Basic Math Examples

$m + 7 \frac{1}{4} = 15$

Step 1

Simplify the left side.

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Step 1.1

Convert $7 \frac{1}{4}$ to an improper fraction.

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Step 1.1.1

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

$m + 7 + \frac{1}{4} = 15$

Step 1.1.2

Add $7$ and $\frac{1}{4}$ .

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Step 1.1.2.1

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

$m + 7 \cdot \frac{4}{4} + \frac{1}{4} = 15$

Step 1.1.2.2

Combine $7$ and $\frac{4}{4}$ .

$m + \frac{7 \cdot 4}{4} + \frac{1}{4} = 15$

Step 1.1.2.3

Combine the numerators over the common denominator.

$m + \frac{7 \cdot 4 + 1}{4} = 15$

Step 1.1.2.4

Simplify the numerator.

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Step 1.1.2.4.1

Multiply $7$ by $4$ .

$m + \frac{28 + 1}{4} = 15$

Step 1.1.2.4.2

Add $28$ and $1$ .

$m + \frac{29}{4} = 15$

Step 2

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

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Step 2.1

Subtract $\frac{29}{4}$ from both sides of the equation.

$m = 15 - \frac{29}{4}$

Step 2.2

To write $15$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$m = 15 \cdot \frac{4}{4} - \frac{29}{4}$

Step 2.3

Combine $15$ and $\frac{4}{4}$ .

$m = \frac{15 \cdot 4}{4} - \frac{29}{4}$

Step 2.4

Combine the numerators over the common denominator.

$m = \frac{15 \cdot 4 - 29}{4}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $15$ by $4$ .

$m = \frac{60 - 29}{4}$

Step 2.5.2

Subtract $29$ from $60$ .

$m = \frac{31}{4}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$m = \frac{31}{4}$

Decimal Form:

$m = 7.75$

Mixed Number Form:

$m = 7 \frac{3}{4}$