Solve Division Problem: 56 ÷ (-7) Step by Step

Q: Why is the answer negative when I'm dividing 56 by 7?

You're dividing by negative 7, not positive 7! When you divide a positive number by a negative number, the result is always negative. Think of it as: $ \frac{56}{-7} = -\frac{56}{7} = -8 $

Q: How do I remember the sign rules for division?

Same signs = positive, different signs = negativePositive ÷ Positive = PositiveNegative ÷ Negative = PositivePositive ÷ Negative = NegativeNegative ÷ Positive = Negative

Q: Can I write this as a regular division problem?

Yes! You can rewrite $ \frac{56}{-7} $ as $ 56 ÷ (-7) $. Just remember to keep the negative sign with the 7 and apply the sign rule for your final answer.

Q: What if both numbers were negative?

If you had $ \frac{-56}{-7} $, both numbers are negative (same signs), so the answer would be positive 8. Negative divided by negative equals positive!

Q: How can I check if -8 is correct?

Multiply your answer by the divisor: $ (-8) \times (-7) = 56 $. Since this equals the original dividend, your answer is correct! Always verify by working backwards.

Division Operations with Negative Numbers

Solve the following problem:

$\frac{56}{-7}=$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following problem:

$\frac{56}{-7}=$

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 -7

We will divide the fraction as follows:

$\frac{56:-7}{-7:-7}=\frac{-8}{1}=-8$

Final Answer

$-8$

Key Points to Remember

Essential concepts to master this topic

Sign Rule: Positive divided by negative always equals negative
Calculation: $\frac{56}{-7} = \frac{56}{7} \times (-1) = -8$
Check: Multiply back: $(-8) \times (-7) = 56$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting the negative sign in the final answer
Don't just divide 56 ÷ 7 = 8 and ignore the negative sign! This gives a positive result when dividing positive by negative should be negative. Always apply the sign rule: positive ÷ negative = negative.

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 56 by 7?

You're dividing by negative 7, not positive 7! When you divide a positive number by a negative number, the result is always negative. Think of it as: $\frac{56}{-7} = -\frac{56}{7} = -8$

How do I remember the sign rules for division?

Same signs = positive, different signs = negative

Positive ÷ Positive = Positive
Negative ÷ Negative = Positive
Positive ÷ Negative = Negative
Negative ÷ Positive = Negative

Can I write this as a regular division problem?

Yes! You can rewrite $\frac{56}{-7}$ as $56 ÷ (-7)$ . Just remember to keep the negative sign with the 7 and apply the sign rule for your final answer.

What if both numbers were negative?

If you had $\frac{-56}{-7}$ , both numbers are negative (same signs), so the answer would be positive 8. Negative divided by negative equals positive!

How can I check if -8 is correct?

Multiply your answer by the divisor: $(-8) \times (-7) = 56$ . Since this equals the original dividend, your answer is correct! Always verify by working backwards.

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