What is -8 Divided by 1/2?

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:

1. Ignore signs for now and divide the numerators. -8 / 1/2 -> 8 / 1 = 8
2. 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.
3. Write the quotient over the denominator: 8/2
4. 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.