Basic Math Examples

$y + \frac{5}{8} = 1 \frac{3}{4}$

Step 1

Simplify the right side.

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Step 1.1

Convert $1 \frac{3}{4}$ to an improper fraction.

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Step 1.1.1

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

$y + \frac{5}{8} = 1 + \frac{3}{4}$

Step 1.1.2

Add $1$ and $\frac{3}{4}$ .

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Step 1.1.2.1

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

$y + \frac{5}{8} = \frac{4}{4} + \frac{3}{4}$

Step 1.1.2.2

Combine the numerators over the common denominator.

$y + \frac{5}{8} = \frac{4 + 3}{4}$

Step 1.1.2.3

Add $4$ and $3$ .

$y + \frac{5}{8} = \frac{7}{4}$

Step 2

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

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Step 2.1

Subtract $\frac{5}{8}$ from both sides of the equation.

$y = \frac{7}{4} - \frac{5}{8}$

Step 2.2

To write $\frac{7}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y = \frac{7}{4} \cdot \frac{2}{2} - \frac{5}{8}$

Step 2.3

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.3.1

Multiply $\frac{7}{4}$ by $\frac{2}{2}$ .

$y = \frac{7 \cdot 2}{4 \cdot 2} - \frac{5}{8}$

Step 2.3.2

Multiply $4$ by $2$ .

$y = \frac{7 \cdot 2}{8} - \frac{5}{8}$

Step 2.4

Combine the numerators over the common denominator.

$y = \frac{7 \cdot 2 - 5}{8}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $7$ by $2$ .

$y = \frac{14 - 5}{8}$

Step 2.5.2

Subtract $5$ from $14$ .

$y = \frac{9}{8}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$y = \frac{9}{8}$

Decimal Form:

$y = 1.125$

Mixed Number Form:

$y = 1 \frac{1}{8}$