Basic Math Examples

$3 \frac{3}{4} - 4 \sqrt{\frac{64}{4}}$

Step 1

Convert $3 \frac{3}{4}$ to an improper fraction.

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Step 1.1

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

$3 + \frac{3}{4} - 4 \sqrt{\frac{64}{4}}$

Step 1.2

Add $3$ and $\frac{3}{4}$ .

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Step 1.2.1

To write $3$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$3 \cdot \frac{4}{4} + \frac{3}{4} - 4 \sqrt{\frac{64}{4}}$

Step 1.2.2

Combine $3$ and $\frac{4}{4}$ .

$\frac{3 \cdot 4}{4} + \frac{3}{4} - 4 \sqrt{\frac{64}{4}}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{3 \cdot 4 + 3}{4} - 4 \sqrt{\frac{64}{4}}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $3$ by $4$ .

$\frac{12 + 3}{4} - 4 \sqrt{\frac{64}{4}}$

Step 1.2.4.2

Add $12$ and $3$ .

$\frac{15}{4} - 4 \sqrt{\frac{64}{4}}$

Step 2

Simplify each term.

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Step 2.1

Divide $64$ by $4$ .

$\frac{15}{4} - 4 \sqrt{16}$

Step 2.2

Rewrite $16$ as $4^{2}$ .

$\frac{15}{4} - 4 \sqrt{4^{2}}$

Step 2.3

Pull terms out from under the radical, assuming positive real numbers.

$\frac{15}{4} - 4 \cdot 4$

Step 2.4

Multiply $- 4$ by $4$ .

$\frac{15}{4} - 16$

Step 3

To write $- 16$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{15}{4} - 16 \cdot \frac{4}{4}$

Step 4

Combine $- 16$ and $\frac{4}{4}$ .

$\frac{15}{4} + \frac{- 16 \cdot 4}{4}$

Step 5

Combine the numerators over the common denominator.

$\frac{15 - 16 \cdot 4}{4}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $- 16$ by $4$ .

$\frac{15 - 64}{4}$

Step 6.2

Subtract $64$ from $15$ .

$\frac{- 49}{4}$

Step 7

Move the negative in front of the fraction.

$- \frac{49}{4}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$- \frac{49}{4}$

Decimal Form:

$- 12.25$

Mixed Number Form:

$- 12 \frac{1}{4}$