## What is -8 Divided by 1/2?

To divide -8 by 1/2, you can multiply -8 by the reciprocal of 1/2, which is 2/1 (since dividing by a fraction is the same as multiplying by its reciprocal):

-8 ÷ (1/2) = -8 * (2/1) = -8 * 2 = -16.

So, -8 divided by 1/2 equals -16.

## Dividing Negative Numbers by Fractions

Dividing negative numbers by fractions combines two math skills – division of negatives and division by fractions. Mastering these operations expands our ability to solve more complex mathematical problems.

## Let’s look at dividing -8 by the fraction 1/2 step-by-step:

- Ignore signs for now and divide the numerators. -8 / 1/2 -> 8 / 1 = 8
- Determine the sign of the quotient based on the divisor: Positive divisor -> Quotient is positive Negative divisor -> Quotient is negative1/2 is positive, so the quotient is positive.
- Write the quotient over the denominator: 8/2
- Apply any negative sign from the dividend to the quotient: -8 was negative, so the quotient is -8/2

Therefore, -8 ÷ 1/2 = -8/2

This process works for dividing any negative number by a positive fraction – divide numerators, make the quotient positive over the denominator, then apply any negative sign.

## Understanding Division of Negatives

The rules for dividing positive and negative numbers relate to the number line:

- Dividing by a positive number moves left on the number line if the dividend is negative. So the quotient becomes more negative.
- Dividing by a negative number moves right on the number line if the dividend is negative. So a negative quotient becomes positive.

Keeping these visuals in mind helps the rules make intuitive sense.

## Checking Our Work

We can verify the solution is correct by multiplying -8/2 by 1/2 to see if we get the original dividend:

-8/2 x 1/2 = -8 ✅

Getting -8 confirms that -8 ÷ 1/2 = -8/2.

Practicing division involving negatives and fractions together builds proficiency with both concepts. Understanding the logic behind dividing negatives allows for mastery.

In summary, when dividing a negative number by a positive fraction, divide numerators, make the quotient positive over the denominator, then reapply the negative sign from the dividend.

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