Basic Math Examples

$13 \frac{7}{9} + 9 \frac{13}{27} = t$

Step 1

Simplify the left side.

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Step 1.1

Simplify $13 \frac{7}{9} + 9 \frac{13}{27}$ .

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Step 1.1.1

Convert $13 \frac{7}{9}$ to an improper fraction.

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Step 1.1.1.1

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

$13 + \frac{7}{9} + 9 \frac{13}{27} = t$

Step 1.1.1.2

Add $13$ and $\frac{7}{9}$ .

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Step 1.1.1.2.1

To write $13$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$13 \cdot \frac{9}{9} + \frac{7}{9} + 9 \frac{13}{27} = t$

Step 1.1.1.2.2

Combine $13$ and $\frac{9}{9}$ .

$\frac{13 \cdot 9}{9} + \frac{7}{9} + 9 \frac{13}{27} = t$

Step 1.1.1.2.3

Combine the numerators over the common denominator.

$\frac{13 \cdot 9 + 7}{9} + 9 \frac{13}{27} = t$

Step 1.1.1.2.4

Simplify the numerator.

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Step 1.1.1.2.4.1

Multiply $13$ by $9$ .

$\frac{117 + 7}{9} + 9 \frac{13}{27} = t$

Step 1.1.1.2.4.2

Add $117$ and $7$ .

$\frac{124}{9} + 9 \frac{13}{27} = t$

Step 1.1.2

Convert $9 \frac{13}{27}$ to an improper fraction.

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Step 1.1.2.1

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

$\frac{124}{9} + 9 + \frac{13}{27} = t$

Step 1.1.2.2

Add $9$ and $\frac{13}{27}$ .

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Step 1.1.2.2.1

To write $9$ as a fraction with a common denominator, multiply by $\frac{27}{27}$ .

$\frac{124}{9} + 9 \cdot \frac{27}{27} + \frac{13}{27} = t$

Step 1.1.2.2.2

Combine $9$ and $\frac{27}{27}$ .

$\frac{124}{9} + \frac{9 \cdot 27}{27} + \frac{13}{27} = t$

Step 1.1.2.2.3

Combine the numerators over the common denominator.

$\frac{124}{9} + \frac{9 \cdot 27 + 13}{27} = t$

Step 1.1.2.2.4

Simplify the numerator.

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Step 1.1.2.2.4.1

Multiply $9$ by $27$ .

$\frac{124}{9} + \frac{243 + 13}{27} = t$

Step 1.1.2.2.4.2

Add $243$ and $13$ .

$\frac{124}{9} + \frac{256}{27} = t$

Step 1.1.3

To write $\frac{124}{9}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{124}{9} \cdot \frac{3}{3} + \frac{256}{27} = t$

Step 1.1.4

Write each expression with a common denominator of $27$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.1.4.1

Multiply $\frac{124}{9}$ by $\frac{3}{3}$ .

$\frac{124 \cdot 3}{9 \cdot 3} + \frac{256}{27} = t$

Step 1.1.4.2

Multiply $9$ by $3$ .

$\frac{124 \cdot 3}{27} + \frac{256}{27} = t$

Step 1.1.5

Combine the numerators over the common denominator.

$\frac{124 \cdot 3 + 256}{27} = t$

Step 1.1.6

Simplify the numerator.

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Step 1.1.6.1

Multiply $124$ by $3$ .

$\frac{372 + 256}{27} = t$

Step 1.1.6.2

Add $372$ and $256$ .

$\frac{628}{27} = t$

Step 2

Rewrite the equation as $t = \frac{628}{27}$ .

$t = \frac{628}{27}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$t = \frac{628}{27}$

Decimal Form:

$t = 23.\overline{259}$

Mixed Number Form:

$t = 23 \frac{7}{27}$