Solve Division Problem: -74 ÷ -1 Step by Step

Q: Why does negative divided by negative equal positive?

Think of it this way: division is the opposite of multiplication. Since (-1) × 74 = -74, we know that (-74) ÷ (-1) must equal 74. The two negative signs 'cancel out' to make positive!

Q: What if I forget the sign rules?

Use this simple memory trick: 'Same signs = positive, different signs = negative'. Since both numbers are negative (same signs), your answer must be positive!

Q: Is dividing by -1 the same as multiplying by -1?

No! Dividing by -1 changes the sign, while multiplying by -1 also changes the sign. But $ (-74) ÷ (-1) = 74 $ while $ (-74) × (-1) = 74 $ - they both give positive results.

Q: How do I remember which operations change signs?

Focus on counting negative signs: Even number of negatives = positive resultOdd number of negatives = negative result Here we have 2 negatives, so the result is positive!

Q: What's the easiest way to solve this type of problem?

First determine the sign of your answer using the rules, then do the basic division with positive numbers. Since 74 ÷ 1 = 74, and our sign is positive, the answer is 74.

Division of Negative Numbers with Sign Rules

$(-74):(-1)=\text{ ?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's solve this problem step by step.

00:09 Remember, when you divide a negative number by another negative number, the result is always positive.

00:17 Think of division as a way to make a fraction.

00:24 Also, any number divided by one is just that number itself.

00:31 And there you have it! That's the solution.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$(-74):(-1)=\text{ ?}$

Step-by-step solution

Firstly we need to realise that since we are dividing two negative numbers, the result must be a positive number.

Let's rewrite the exercise in the form of a simple fraction:

$\frac{74}{1}=$

Remember the formula:

$\frac{x}{1}=x$

Any number we divide by 1 equals the number itself, therefore:

$\frac{74}{1}=74$

Final Answer

$74$

Key Points to Remember

Essential concepts to master this topic

Sign Rule: Negative divided by negative always equals positive
Technique: Remove signs first: (-74) ÷ (-1) becomes 74 ÷ 1
Check: Verify that (-1) × 74 = -74, confirming our answer ✓

Common Mistakes

Avoid these frequent errors

Keeping the negative sign in the final answer
Don't write (-74) ÷ (-1) = -74! This ignores the fundamental rule that negative ÷ negative = positive, giving you the wrong sign. Always remember: two negatives make a positive when dividing.

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 it this way: division is the opposite of multiplication. Since (-1) × 74 = -74, we know that (-74) ÷ (-1) must equal 74. The two negative signs 'cancel out' to make positive!

What if I forget the sign rules?

Use this simple memory trick: 'Same signs = positive, different signs = negative'. Since both numbers are negative (same signs), your answer must be positive!

Is dividing by -1 the same as multiplying by -1?

No! Dividing by -1 changes the sign, while multiplying by -1 also changes the sign. But $(-74) ÷ (-1) = 74$ while $(-74) × (-1) = 74$ - they both give positive results.

How do I remember which operations change signs?

Focus on counting negative signs:

Even number of negatives = positive result
Odd number of negatives = negative result

Here we have 2 negatives, so the result is positive!

What's the easiest way to solve this type of problem?

First determine the sign of your answer using the rules, then do the basic division with positive numbers. Since 74 ÷ 1 = 74, and our sign is positive, the answer is 74.

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