Pre-Algebra Examples

$- 7 \frac{3}{8} + 4 \frac{3}{16}$

Step 1

Convert $7 \frac{3}{8}$ to an improper fraction.

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Step 1.1

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

$- (7 + \frac{3}{8}) + 4 \frac{3}{16}$

Step 1.2

Add $7$ and $\frac{3}{8}$ .

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Step 1.2.1

To write $7$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$- (7 \cdot \frac{8}{8} + \frac{3}{8}) + 4 \frac{3}{16}$

Step 1.2.2

Combine $7$ and $\frac{8}{8}$ .

$- (\frac{7 \cdot 8}{8} + \frac{3}{8}) + 4 \frac{3}{16}$

Step 1.2.3

Combine the numerators over the common denominator.

$- \frac{7 \cdot 8 + 3}{8} + 4 \frac{3}{16}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $7$ by $8$ .

$- \frac{56 + 3}{8} + 4 \frac{3}{16}$

Step 1.2.4.2

Add $56$ and $3$ .

$- \frac{59}{8} + 4 \frac{3}{16}$

Step 2

Convert $4 \frac{3}{16}$ to an improper fraction.

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Step 2.1

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

$- \frac{59}{8} + 4 + \frac{3}{16}$

Step 2.2

Add $4$ and $\frac{3}{16}$ .

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Step 2.2.1

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

$- \frac{59}{8} + 4 \cdot \frac{16}{16} + \frac{3}{16}$

Step 2.2.2

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

$- \frac{59}{8} + \frac{4 \cdot 16}{16} + \frac{3}{16}$

Step 2.2.3

Combine the numerators over the common denominator.

$- \frac{59}{8} + \frac{4 \cdot 16 + 3}{16}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $4$ by $16$ .

$- \frac{59}{8} + \frac{64 + 3}{16}$

Step 2.2.4.2

Add $64$ and $3$ .

$- \frac{59}{8} + \frac{67}{16}$

Step 3

To write $- \frac{59}{8}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{59}{8} \cdot \frac{2}{2} + \frac{67}{16}$

Step 4

Write each expression with a common denominator of $16$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{59}{8}$ by $\frac{2}{2}$ .

$- \frac{59 \cdot 2}{8 \cdot 2} + \frac{67}{16}$

Step 4.2

Multiply $8$ by $2$ .

$- \frac{59 \cdot 2}{16} + \frac{67}{16}$

Step 5

Combine the numerators over the common denominator.

$\frac{- 59 \cdot 2 + 67}{16}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $- 59$ by $2$ .

$\frac{- 118 + 67}{16}$

Step 6.2

Add $- 118$ and $67$ .

$\frac{- 51}{16}$

Step 7

Move the negative in front of the fraction.

$- \frac{51}{16}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$- \frac{51}{16}$

Decimal Form:

$- 3.1875$

Mixed Number Form:

$- 3 \frac{3}{16}$