Solve Division Problem: -35 ÷ -7 Finding the Quotient

Q: Why does negative divided by negative equal positive?

Think of division as "how many groups". When you have -35 and divide by -7, you're asking "how many groups of negative 7 fit into negative 35?" The answer is 5 positive groups!

Q: What's the easiest way to remember sign rules?

Use this simple rule: Same signs = Positive, Different signs = Negative. Since both -35 and -7 are negative (same signs), the result must be positive!

Q: Can I ignore the signs and add them back later?

No! This often leads to errors. Instead, apply the sign rules first, then do the division. It's safer and more reliable.

Q: What if I wrote the problem as 35 ÷ 7 first?

That's a great strategy! $ 35 ÷ 7 = 5 $, then apply the sign rule: negative ÷ negative = positive, so the final answer is +5.

Division Operations with Negative Numbers

Solve the following problem:

$-35:-7=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's start solving the problem.

00:08 First, write the division in a fraction form.

00:14 Next, break down 35 into two factors: 7 and 5.

00:22 Remember, when a negative is divided by a negative, it equals a positive.

00:30 Now, reduce the fraction by canceling out common factors.

00:35 And that's how we find the solution to the question!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following problem:

$-35:-7=$

Step-by-step solution

First, let's write the exercise in the form of a simple fraction:

$\frac{-35}{-7}=$

Now let's factor 35 in the numerator:

$\frac{-7\times5}{-7}=$

Since we have negative numbers in the numerator and denominator of the fraction, the result of the fraction must be positive.

Let's simplify between the 7 in the numerator and denominator of the fraction, and we obtain the following:

$+5$

Final Answer

$+5$

Key Points to Remember

Essential concepts to master this topic

Sign Rule: Negative divided by negative equals positive result
Technique: Rewrite as fraction $\frac{-35}{-7}$ then simplify
Check: Verify that $(+5) \times (-7) = -35$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting the sign rules for division
Don't assume negative ÷ negative = negative! This leads to -5 instead of +5. When both dividend and divisor are negative, the quotient is always positive. Always remember: same signs give positive results.

Practice Quiz

Test your knowledge with interactive questions

What will be the sign of the result of the next exercise?

$(-2)\cdot(-4)=$

FAQ

Everything you need to know about this question

Why does negative divided by negative equal positive?

Think of division as "how many groups". When you have -35 and divide by -7, you're asking "how many groups of negative 7 fit into negative 35?" The answer is 5 positive groups!

What's the easiest way to remember sign rules?

Use this simple rule: Same signs = Positive, Different signs = Negative. Since both -35 and -7 are negative (same signs), the result must be positive!

Can I ignore the signs and add them back later?

No! This often leads to errors. Instead, apply the sign rules first, then do the division. It's safer and more reliable.

How do I check if my division answer is correct?

Multiply your answer by the divisor - you should get the original dividend. For this problem: $5 \times (-7) = -35$ ✓

What if I wrote the problem as 35 ÷ 7 first?

That's a great strategy! $35 ÷ 7 = 5$ , then apply the sign rule: negative ÷ negative = positive, so the final answer is +5.

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