Pre-Algebra Examples

$(35) \cdot 10^{9} \div 9 \frac{1}{2}$

Step 1

Convert $9 \frac{1}{2}$ to an improper fraction.

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Step 1.1

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

$(35) \cdot 10^{9} \div (9 + \frac{1}{2})$

Step 1.2

Add $9$ and $\frac{1}{2}$ .

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Step 1.2.1

To write $9$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$(35) \cdot 10^{9} \div (9 \cdot \frac{2}{2} + \frac{1}{2})$

Step 1.2.2

Combine $9$ and $\frac{2}{2}$ .

$(35) \cdot 10^{9} \div (\frac{9 \cdot 2}{2} + \frac{1}{2})$

Step 1.2.3

Combine the numerators over the common denominator.

$(35) \cdot 10^{9} \div \frac{9 \cdot 2 + 1}{2}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $9$ by $2$ .

$(35) \cdot 10^{9} \div \frac{18 + 1}{2}$

Step 1.2.4.2

Add $18$ and $1$ .

$(35) \cdot 10^{9} \div \frac{19}{2}$

Step 2

To divide by a fraction, multiply by its reciprocal.

$(35) \cdot 10^{9} \frac{2}{19}$

Step 3

Move the decimal point in $35$ to the left by $1$ place and increase the power of $10^{9}$ by $1$ .

$3.5 \cdot 10^{10} \frac{2}{19}$

Step 4

Multiply $3.5 \cdot 10^{10} \frac{2}{19}$ .

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Step 4.1

Combine $3.5$ and $\frac{2}{19}$ .

$10^{10} \frac{3.5 \cdot 2}{19}$

Step 4.2

Multiply $3.5$ by $2$ .

$10^{10} \frac{7}{19}$

Step 4.3

Combine $10^{10}$ and $\frac{7}{19}$ .

$\frac{10^{10} \cdot 7}{19}$

Step 5

Cancel the common factor of $7$ and $19$ .

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Step 5.1

Factor $1$ out of $10^{10} \cdot 7$ .

$\frac{1 (10^{10} \cdot 7)}{19}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Rewrite $19$ as $1 (19)$ .

$\frac{1 (10^{10} \cdot 7)}{1 (19)}$

Step 5.2.2

Cancel the common factor.

$\frac{1 (10^{10} \cdot 7)}{1 \cdot 19}$

Step 5.2.3

Rewrite the expression.

$\frac{10^{10} \cdot 7}{19}$

Step 6

Raise $10$ to the power of $10$ .

$\frac{10000000000 \cdot 7}{19}$

Step 7

Multiply $10000000000$ by $7$ .

$\frac{70000000000}{19}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{70000000000}{19}$

Decimal Form:

$3684210526.31579$

Mixed Number Form:

$3684210526 \frac{6}{19}$