Basic Math Examples

$\frac{1}{2} \cdot (f^{2} g h) \div 1 \frac{1}{4} \cdot (g^{2} f) \cdot (25 g^{3} k h)$

Step 1

Convert $1 \frac{1}{4}$ to an improper fraction.

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Step 1.1

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

$\frac{1}{2} \cdot (f^{2} g h) \div (1 + \frac{1}{4}) \cdot (g^{2} f) \cdot (25 g^{3} k h)$

Step 1.2

Add $1$ and $\frac{1}{4}$ .

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Step 1.2.1

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

$\frac{1}{2} \cdot (f^{2} g h) \div (\frac{4}{4} + \frac{1}{4}) \cdot (g^{2} f) \cdot (25 g^{3} k h)$

Step 1.2.2

Combine the numerators over the common denominator.

$\frac{1}{2} \cdot (f^{2} g h) \div \frac{4 + 1}{4} \cdot (g^{2} f) \cdot (25 g^{3} k h)$

Step 1.2.3

Add $4$ and $1$ .

$\frac{1}{2} \cdot (f^{2} g h) \div \frac{5}{4} \cdot (g^{2} f) \cdot (25 g^{3} k h)$

Step 2

Rewrite using the commutative property of multiplication.

$25 \frac{1}{2} \cdot f^{2} g h \div \frac{5}{4} g^{2} f (g^{3} k h)$

Step 3

Multiply $g^{2}$ by $g^{3}$ by adding the exponents.

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Step 3.1

Move $g^{3}$ .

$25 \frac{1}{2} \cdot f^{2} g h \div \frac{5}{4} (g^{3} g^{2}) f (k h)$

Step 3.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$25 \frac{1}{2} \cdot f^{2} g h \div \frac{5}{4} g^{3 + 2} f (k h)$

Step 3.3

Add $3$ and $2$ .

$25 \frac{1}{2} \cdot f^{2} g h \div \frac{5}{4} g^{5} f (k h)$

Step 4

To divide by a fraction, multiply by its reciprocal.

$25 (\frac{1}{2} \cdot f^{2} g h \frac{4}{5}) g^{5} f (k h)$

Step 5

Multiply $f^{2}$ by $f$ by adding the exponents.

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Step 5.1

Move $f$ .

$25 (\frac{1}{2} \cdot (f \cdot f^{2}) g h \frac{4}{5}) g^{5} (k h)$

Step 5.2

Multiply $f$ by $f^{2}$ .

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Step 5.2.1

Raise $f$ to the power of $1$ .

$25 (\frac{1}{2} \cdot (f^{1} f^{2}) g h \frac{4}{5}) g^{5} (k h)$

Step 5.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$25 (\frac{1}{2} \cdot f^{1 + 2} g h \frac{4}{5}) g^{5} (k h)$

Step 5.3

Add $1$ and $2$ .

$25 (\frac{1}{2} \cdot f^{3} g h \frac{4}{5}) g^{5} (k h)$

Step 6

Multiply $g$ by $g^{5}$ by adding the exponents.

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Step 6.1

Move $g^{5}$ .

$25 (\frac{1}{2} \cdot f^{3} (g^{5} g) h \frac{4}{5}) (k h)$

Step 6.2

Multiply $g^{5}$ by $g$ .

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Step 6.2.1

Raise $g$ to the power of $1$ .

$25 (\frac{1}{2} \cdot f^{3} (g^{5} g^{1}) h \frac{4}{5}) (k h)$

Step 6.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$25 (\frac{1}{2} \cdot f^{3} g^{5 + 1} h \frac{4}{5}) (k h)$

Step 6.3

Add $5$ and $1$ .

$25 (\frac{1}{2} \cdot f^{3} g^{6} h \frac{4}{5}) (k h)$

Step 7

Multiply $h$ by $h$ by adding the exponents.

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Step 7.1

Move $h$ .

$25 (\frac{1}{2} \cdot f^{3} g^{6} (h \cdot h) \frac{4}{5}) k$

Step 7.2

Multiply $h$ by $h$ .

$25 (\frac{1}{2} \cdot f^{3} g^{6} h^{2} \frac{4}{5}) k$

Step 8

Combine $\frac{1}{2}$ and $f^{3}$ .

$25 (\frac{f^{3}}{2} g^{6} h^{2} \frac{4}{5}) k$

Step 9

Combine $\frac{f^{3}}{2}$ and $g^{6}$ .

$25 (\frac{f^{3} g^{6}}{2} h^{2} \frac{4}{5}) k$

Step 10

Combine $\frac{f^{3} g^{6}}{2}$ and $h^{2}$ .

$25 (\frac{f^{3} g^{6} h^{2}}{2} \cdot \frac{4}{5}) k$

Step 11

Combine.

$25 \frac{f^{3} g^{6} h^{2} \cdot 4}{2 \cdot 5} k$

Step 12

Cancel the common factor of $4$ and $2$ .

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Step 12.1

Factor $2$ out of $f^{3} g^{6} h^{2} \cdot 4$ .

$25 \frac{2 (f^{3} g^{6} h^{2} \cdot 2)}{2 \cdot 5} k$

Step 12.2

Cancel the common factors.

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Step 12.2.1

Factor $2$ out of $2 \cdot 5$ .

$25 \frac{2 (f^{3} g^{6} h^{2} \cdot 2)}{2 (5)} k$

Step 12.2.2

Cancel the common factor.

$25 \frac{2 (f^{3} g^{6} h^{2} \cdot 2)}{2 \cdot 5} k$

Step 12.2.3

Rewrite the expression.

$25 \frac{f^{3} g^{6} h^{2} \cdot 2}{5} k$

Step 13

Cancel the common factor of $5$ .

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Step 13.1

Factor $5$ out of $25$ .

$5 (5) \frac{f^{3} g^{6} h^{2} \cdot 2}{5} k$

Step 13.2

Cancel the common factor.

$5 \cdot 5 \frac{f^{3} g^{6} h^{2} \cdot 2}{5} k$

Step 13.3

Rewrite the expression.

$5 (f^{3} g^{6} h^{2} \cdot 2) k$

Step 14

Multiply $2$ by $5$ .

$10 f^{3} g^{6} h^{2} k$