Basic Math Examples

$\frac{4}{9} + \frac{7}{81} + \frac{10}{27} + s = 1$

Step 1

Simplify $\frac{4}{9} + \frac{7}{81} + \frac{10}{27} + s$ .

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Step 1.1

To write $\frac{4}{9}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{4}{9} \cdot \frac{9}{9} + \frac{7}{81} + \frac{10}{27} + s = 1$

Step 1.2

Write each expression with a common denominator of $81$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.2.1

Multiply $\frac{4}{9}$ by $\frac{9}{9}$ .

$\frac{4 \cdot 9}{9 \cdot 9} + \frac{7}{81} + \frac{10}{27} + s = 1$

Step 1.2.2

Multiply $9$ by $9$ .

$\frac{4 \cdot 9}{81} + \frac{7}{81} + \frac{10}{27} + s = 1$

Step 1.3

Combine the numerators over the common denominator.

$\frac{4 \cdot 9 + 7}{81} + \frac{10}{27} + s = 1$

Step 1.4

Simplify the numerator.

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Step 1.4.1

Multiply $4$ by $9$ .

$\frac{36 + 7}{81} + \frac{10}{27} + s = 1$

Step 1.4.2

Add $36$ and $7$ .

$\frac{43}{81} + \frac{10}{27} + s = 1$

Step 1.5

To write $\frac{10}{27}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{43}{81} + \frac{10}{27} \cdot \frac{3}{3} + s = 1$

Step 1.6

Write each expression with a common denominator of $81$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.6.1

Multiply $\frac{10}{27}$ by $\frac{3}{3}$ .

$\frac{43}{81} + \frac{10 \cdot 3}{27 \cdot 3} + s = 1$

Step 1.6.2

Multiply $27$ by $3$ .

$\frac{43}{81} + \frac{10 \cdot 3}{81} + s = 1$

Step 1.7

Combine the numerators over the common denominator.

$\frac{43 + 10 \cdot 3}{81} + s = 1$

Step 1.8

Simplify the numerator.

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Step 1.8.1

Multiply $10$ by $3$ .

$\frac{43 + 30}{81} + s = 1$

Step 1.8.2

Add $43$ and $30$ .

$\frac{73}{81} + s = 1$

Step 2

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

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Step 2.1

Subtract $\frac{73}{81}$ from both sides of the equation.

$s = 1 - \frac{73}{81}$

Step 2.2

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

$s = \frac{81}{81} - \frac{73}{81}$

Step 2.3

Combine the numerators over the common denominator.

$s = \frac{81 - 73}{81}$

Step 2.4

Subtract $73$ from $81$ .

$s = \frac{8}{81}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$s = \frac{8}{81}$

Decimal Form:

$s = 0.09876543 \dots$