Basic Math Examples

$1 \frac{3}{4} \cdot y - 2 = 12$

Step 1

Simplify the left side.

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Step 1.1

Simplify $1 \frac{3}{4} \cdot y - 2$ .

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Step 1.1.1

Convert $1 \frac{3}{4}$ 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.

$(1 + \frac{3}{4}) \cdot y - 2 = 12$

Step 1.1.1.2

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

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Step 1.1.1.2.1

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

$(\frac{4}{4} + \frac{3}{4}) \cdot y - 2 = 12$

Step 1.1.1.2.2

Combine the numerators over the common denominator.

$\frac{4 + 3}{4} \cdot y - 2 = 12$

Step 1.1.1.2.3

Add $4$ and $3$ .

$\frac{7}{4} \cdot y - 2 = 12$

Step 1.1.2

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

$\frac{7 y}{4} - 2 = 12$

Step 2

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

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Step 2.1

Add $2$ to both sides of the equation.

$\frac{7 y}{4} = 12 + 2$

Step 2.2

Add $12$ and $2$ .

$\frac{7 y}{4} = 14$

Step 3

Multiply both sides of the equation by $\frac{4}{7}$ .

$\frac{4}{7} \cdot \frac{7 y}{4} = \frac{4}{7} \cdot 14$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $\frac{4}{7} \cdot \frac{7 y}{4}$ .

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Step 4.1.1.1

Cancel the common factor of $4$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{4}{7} \cdot \frac{7 y}{4} = \frac{4}{7} \cdot 14$

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{7} (7 y) = \frac{4}{7} \cdot 14$

Step 4.1.1.2

Cancel the common factor of $7$ .

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Step 4.1.1.2.1

Factor $7$ out of $7 y$ .

$\frac{1}{7} (7 (y)) = \frac{4}{7} \cdot 14$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{1}{7} (7 y) = \frac{4}{7} \cdot 14$

Step 4.1.1.2.3

Rewrite the expression.

$y = \frac{4}{7} \cdot 14$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{4}{7} \cdot 14$ .

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Step 4.2.1.1

Cancel the common factor of $7$ .

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Step 4.2.1.1.1

Factor $7$ out of $14$ .

$y = \frac{4}{7} \cdot (7 (2))$

Step 4.2.1.1.2

Cancel the common factor.

$y = \frac{4}{7} \cdot (7 \cdot 2)$

Step 4.2.1.1.3

Rewrite the expression.

$y = 4 \cdot 2$

Step 4.2.1.2

Multiply $4$ by $2$ .

$y = 8$