Pre-Algebra Examples

$\frac{\frac{t}{s} - 1}{\frac{t}{s}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$(\frac{t}{s} - 1) \frac{s}{t}$

Step 2

Multiply $\frac{t}{s} - 1$ by $\frac{s}{t}$ .

$\frac{(\frac{t}{s} - 1) s}{t}$

Step 3

Simplify the numerator.

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Step 3.1

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{s}{s}$ .

$\frac{(\frac{t}{s} - 1 \cdot \frac{s}{s}) s}{t}$

Step 3.2

Combine $- 1$ and $\frac{s}{s}$ .

$\frac{(\frac{t}{s} + \frac{- s}{s}) s}{t}$

Step 3.3

Combine the numerators over the common denominator.

$\frac{\frac{t - s}{s} s}{t}$

Step 4

Combine $\frac{t - s}{s}$ and $s$ .

$\frac{\frac{(t - s) s}{s}}{t}$

Step 5

Reduce the expression by cancelling the common factors.

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Step 5.1

Reduce the expression $\frac{(t - s) s}{s}$ by cancelling the common factors.

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Step 5.1.1

Cancel the common factor.

$\frac{\frac{(t - s) s}{s}}{t}$

Step 5.1.2

Rewrite the expression.

$\frac{\frac{t - s}{1}}{t}$

Step 5.2

Divide $t - s$ by $1$ .

$\frac{t - s}{t}$

Step 6

Split the fraction $\frac{t - s}{t}$ into two fractions.

$\frac{t}{t} + \frac{- s}{t}$

Step 7

Cancel the common factor of $t$ .

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Step 7.1

Cancel the common factor.

$\frac{t}{t} + \frac{- s}{t}$

Step 7.2

Rewrite the expression.

$1 + \frac{- s}{t}$

Step 8

Move the negative in front of the fraction.

$1 - \frac{s}{t}$