Algebra Examples

$\frac{4}{3} + (\frac{50}{7} + \frac{8}{15})$

Step 1

Remove parentheses.

$\frac{4}{3} + \frac{50}{7} + \frac{8}{15}$

Step 2

Find the common denominator.

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Step 2.1

Multiply $\frac{4}{3}$ by $\frac{35}{35}$ .

$\frac{4}{3} \cdot \frac{35}{35} + \frac{50}{7} + \frac{8}{15}$

Step 2.2

Multiply $\frac{4}{3}$ by $\frac{35}{35}$ .

$\frac{4 \cdot 35}{3 \cdot 35} + \frac{50}{7} + \frac{8}{15}$

Step 2.3

Multiply $\frac{50}{7}$ by $\frac{15}{15}$ .

$\frac{4 \cdot 35}{3 \cdot 35} + \frac{50}{7} \cdot \frac{15}{15} + \frac{8}{15}$

Step 2.4

Multiply $\frac{50}{7}$ by $\frac{15}{15}$ .

$\frac{4 \cdot 35}{3 \cdot 35} + \frac{50 \cdot 15}{7 \cdot 15} + \frac{8}{15}$

Step 2.5

Multiply $\frac{8}{15}$ by $\frac{7}{7}$ .

$\frac{4 \cdot 35}{3 \cdot 35} + \frac{50 \cdot 15}{7 \cdot 15} + \frac{8}{15} \cdot \frac{7}{7}$

Step 2.6

Multiply $\frac{8}{15}$ by $\frac{7}{7}$ .

$\frac{4 \cdot 35}{3 \cdot 35} + \frac{50 \cdot 15}{7 \cdot 15} + \frac{8 \cdot 7}{15 \cdot 7}$

Step 2.7

Multiply $3$ by $35$ .

$\frac{4 \cdot 35}{105} + \frac{50 \cdot 15}{7 \cdot 15} + \frac{8 \cdot 7}{15 \cdot 7}$

Step 2.8

Multiply $7$ by $15$ .

$\frac{4 \cdot 35}{105} + \frac{50 \cdot 15}{105} + \frac{8 \cdot 7}{15 \cdot 7}$

Step 2.9

Reorder the factors of $15 \cdot 7$ .

$\frac{4 \cdot 35}{105} + \frac{50 \cdot 15}{105} + \frac{8 \cdot 7}{7 \cdot 15}$

Step 2.10

Multiply $7$ by $15$ .

$\frac{4 \cdot 35}{105} + \frac{50 \cdot 15}{105} + \frac{8 \cdot 7}{105}$

Step 3

Combine the numerators over the common denominator.

$\frac{4 \cdot 35 + 50 \cdot 15 + 8 \cdot 7}{105}$

Step 4

Simplify each term.

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Step 4.1

Multiply $4$ by $35$ .

$\frac{140 + 50 \cdot 15 + 8 \cdot 7}{105}$

Step 4.2

Multiply $50$ by $15$ .

$\frac{140 + 750 + 8 \cdot 7}{105}$

Step 4.3

Multiply $8$ by $7$ .

$\frac{140 + 750 + 56}{105}$

Step 5

Simplify by adding numbers.

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Step 5.1

Add $140$ and $750$ .

$\frac{890 + 56}{105}$

Step 5.2

Add $890$ and $56$ .

$\frac{946}{105}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{946}{105}$

Decimal Form:

$9.00952380 \dots$

Mixed Number Form:

$9 \frac{1}{105}$