Solve (-1/2) × (-2): Multiplying Negative Numbers and Fractions

Q: Why does negative times negative equal positive?

Think of it this way: a negative number represents the opposite direction. When you multiply by another negative, you're taking the opposite of the opposite, which brings you back to positive!

Q: How do I multiply a fraction by a whole number?

Multiply the numerator by the whole number: $ \frac{1}{2} \times 2 = \frac{1 \times 2}{2} = \frac{2}{2} = 1 $. The denominator stays the same!

Q: What if I'm confused about the signs?

Use this simple rule: same signs = positive, different signs = negative. Since both numbers are negative (same signs), the answer is positive.

Q: Can I solve this step by step?

Step 1: Handle signs: negative × negative = positiveStep 2: Multiply numbers: $ \frac{1}{2} \times 2 = 1 $Step 3: Combine: positive × 1 = +1

Q: How can I remember the sign rules?

Try this memory trick: "Friends agree, enemies disagree" - same signs (friends) give positive results, different signs (enemies) give negative results!

Negative Fraction Multiplication with Sign Rules

Complete the following exercise:

$(-\frac{1}{2})\cdot(-2)=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:10 Negative times negative always equals positive

00:24 Let's move the multiplication to the numerator and reduce

00:27 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Complete the following exercise:

$(-\frac{1}{2})\cdot(-2)=$

Step-by-step solution

Let's recall the rule:

$(-x)\times(-x)=+x$

Therefore, the sign of the exercise result will be positive:

$-\frac{1}{2}\times-2=+1$

Final Answer

$1$

Key Points to Remember

Essential concepts to master this topic

Sign Rule: Negative times negative equals positive
Technique: $(-\frac{1}{2}) \times (-2) = +(\frac{1}{2} \times 2) = +1$
Check: Two negative signs cancel to give positive result ✓

Common Mistakes

Avoid these frequent errors

Forgetting that negative times negative equals positive
Don't keep the negative sign when multiplying two negatives = $-1$ instead of $+1$ ! Two negatives always cancel each other out to make a positive. Always remember: negative × negative = positive.

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 times negative equal positive?

Think of it this way: a negative number represents the opposite direction. When you multiply by another negative, you're taking the opposite of the opposite, which brings you back to positive!

How do I multiply a fraction by a whole number?

Multiply the numerator by the whole number: $\frac{1}{2} \times 2 = \frac{1 \times 2}{2} = \frac{2}{2} = 1$ . The denominator stays the same!

What if I'm confused about the signs?

Use this simple rule: same signs = positive, different signs = negative. Since both numbers are negative (same signs), the answer is positive.

Can I solve this step by step?

Step 1: Handle signs: negative × negative = positive
Step 2: Multiply numbers: $\frac{1}{2} \times 2 = 1$
Step 3: Combine: positive × 1 = +1

How can I remember the sign rules?

Try this memory trick: "Friends agree, enemies disagree" - same signs (friends) give positive results, different signs (enemies) give negative results!

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