Algebra Examples

$1 \frac{3}{4} + z = 2 \frac{2}{3}$

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.

$1 + \frac{3}{4} + z = 2 \frac{2}{3}$

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.

$\frac{4}{4} + \frac{3}{4} + z = 2 \frac{2}{3}$

Step 1.1.2.2

Combine the numerators over the common denominator.

$\frac{4 + 3}{4} + z = 2 \frac{2}{3}$

Step 1.1.2.3

Add $4$ and $3$ .

$\frac{7}{4} + z = 2 \frac{2}{3}$

Step 2

Simplify the right side.

Tap for more steps...

Step 2.1

Convert $2 \frac{2}{3}$ to an improper fraction.

Tap for more steps...

Step 2.1.1

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

$\frac{7}{4} + z = 2 + \frac{2}{3}$

Step 2.1.2

Add $2$ and $\frac{2}{3}$ .

Tap for more steps...

Step 2.1.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{7}{4} + z = 2 \cdot \frac{3}{3} + \frac{2}{3}$

Step 2.1.2.2

Combine $2$ and $\frac{3}{3}$ .

$\frac{7}{4} + z = \frac{2 \cdot 3}{3} + \frac{2}{3}$

Step 2.1.2.3

Combine the numerators over the common denominator.

$\frac{7}{4} + z = \frac{2 \cdot 3 + 2}{3}$

Step 2.1.2.4

Simplify the numerator.

Tap for more steps...

Step 2.1.2.4.1

Multiply $2$ by $3$ .

$\frac{7}{4} + z = \frac{6 + 2}{3}$

Step 2.1.2.4.2

Add $6$ and $2$ .

$\frac{7}{4} + z = \frac{8}{3}$

Step 3

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

Tap for more steps...

Step 3.1

Subtract $\frac{7}{4}$ from both sides of the equation.

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

Step 3.2

To write $\frac{8}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

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

Step 3.3

To write $- \frac{7}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 3.4

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 3.4.1

Multiply $\frac{8}{3}$ by $\frac{4}{4}$ .

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

Step 3.4.2

Multiply $3$ by $4$ .

$z = \frac{8 \cdot 4}{12} - \frac{7}{4} \cdot \frac{3}{3}$

Step 3.4.3

Multiply $\frac{7}{4}$ by $\frac{3}{3}$ .

$z = \frac{8 \cdot 4}{12} - \frac{7 \cdot 3}{4 \cdot 3}$

Step 3.4.4

Multiply $4$ by $3$ .

$z = \frac{8 \cdot 4}{12} - \frac{7 \cdot 3}{12}$

Step 3.5

Combine the numerators over the common denominator.

$z = \frac{8 \cdot 4 - 7 \cdot 3}{12}$

Step 3.6

Simplify the numerator.

Tap for more steps...

Step 3.6.1

Multiply $8$ by $4$ .

$z = \frac{32 - 7 \cdot 3}{12}$

Step 3.6.2

Multiply $- 7$ by $3$ .

$z = \frac{32 - 21}{12}$

Step 3.6.3

Subtract $21$ from $32$ .

$z = \frac{11}{12}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$z = \frac{11}{12}$

Decimal Form:

$z = 0.91\overline{6}$