Solve the Fraction Division: 8 ÷ (-48)

Fraction Division with Negative Numbers

Solve the following problem:

848= \frac{8}{-48}=

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Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the following problem:

848= \frac{8}{-48}=

2

Step-by-step solution

Remember that we are dividing a positive number by a negative number, so the result must be a negative number.

We will divide both the numerator and the denominator by the highest number that both are divisible by.

In this case, that number is 8

We will divide the fraction as follows:

8:848:8=16=16 \frac{8:8}{-48:8}=\frac{1}{-6}=-\frac{1}{6}

3

Final Answer

16 -\frac{1}{6}

Key Points to Remember

Essential concepts to master this topic
  • Sign Rule: Positive divided by negative always equals negative
  • Simplification: Find GCD of 8 and 48, which is 8
  • Check: Verify 16×(48)=8 -\frac{1}{6} \times (-48) = 8

Common Mistakes

Avoid these frequent errors
  • Ignoring the negative sign
    Don't treat 848 \frac{8}{-48} as just 848=16 \frac{8}{48} = \frac{1}{6} ! This gives a positive answer when the result must be negative. Always apply the sign rule: positive ÷ negative = negative, so the answer is 16 -\frac{1}{6} .

Practice Quiz

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Write the fraction shown in the picture, in words:

FAQ

Everything you need to know about this question

Why is the answer negative when I'm dividing 8 by 48?

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Because you're dividing by -48, not +48! When you divide a positive number by a negative number, the result is always negative. Think of it as: 8 ÷ (-48) = -(8 ÷ 48).

How do I know what number to divide both parts by?

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Find the Greatest Common Divisor (GCD) of the numerator and denominator. For 8 and 48, list the factors: 8 = 1, 2, 4, 8 and 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. The largest common factor is 8.

Can I write the answer as 16 \frac{1}{-6} instead?

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Technically yes, but it's better practice to write negative fractions as 16 -\frac{1}{6} with the negative sign in front. This makes it clearer that the entire fraction is negative.

What if I can't find a common factor?

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If 8 and 48 had no common factors other than 1, then 848 \frac{8}{-48} would already be in simplest form. But since both are divisible by 8, we must simplify to get the correct answer.

How can I double-check my work?

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Multiply your answer by the denominator: 16×(48)=486=8 -\frac{1}{6} \times (-48) = \frac{48}{6} = 8 ✓. If you get the original numerator, your answer is correct!

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