Question

How do you evaluate `\frac { 1} { 4} + - 1`?

Answer 1

Change both terms to fractions and add them algebraically

Explanation:

`-1 = - 1 xx 4/4 = - 4/4` Changing the negative whole number to a fraction with the same denominator

`1/4 +(- 4/4)`

`=1/4 -4/4`

`= - 3/4`

The absolute value of the negative is larger, so the answer is negative.

Answer 2

`1/4 + -1=color(blue)(-3/4`

Refer to the explanation for the process.

Explanation:

Evaluate:

`1/4 + -1`

Any whole number `n` is understood to be `n/1`, so `-1=-1/1`. In order to add or subtract fractions, all denominators need to be the same. We can multiply a fraction by an `color(red)("equivalent fraction"` in order to change the denominator. An equivalent fraction equals `1`. Examples include `color(red)(3/3` and `color(red)(12/12`. You can see that `color(red)(3/3)=color(red)1` and `color(red)(12/12)=color(red)1` by dividing the numerator by the denominator. By doing this, we are not changing the value of the fraction.

Rewrite the original expression as:

`1/4-1/1` `larr` (A positive and a negative equal a negative.)

Multiply `-1/1` by an equivalent fraction that will convert the denominator to `4`.

`1/4-1/1xxcolor(red)(4/4`

Multiply the numerators and denominators across.

`1/4-(1xxcolor(red)(4))/(1xxcolor(red)(4))`

`1/4-4/4`

Place both numerators over the denominator and subtract.

`(1-4)/4=-3/4`