Pre-Algebra Examples

$1 \frac{3}{4} = c - 3 \frac{7}{8}$

Step 1

Simplify the left side.

Tap for more steps...

Step 1.1

Convert $1 \frac{3}{4}$ to an improper fraction.

Tap for more steps...

Step 1.1.1

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

$1 + \frac{3}{4} = c - 3 \frac{7}{8}$

Step 1.1.2

Add $1$ and $\frac{3}{4}$ .

Tap for more steps...

Step 1.1.2.1

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

$\frac{4}{4} + \frac{3}{4} = c - 3 \frac{7}{8}$

Step 1.1.2.2

Combine the numerators over the common denominator.

$\frac{4 + 3}{4} = c - 3 \frac{7}{8}$

Step 1.1.2.3

Add $4$ and $3$ .

$\frac{7}{4} = c - 3 \frac{7}{8}$

Step 2

Simplify the right side.

Tap for more steps...

Step 2.1

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

Tap for more steps...

Step 2.1.1

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

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

Step 2.1.2

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

Tap for more steps...

Step 2.1.2.1

To write $3$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

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

Step 2.1.2.2

Combine $3$ and $\frac{8}{8}$ .

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

Step 2.1.2.3

Combine the numerators over the common denominator.

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

Step 2.1.2.4

Simplify the numerator.

Tap for more steps...

Step 2.1.2.4.1

Multiply $3$ by $8$ .

$\frac{7}{4} = c - \frac{24 + 7}{8}$

Step 2.1.2.4.2

Add $24$ and $7$ .

$\frac{7}{4} = c - \frac{31}{8}$

Step 3

Rewrite the equation as $c - \frac{31}{8} = \frac{7}{4}$ .

$c - \frac{31}{8} = \frac{7}{4}$

Step 4

Move all terms not containing $c$ to the right side of the equation.

Tap for more steps...

Step 4.1

Add $\frac{31}{8}$ to both sides of the equation.

$c = \frac{7}{4} + \frac{31}{8}$

Step 4.2

To write $\frac{7}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$c = \frac{7}{4} \cdot \frac{2}{2} + \frac{31}{8}$

Step 4.3

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 4.3.1

Multiply $\frac{7}{4}$ by $\frac{2}{2}$ .

$c = \frac{7 \cdot 2}{4 \cdot 2} + \frac{31}{8}$

Step 4.3.2

Multiply $4$ by $2$ .

$c = \frac{7 \cdot 2}{8} + \frac{31}{8}$

Step 4.4

Combine the numerators over the common denominator.

$c = \frac{7 \cdot 2 + 31}{8}$

Step 4.5

Simplify the numerator.

Tap for more steps...

Step 4.5.1

Multiply $7$ by $2$ .

$c = \frac{14 + 31}{8}$

Step 4.5.2

Add $14$ and $31$ .

$c = \frac{45}{8}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$c = \frac{45}{8}$

Decimal Form:

$c = 5.625$

Mixed Number Form:

$c = 5 \frac{5}{8}$