Basic Math Examples

$\frac{250 \cdot \frac{448}{658} + 1000 \cdot \frac{33}{658} + 12.5 \cdot \frac{4620}{658} + 6.25 - (1250 \frac{22}{658})}{3}$

Step 1

Convert $1250 \frac{22}{658}$ to an improper fraction.

Tap for more steps...

Step 1.1

A mixed number is an addition of its whole and fractional parts.

$\frac{250 \cdot \frac{448}{658} + 1000 \cdot \frac{33}{658} + 12.5 \cdot \frac{4620}{658} + 6.25 - (1250 + \frac{22}{658})}{3}$

Step 1.2

Add $1250$ and $\frac{22}{658}$ .

Tap for more steps...

Step 1.2.1

To write $1250$ as a fraction with a common denominator, multiply by $\frac{658}{658}$ .

$\frac{250 \cdot \frac{448}{658} + 1000 \cdot \frac{33}{658} + 12.5 \cdot \frac{4620}{658} + 6.25 - (1250 \cdot \frac{658}{658} + \frac{22}{658})}{3}$

Step 1.2.2

Combine $1250$ and $\frac{658}{658}$ .

$\frac{250 \cdot \frac{448}{658} + 1000 \cdot \frac{33}{658} + 12.5 \cdot \frac{4620}{658} + 6.25 - (\frac{1250 \cdot 658}{658} + \frac{22}{658})}{3}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{250 \cdot \frac{448}{658} + 1000 \cdot \frac{33}{658} + 12.5 \cdot \frac{4620}{658} + 6.25 - \frac{1250 \cdot 658 + 22}{658}}{3}$

Step 1.2.4

Simplify the numerator.

Tap for more steps...

Step 1.2.4.1

Multiply $1250$ by $658$ .

$\frac{250 \cdot \frac{448}{658} + 1000 \cdot \frac{33}{658} + 12.5 \cdot \frac{4620}{658} + 6.25 - \frac{822500 + 22}{658}}{3}$

Step 1.2.4.2

Add $822500$ and $22$ .

$\frac{250 \cdot \frac{448}{658} + 1000 \cdot \frac{33}{658} + 12.5 \cdot \frac{4620}{658} + 6.25 - \frac{822522}{658}}{3}$

Step 2

Reduce the expression by cancelling the common factors.

Tap for more steps...

Step 2.1

Cancel the common factor of $448$ and $658$ .

Tap for more steps...

Step 2.1.1

Factor $14$ out of $448$ .

$\frac{250 \cdot \frac{14 (32)}{658} + 1000 \cdot \frac{33}{658} + 12.5 \cdot \frac{4620}{658} + 6.25 - \frac{822522}{658}}{3}$

Step 2.1.2

Cancel the common factors.

Tap for more steps...

Step 2.1.2.1

Factor $14$ out of $658$ .

$\frac{250 \cdot \frac{14 \cdot 32}{14 \cdot 47} + 1000 \cdot \frac{33}{658} + 12.5 \cdot \frac{4620}{658} + 6.25 - \frac{822522}{658}}{3}$

Step 2.1.2.2

Cancel the common factor.

$\frac{250 \cdot \frac{14 \cdot 32}{14 \cdot 47} + 1000 \cdot \frac{33}{658} + 12.5 \cdot \frac{4620}{658} + 6.25 - \frac{822522}{658}}{3}$

Step 2.1.2.3

Rewrite the expression.

$\frac{250 \cdot \frac{32}{47} + 1000 \cdot \frac{33}{658} + 12.5 \cdot \frac{4620}{658} + 6.25 - \frac{822522}{658}}{3}$

Step 2.2

Cancel the common factor of $4620$ and $658$ .

Tap for more steps...

Step 2.2.1

Factor $14$ out of $4620$ .

$\frac{250 \cdot \frac{32}{47} + 1000 \cdot \frac{33}{658} + 12.5 \cdot \frac{14 (330)}{658} + 6.25 - \frac{822522}{658}}{3}$

Step 2.2.2

Cancel the common factors.

Tap for more steps...

Step 2.2.2.1

Factor $14$ out of $658$ .

$\frac{250 \cdot \frac{32}{47} + 1000 \cdot \frac{33}{658} + 12.5 \cdot \frac{14 \cdot 330}{14 \cdot 47} + 6.25 - \frac{822522}{658}}{3}$

Step 2.2.2.2

Cancel the common factor.

$\frac{250 \cdot \frac{32}{47} + 1000 \cdot \frac{33}{658} + 12.5 \cdot \frac{14 \cdot 330}{14 \cdot 47} + 6.25 - \frac{822522}{658}}{3}$

Step 2.2.2.3

Rewrite the expression.

$\frac{250 \cdot \frac{32}{47} + 1000 \cdot \frac{33}{658} + 12.5 \cdot \frac{330}{47} + 6.25 - \frac{822522}{658}}{3}$

Step 2.3

Cancel the common factor of $822522$ and $658$ .

Tap for more steps...

Step 2.3.1

Factor $2$ out of $822522$ .

$\frac{250 \cdot \frac{32}{47} + 1000 \cdot \frac{33}{658} + 12.5 \cdot \frac{330}{47} + 6.25 - \frac{2 (411261)}{658}}{3}$

Step 2.3.2

Cancel the common factors.

Tap for more steps...

Step 2.3.2.1

Factor $2$ out of $658$ .

$\frac{250 \cdot \frac{32}{47} + 1000 \cdot \frac{33}{658} + 12.5 \cdot \frac{330}{47} + 6.25 - \frac{2 \cdot 411261}{2 \cdot 329}}{3}$

Step 2.3.2.2

Cancel the common factor.

$\frac{250 \cdot \frac{32}{47} + 1000 \cdot \frac{33}{658} + 12.5 \cdot \frac{330}{47} + 6.25 - \frac{2 \cdot 411261}{2 \cdot 329}}{3}$

Step 2.3.2.3

Rewrite the expression.

$\frac{250 \cdot \frac{32}{47} + 1000 \cdot \frac{33}{658} + 12.5 \cdot \frac{330}{47} + 6.25 - \frac{411261}{329}}{3}$

Step 3

Simplify the numerator.

Tap for more steps...

Step 3.1

Multiply $250 (\frac{32}{47})$ .

Tap for more steps...

Step 3.1.1

Combine $250$ and $\frac{32}{47}$ .

$\frac{\frac{250 \cdot 32}{47} + 1000 \cdot \frac{33}{658} + 12.5 \cdot \frac{330}{47} + 6.25 - \frac{411261}{329}}{3}$

Step 3.1.2

Multiply $250$ by $32$ .

$\frac{\frac{8000}{47} + 1000 \cdot \frac{33}{658} + 12.5 \cdot \frac{330}{47} + 6.25 - \frac{411261}{329}}{3}$

Step 3.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.2.1

Factor $2$ out of $1000$ .

$\frac{\frac{8000}{47} + 2 (500) \cdot \frac{33}{658} + 12.5 \cdot \frac{330}{47} + 6.25 - \frac{411261}{329}}{3}$

Step 3.2.2

Factor $2$ out of $658$ .

$\frac{\frac{8000}{47} + 2 \cdot 500 \cdot \frac{33}{2 \cdot 329} + 12.5 \cdot \frac{330}{47} + 6.25 - \frac{411261}{329}}{3}$

Step 3.2.3

Cancel the common factor.

$\frac{\frac{8000}{47} + 2 \cdot 500 \cdot \frac{33}{2 \cdot 329} + 12.5 \cdot \frac{330}{47} + 6.25 - \frac{411261}{329}}{3}$

Step 3.2.4

Rewrite the expression.

$\frac{\frac{8000}{47} + 500 \cdot \frac{33}{329} + 12.5 \cdot \frac{330}{47} + 6.25 - \frac{411261}{329}}{3}$

Step 3.3

Combine $500$ and $\frac{33}{329}$ .

$\frac{\frac{8000}{47} + \frac{500 \cdot 33}{329} + 12.5 \cdot \frac{330}{47} + 6.25 - \frac{411261}{329}}{3}$

Step 3.4

Multiply $500$ by $33$ .

$\frac{\frac{8000}{47} + \frac{16500}{329} + 12.5 \cdot \frac{330}{47} + 6.25 - \frac{411261}{329}}{3}$

Step 3.5

Multiply $12.5 (\frac{330}{47})$ .

Tap for more steps...

Step 3.5.1

Combine $12.5$ and $\frac{330}{47}$ .

$\frac{\frac{8000}{47} + \frac{16500}{329} + \frac{12.5 \cdot 330}{47} + 6.25 - \frac{411261}{329}}{3}$

Step 3.5.2

Multiply $12.5$ by $330$ .

$\frac{\frac{8000}{47} + \frac{16500}{329} + \frac{4125}{47} + 6.25 - \frac{411261}{329}}{3}$

Step 3.6

Cancel the common factor of $4125$ and $47$ .

Tap for more steps...

Step 3.6.1

Rewrite $4125$ as $1 (4125)$ .

$\frac{\frac{8000}{47} + \frac{16500}{329} + \frac{1 (4125)}{47} + 6.25 - \frac{411261}{329}}{3}$

Step 3.6.2

Cancel the common factors.

Tap for more steps...

Step 3.6.2.1

Rewrite $47$ as $1 (47)$ .

$\frac{\frac{8000}{47} + \frac{16500}{329} + \frac{1 \cdot 4125}{1 \cdot 47} + 6.25 - \frac{411261}{329}}{3}$

Step 3.6.2.2

Cancel the common factor.

$\frac{\frac{8000}{47} + \frac{16500}{329} + \frac{1 \cdot 4125}{1 \cdot 47} + 6.25 - \frac{411261}{329}}{3}$

Step 3.6.2.3

Rewrite the expression.

$\frac{\frac{8000}{47} + \frac{16500}{329} + \frac{4125}{47} + 6.25 - \frac{411261}{329}}{3}$

Step 3.7

To write $\frac{8000}{47}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{\frac{8000}{47} \cdot \frac{7}{7} + \frac{16500}{329} + \frac{4125}{47} + 6.25 - \frac{411261}{329}}{3}$

Step 3.8

Write each expression with a common denominator of $329$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 3.8.1

Multiply $\frac{8000}{47}$ by $\frac{7}{7}$ .

$\frac{\frac{8000 \cdot 7}{47 \cdot 7} + \frac{16500}{329} + \frac{4125}{47} + 6.25 - \frac{411261}{329}}{3}$

Step 3.8.2

Multiply $47$ by $7$ .

$\frac{\frac{8000 \cdot 7}{329} + \frac{16500}{329} + \frac{4125}{47} + 6.25 - \frac{411261}{329}}{3}$

Step 3.9

Combine the numerators over the common denominator.

$\frac{\frac{8000 \cdot 7 + 16500}{329} + \frac{4125}{47} + 6.25 - \frac{411261}{329}}{3}$

Step 3.10

Simplify the numerator.

Tap for more steps...

Step 3.10.1

Multiply $8000$ by $7$ .

$\frac{\frac{56000 + 16500}{329} + \frac{4125}{47} + 6.25 - \frac{411261}{329}}{3}$

Step 3.10.2

Add $56000$ and $16500$ .

$\frac{\frac{72500}{329} + \frac{4125}{47} + 6.25 - \frac{411261}{329}}{3}$

Step 3.11

To write $\frac{4125}{47}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{\frac{72500}{329} + \frac{4125}{47} \cdot \frac{7}{7} + 6.25 - \frac{411261}{329}}{3}$

Step 3.12

Write each expression with a common denominator of $329$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 3.12.1

Multiply $\frac{4125}{47}$ by $\frac{7}{7}$ .

$\frac{\frac{72500}{329} + \frac{4125 \cdot 7}{47 \cdot 7} + 6.25 - \frac{411261}{329}}{3}$

Step 3.12.2

Multiply $47$ by $7$ .

$\frac{\frac{72500}{329} + \frac{4125 \cdot 7}{329} + 6.25 - \frac{411261}{329}}{3}$

Step 3.13

Combine the numerators over the common denominator.

$\frac{\frac{72500 + 4125 \cdot 7}{329} + 6.25 - \frac{411261}{329}}{3}$

Step 3.14

Simplify the numerator.

Tap for more steps...

Step 3.14.1

Multiply $4125$ by $7$ .

$\frac{\frac{72500 + 28875}{329} + 6.25 - \frac{411261}{329}}{3}$

Step 3.14.2

Add $72500$ and $28875$ .

$\frac{\frac{101375}{329} + 6.25 - \frac{411261}{329}}{3}$

Step 3.15

To write $6.25$ as a fraction with a common denominator, multiply by $\frac{329}{329}$ .

$\frac{\frac{101375}{329} + 6.25 \cdot \frac{329}{329} - \frac{411261}{329}}{3}$

Step 3.16

Combine $6.25$ and $\frac{329}{329}$ .

$\frac{\frac{101375}{329} + \frac{6.25 \cdot 329}{329} - \frac{411261}{329}}{3}$

Step 3.17

Combine the numerators over the common denominator.

$\frac{\frac{101375 + 6.25 \cdot 329}{329} - \frac{411261}{329}}{3}$

Step 3.18

Combine the numerators over the common denominator.

$\frac{\frac{101375 + 6.25 \cdot 329 - 411261}{329}}{3}$

Step 3.19

Rewrite $\frac{101375 + 6.25 \cdot 329 - 411261}{329}$ in a factored form.

Tap for more steps...

Step 3.19.1

Multiply $6.25$ by $329$ .

$\frac{\frac{101375 + 2056.25 - 411261}{329}}{3}$

Step 3.19.2

Add $101375$ and $2056.25$ .

$\frac{\frac{103431.25 - 411261}{329}}{3}$

Step 3.19.3

Subtract $411261$ from $103431.25$ .

$\frac{\frac{- 307829.75}{329}}{3}$

Step 3.19.4

Divide $- 307829.75$ by $329$ .

$\frac{- 935.65273556}{3}$

Step 4

Divide $- 935.65273556$ by $3$ .

$- 311.88424518$