Pre-Algebra Examples

$\frac{100}{\frac{50}{70}} + 100 + \frac{100}{75} + \frac{1}{105} \cdot (10643)$

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $50$ and $70$ .

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Step 1.1.1

Factor $10$ out of $50$ .

$\frac{100}{\frac{10 (5)}{70}} + 100 + \frac{100}{75} + \frac{1}{105} \cdot (10643)$

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $10$ out of $70$ .

$\frac{100}{\frac{10 \cdot 5}{10 \cdot 7}} + 100 + \frac{100}{75} + \frac{1}{105} \cdot (10643)$

Step 1.1.2.2

Cancel the common factor.

$\frac{100}{\frac{10 \cdot 5}{10 \cdot 7}} + 100 + \frac{100}{75} + \frac{1}{105} \cdot (10643)$

Step 1.1.2.3

Rewrite the expression.

$\frac{100}{\frac{5}{7}} + 100 + \frac{100}{75} + \frac{1}{105} \cdot (10643)$

Step 1.2

Multiply the numerator by the reciprocal of the denominator.

$100 (\frac{7}{5}) + 100 + \frac{100}{75} + \frac{1}{105} \cdot (10643)$

Step 1.3

Cancel the common factor of $5$ .

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Step 1.3.1

Factor $5$ out of $100$ .

$5 (20) \frac{7}{5} + 100 + \frac{100}{75} + \frac{1}{105} \cdot (10643)$

Step 1.3.2

Cancel the common factor.

$5 \cdot 20 \frac{7}{5} + 100 + \frac{100}{75} + \frac{1}{105} \cdot (10643)$

Step 1.3.3

Rewrite the expression.

$20 \cdot 7 + 100 + \frac{100}{75} + \frac{1}{105} \cdot (10643)$

Step 1.4

Multiply $20$ by $7$ .

$140 + 100 + \frac{100}{75} + \frac{1}{105} \cdot (10643)$

Step 1.5

Cancel the common factor of $100$ and $75$ .

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Step 1.5.1

Factor $25$ out of $100$ .

$140 + 100 + \frac{25 (4)}{75} + \frac{1}{105} \cdot (10643)$

Step 1.5.2

Cancel the common factors.

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Step 1.5.2.1

Factor $25$ out of $75$ .

$140 + 100 + \frac{25 \cdot 4}{25 \cdot 3} + \frac{1}{105} \cdot (10643)$

Step 1.5.2.2

Cancel the common factor.

$140 + 100 + \frac{25 \cdot 4}{25 \cdot 3} + \frac{1}{105} \cdot (10643)$

Step 1.5.2.3

Rewrite the expression.

$140 + 100 + \frac{4}{3} + \frac{1}{105} \cdot (10643)$

Step 1.6

Combine $\frac{1}{105}$ and $10643$ .

$140 + 100 + \frac{4}{3} + \frac{10643}{105}$

Step 2

Find the common denominator.

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Step 2.1

Write $140$ as a fraction with denominator $1$ .

$\frac{140}{1} + 100 + \frac{4}{3} + \frac{10643}{105}$

Step 2.2

Multiply $\frac{140}{1}$ by $\frac{105}{105}$ .

$\frac{140}{1} \cdot \frac{105}{105} + 100 + \frac{4}{3} + \frac{10643}{105}$

Step 2.3

Multiply $\frac{140}{1}$ by $\frac{105}{105}$ .

$\frac{140 \cdot 105}{105} + 100 + \frac{4}{3} + \frac{10643}{105}$

Step 2.4

Write $100$ as a fraction with denominator $1$ .

$\frac{140 \cdot 105}{105} + \frac{100}{1} + \frac{4}{3} + \frac{10643}{105}$

Step 2.5

Multiply $\frac{100}{1}$ by $\frac{105}{105}$ .

$\frac{140 \cdot 105}{105} + \frac{100}{1} \cdot \frac{105}{105} + \frac{4}{3} + \frac{10643}{105}$

Step 2.6

Multiply $\frac{100}{1}$ by $\frac{105}{105}$ .

$\frac{140 \cdot 105}{105} + \frac{100 \cdot 105}{105} + \frac{4}{3} + \frac{10643}{105}$

Step 2.7

Multiply $\frac{4}{3}$ by $\frac{35}{35}$ .

$\frac{140 \cdot 105}{105} + \frac{100 \cdot 105}{105} + \frac{4}{3} \cdot \frac{35}{35} + \frac{10643}{105}$

Step 2.8

Multiply $\frac{4}{3}$ by $\frac{35}{35}$ .

$\frac{140 \cdot 105}{105} + \frac{100 \cdot 105}{105} + \frac{4 \cdot 35}{3 \cdot 35} + \frac{10643}{105}$

Step 2.9

Multiply $3$ by $35$ .

$\frac{140 \cdot 105}{105} + \frac{100 \cdot 105}{105} + \frac{4 \cdot 35}{105} + \frac{10643}{105}$

Step 3

Combine the numerators over the common denominator.

$\frac{140 \cdot 105 + 100 \cdot 105 + 4 \cdot 35 + 10643}{105}$

Step 4

Simplify each term.

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Step 4.1

Multiply $140$ by $105$ .

$\frac{14700 + 100 \cdot 105 + 4 \cdot 35 + 10643}{105}$

Step 4.2

Multiply $100$ by $105$ .

$\frac{14700 + 10500 + 4 \cdot 35 + 10643}{105}$

Step 4.3

Multiply $4$ by $35$ .

$\frac{14700 + 10500 + 140 + 10643}{105}$

Step 5

Simplify by adding numbers.

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Step 5.1

Add $14700$ and $10500$ .

$\frac{25200 + 140 + 10643}{105}$

Step 5.2

Add $25200$ and $140$ .

$\frac{25340 + 10643}{105}$

Step 5.3

Add $25340$ and $10643$ .

$\frac{35983}{105}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{35983}{105}$

Decimal Form:

$342.69523809 \dots$

Mixed Number Form:

$342 \frac{73}{105}$