Basic Math Examples

$a + 2 \frac{2}{5} = 7 \frac{3}{5}$

Step 1

Simplify the left side.

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Step 1.1

Convert $2 \frac{2}{5}$ to an improper fraction.

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Step 1.1.1

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

$a + 2 + \frac{2}{5} = 7 \frac{3}{5}$

Step 1.1.2

Add $2$ and $\frac{2}{5}$ .

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Step 1.1.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$a + 2 \cdot \frac{5}{5} + \frac{2}{5} = 7 \frac{3}{5}$

Step 1.1.2.2

Combine $2$ and $\frac{5}{5}$ .

$a + \frac{2 \cdot 5}{5} + \frac{2}{5} = 7 \frac{3}{5}$

Step 1.1.2.3

Combine the numerators over the common denominator.

$a + \frac{2 \cdot 5 + 2}{5} = 7 \frac{3}{5}$

Step 1.1.2.4

Simplify the numerator.

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Step 1.1.2.4.1

Multiply $2$ by $5$ .

$a + \frac{10 + 2}{5} = 7 \frac{3}{5}$

Step 1.1.2.4.2

Add $10$ and $2$ .

$a + \frac{12}{5} = 7 \frac{3}{5}$

Step 2

Simplify the right side.

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Step 2.1

Convert $7 \frac{3}{5}$ to an improper fraction.

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Step 2.1.1

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

$a + \frac{12}{5} = 7 + \frac{3}{5}$

Step 2.1.2

Add $7$ and $\frac{3}{5}$ .

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Step 2.1.2.1

To write $7$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$a + \frac{12}{5} = 7 \cdot \frac{5}{5} + \frac{3}{5}$

Step 2.1.2.2

Combine $7$ and $\frac{5}{5}$ .

$a + \frac{12}{5} = \frac{7 \cdot 5}{5} + \frac{3}{5}$

Step 2.1.2.3

Combine the numerators over the common denominator.

$a + \frac{12}{5} = \frac{7 \cdot 5 + 3}{5}$

Step 2.1.2.4

Simplify the numerator.

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Step 2.1.2.4.1

Multiply $7$ by $5$ .

$a + \frac{12}{5} = \frac{35 + 3}{5}$

Step 2.1.2.4.2

Add $35$ and $3$ .

$a + \frac{12}{5} = \frac{38}{5}$

Step 3

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

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Step 3.1

Subtract $\frac{12}{5}$ from both sides of the equation.

$a = \frac{38}{5} - \frac{12}{5}$

Step 3.2

Combine the numerators over the common denominator.

$a = \frac{38 - 12}{5}$

Step 3.3

Subtract $12$ from $38$ .

$a = \frac{26}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$a = \frac{26}{5}$

Decimal Form:

$a = 5.2$

Mixed Number Form:

$a = 5 \frac{1}{5}$