Solve for y -2 1/4=-1 2/5+y

$- 2 \frac{1}{4} = - 1 \frac{2}{5} + y$

Step 1

Simplify the left side.

Convert $2 \frac{1}{4}$ to an improper fraction.

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

$- (2 + \frac{1}{4}) = - 1 \frac{2}{5} + y$

Add $2$ and $\frac{1}{4}$ .

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

$- (2 \cdot \frac{4}{4} + \frac{1}{4}) = - 1 \frac{2}{5} + y$

Combine $2$ and $\frac{4}{4}$ .

$- (\frac{2 \cdot 4}{4} + \frac{1}{4}) = - 1 \frac{2}{5} + y$

Combine the numerators over the common denominator.

$- \frac{2 \cdot 4 + 1}{4} = - 1 \frac{2}{5} + y$

Simplify the numerator.

Multiply $2$ by $4$ .

$- \frac{8 + 1}{4} = - 1 \frac{2}{5} + y$

Add $8$ and $1$ .

$- \frac{9}{4} = - 1 \frac{2}{5} + y$

Step 2

Simplify the right side.

Convert $1 \frac{2}{5}$ to an improper fraction.

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

$- \frac{9}{4} = - (1 + \frac{2}{5}) + y$

Add $1$ and $\frac{2}{5}$ .

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

$- \frac{9}{4} = - (\frac{5}{5} + \frac{2}{5}) + y$

Combine the numerators over the common denominator.

$- \frac{9}{4} = - \frac{5 + 2}{5} + y$

Add $5$ and $2$ .

$- \frac{9}{4} = - \frac{7}{5} + y$

Step 3

Rewrite the equation as $- \frac{7}{5} + y = - \frac{9}{4}$ .

$- \frac{7}{5} + y = - \frac{9}{4}$

Step 4

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

Add $\frac{7}{5}$ to both sides of the equation.

$y = - \frac{9}{4} + \frac{7}{5}$

To write $- \frac{9}{4}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$y = - \frac{9}{4} \cdot \frac{5}{5} + \frac{7}{5}$

To write $\frac{7}{5}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$y = - \frac{9}{4} \cdot \frac{5}{5} + \frac{7}{5} \cdot \frac{4}{4}$

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{9}{4}$ by $\frac{5}{5}$ .

$y = - \frac{9 \cdot 5}{4 \cdot 5} + \frac{7}{5} \cdot \frac{4}{4}$

Multiply $4$ by $5$ .

$y = - \frac{9 \cdot 5}{20} + \frac{7}{5} \cdot \frac{4}{4}$

Multiply $\frac{7}{5}$ by $\frac{4}{4}$ .

$y = - \frac{9 \cdot 5}{20} + \frac{7 \cdot 4}{5 \cdot 4}$

Multiply $5$ by $4$ .

$y = - \frac{9 \cdot 5}{20} + \frac{7 \cdot 4}{20}$

Combine the numerators over the common denominator.

$y = \frac{- 9 \cdot 5 + 7 \cdot 4}{20}$

Simplify the numerator.

Multiply $- 9$ by $5$ .

$y = \frac{- 45 + 7 \cdot 4}{20}$

Multiply $7$ by $4$ .

$y = \frac{- 45 + 28}{20}$

Add $- 45$ and $28$ .

$y = \frac{- 17}{20}$

Move the negative in front of the fraction.

$y = - \frac{17}{20}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$y = - \frac{17}{20}$

Decimal Form:

$y = - 0.85$

Solve for y -2 1/4=-1 2/5+y

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