{3} + \frac{80}{1} \cdot \frac{3}{3} + 64 + \frac{144}{3}$

Step 3.9

Multiply $\frac{80}{1}$ by $\frac{3}{3}$ .

$\frac{36 \cdot 3}{3} + \frac{112 \cdot 3}{3} + \frac{80 \cdot 3}{3} + 64 + \frac{144}{3}$

Step 3.10

Write $64$ as a fraction with denominator $1$ .

$\frac{36 \cdot 3}{3} + \frac{112 \cdot 3}{3} + \frac{80 \cdot 3}{3} + \frac{64}{1} + \frac{144}{3}$

Step 3.11

Multiply $\frac{64}{1}$ by $\frac{3}{3}$ .

$\frac{36 \cdot 3}{3} + \frac{112 \cdot 3}{3} + \frac{80 \cdot 3}{3} + \frac{64}{1} \cdot \frac{3}{3} + \frac{144}{3}$

Step 3.12

Multiply $\frac{64}{1}$ by $\frac{3}{3}$ .

$\frac{36 \cdot 3}{3} + \frac{112 \cdot 3}{3} + \frac{80 \cdot 3}{3} + \frac{64 \cdot 3}{3} + \frac{144}{3}$

Step 4

Combine the numerators over the common denominator.

$\frac{36 \cdot 3 + 112 \cdot 3 + 80 \cdot 3 + 64 \cdot 3 + 144}{3}$

Step 5

Simplify each term.

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Step 5.1

Multiply $36$ by $3$ .

$\frac{108 + 112 \cdot 3 + 80 \cdot 3 + 64 \cdot 3 + 144}{3}$

Step 5.2

Multiply $112$ by $3$ .

$\frac{108 + 336 + 80 \cdot 3 + 64 \cdot 3 + 144}{3}$

Step 5.3

Multiply $80$ by $3$ .

$\frac{108 + 336 + 240 + 64 \cdot 3 + 144}{3}$

Step 5.4

Multiply $64$ by $3$ .

$\frac{108 + 336 + 240 + 192 + 144}{3}$

Step 6

Simplify the expression.

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Step 6.1

Add $108$ and $336$ .

$\frac{444 + 240 + 192 + 144}{3}$

Step 6.2

Add $444$ and $240$ .

$\frac{684 + 192 + 144}{3}$

Step 6.3

Add $684$ and $192$ .

$\frac{876 + 144}{3}$

Step 6.4

Add $876$ and $144$ .

$\frac{1020}{3}$

Step 6.5

Divide $1020$ by $3$ .

$340$