Basic Math Examples

$\frac{1}{6} - \frac{4}{36} + \frac{9}{216} - \frac{16}{1296} + \frac{25}{7775} - \frac{36}{46656}$

Step 1

Find the common denominator.

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Step 1.1

Multiply $\frac{1}{6}$ by $\frac{60458400}{60458400}$ .

$\frac{1}{6} \cdot \frac{60458400}{60458400} - \frac{4}{36} + \frac{9}{216} - \frac{16}{1296} + \frac{25}{7775} - \frac{36}{46656}$

Step 1.2

Multiply $\frac{1}{6}$ by $\frac{60458400}{60458400}$ .

$\frac{60458400}{6 \cdot 60458400} - \frac{4}{36} + \frac{9}{216} - \frac{16}{1296} + \frac{25}{7775} - \frac{36}{46656}$

Step 1.3

Multiply $\frac{4}{36}$ by $\frac{10076400}{10076400}$ .

$\frac{60458400}{6 \cdot 60458400} - (\frac{4}{36} \cdot \frac{10076400}{10076400}) + \frac{9}{216} - \frac{16}{1296} + \frac{25}{7775} - \frac{36}{46656}$

Step 1.4

Multiply $\frac{4}{36}$ by $\frac{10076400}{10076400}$ .

$\frac{60458400}{6 \cdot 60458400} - \frac{4 \cdot 10076400}{36 \cdot 10076400} + \frac{9}{216} - \frac{16}{1296} + \frac{25}{7775} - \frac{36}{46656}$

Step 1.5

Multiply $\frac{9}{216}$ by $\frac{1679400}{1679400}$ .

$\frac{60458400}{6 \cdot 60458400} - \frac{4 \cdot 10076400}{36 \cdot 10076400} + \frac{9}{216} \cdot \frac{1679400}{1679400} - \frac{16}{1296} + \frac{25}{7775} - \frac{36}{46656}$

Step 1.6

Multiply $\frac{9}{216}$ by $\frac{1679400}{1679400}$ .

$\frac{60458400}{6 \cdot 60458400} - \frac{4 \cdot 10076400}{36 \cdot 10076400} + \frac{9 \cdot 1679400}{216 \cdot 1679400} - \frac{16}{1296} + \frac{25}{7775} - \frac{36}{46656}$

Step 1.7

Multiply $\frac{16}{1296}$ by $\frac{279900}{279900}$ .

$\frac{60458400}{6 \cdot 60458400} - \frac{4 \cdot 10076400}{36 \cdot 10076400} + \frac{9 \cdot 1679400}{216 \cdot 1679400} - (\frac{16}{1296} \cdot \frac{279900}{279900}) + \frac{25}{7775} - \frac{36}{46656}$

Step 1.8

Multiply $\frac{16}{1296}$ by $\frac{279900}{279900}$ .

$\frac{60458400}{6 \cdot 60458400} - \frac{4 \cdot 10076400}{36 \cdot 10076400} + \frac{9 \cdot 1679400}{216 \cdot 1679400} - \frac{16 \cdot 279900}{1296 \cdot 279900} + \frac{25}{7775} - \frac{36}{46656}$

Step 1.9

Multiply $\frac{25}{7775}$ by $\frac{46656}{46656}$ .

Step 1.10

Multiply $\frac{25}{7775}$ by $\frac{46656}{46656}$ .

Step 1.11

Multiply $\frac{36}{46656}$ by $\frac{7775}{7775}$ .

Step 1.12

Multiply $\frac{36}{46656}$ by $\frac{7775}{7775}$ .

Step 1.13

Multiply $6$ by $60458400$ .

$\frac{60458400}{362750400} - \frac{4 \cdot 10076400}{36 \cdot 10076400} + \frac{9 \cdot 1679400}{216 \cdot 1679400} - \frac{16 \cdot 279900}{1296 \cdot 279900} + \frac{25 \cdot 46656}{7775 \cdot 46656} - \frac{36 \cdot 7775}{46656 \cdot 7775}$

Step 1.14

Multiply $36$ by $10076400$ .

$\frac{60458400}{362750400} - \frac{4 \cdot 10076400}{362750400} + \frac{9 \cdot 1679400}{216 \cdot 1679400} - \frac{16 \cdot 279900}{1296 \cdot 279900} + \frac{25 \cdot 46656}{7775 \cdot 46656} - \frac{36 \cdot 7775}{46656 \cdot 7775}$

Step 1.15

Multiply $216$ by $1679400$ .

$\frac{60458400}{362750400} - \frac{4 \cdot 10076400}{362750400} + \frac{9 \cdot 1679400}{362750400} - \frac{16 \cdot 279900}{1296 \cdot 279900} + \frac{25 \cdot 46656}{7775 \cdot 46656} - \frac{36 \cdot 7775}{46656 \cdot 7775}$

Step 1.16

Multiply $1296$ by $279900$ .

$\frac{60458400}{362750400} - \frac{4 \cdot 10076400}{362750400} + \frac{9 \cdot 1679400}{362750400} - \frac{16 \cdot 279900}{362750400} + \frac{25 \cdot 46656}{7775 \cdot 46656} - \frac{36 \cdot 7775}{46656 \cdot 7775}$

Step 1.17

Multiply $7775$ by $46656$ .

$\frac{60458400}{362750400} - \frac{4 \cdot 10076400}{362750400} + \frac{9 \cdot 1679400}{362750400} - \frac{16 \cdot 279900}{362750400} + \frac{25 \cdot 46656}{362750400} - \frac{36 \cdot 7775}{46656 \cdot 7775}$

Step 1.18

Reorder the factors of $46656 \cdot 7775$ .

Step 1.19

Multiply $7775$ by $46656$ .

Step 2

Combine the numerators over the common denominator.

$\frac{60458400 - 4 \cdot 10076400 + 9 \cdot 1679400 - 16 \cdot 279900 + 25 \cdot 46656 - 36 \cdot 7775}{362750400}$

Step 3

Simplify each term.

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Step 3.1

Multiply $- 4$ by $10076400$ .

$\frac{60458400 - 40305600 + 9 \cdot 1679400 - 16 \cdot 279900 + 25 \cdot 46656 - 36 \cdot 7775}{362750400}$

Step 3.2

Multiply $9$ by $1679400$ .

$\frac{60458400 - 40305600 + 15114600 - 16 \cdot 279900 + 25 \cdot 46656 - 36 \cdot 7775}{362750400}$

Step 3.3

Multiply $- 16$ by $279900$ .

$\frac{60458400 - 40305600 + 15114600 - 4478400 + 25 \cdot 46656 - 36 \cdot 7775}{362750400}$

Step 3.4

Multiply $25$ by $46656$ .

$\frac{60458400 - 40305600 + 15114600 - 4478400 + 1166400 - 36 \cdot 7775}{362750400}$

Step 3.5

Multiply $- 36$ by $7775$ .

$\frac{60458400 - 40305600 + 15114600 - 4478400 + 1166400 - 279900}{362750400}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Subtract $40305600$ from $60458400$ .

$\frac{20152800 + 15114600 - 4478400 + 1166400 - 279900}{362750400}$

Step 4.2

Simplify by adding and subtracting.

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Step 4.2.1

Add $20152800$ and $15114600$ .

$\frac{35267400 - 4478400 + 1166400 - 279900}{362750400}$

Step 4.2.2

Subtract $4478400$ from $35267400$ .

$\frac{30789000 + 1166400 - 279900}{362750400}$

Step 4.2.3

Add $30789000$ and $1166400$ .

$\frac{31955400 - 279900}{362750400}$

Step 4.2.4

Subtract $279900$ from $31955400$ .

$\frac{31675500}{362750400}$

Step 4.3

Cancel the common factor of $31675500$ and $362750400$ .

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Step 4.3.1

Factor $900$ out of $31675500$ .

$\frac{900 (35195)}{362750400}$

Step 4.3.2

Cancel the common factors.

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Step 4.3.2.1

Factor $900$ out of $362750400$ .

$\frac{900 \cdot 35195}{900 \cdot 403056}$

Step 4.3.2.2

Cancel the common factor.

$\frac{900 \cdot 35195}{900 \cdot 403056}$

Step 4.3.2.3

Rewrite the expression.

$\frac{35195}{403056}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{35195}{403056}$

Decimal Form:

$0.08732037 \dots$