Solve -a·b: Calculate the Product When a=-3 and b=5

Q: Can I just multiply -3 × 5 directly?

No! The expression is -a·b, not a·b. You must first find what -a equals when a = -3. Since -a = -(-3) = +3, then multiply: 3 × 5 = 15.

Q: How do I handle the negative sign before a variable?

Treat the negative sign as multiplying by -1. So -a becomes -1 × a. When a = -3: $ -1 \times (-3) = +3 $.

Q: What's the difference between -a·b and (-a)·b?

They're the same thing! Both mean "negative a times b". The parentheses in (-a)·b just make it clearer that the negative applies to the variable a.

Negative Multiplication with Variable Substitution

$-a\cdot b=$

Replace and calculate if $a=-3\text{, }b=5$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Set up and calculate

00:05 Let's substitute appropriate values according to the given data, being careful with parentheses

00:21 Negative times negative is always positive

00:26 Let's calculate the multiplication

00:29 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

$-a\cdot b=$

Replace and calculate if $a=-3\text{, }b=5$

Step-by-step solution

First, we replace the data in the exercise

-(-3)*5 =

To better understand the minus sign multiplied at the beginning, we will write it like this:

-1*-3*5 =

Now we see that we have an exercise that is all multiplication,

We will solve according to the order of arithmetic operations, from left to right:

-1*-3 = 3

3*5 = 15

Final Answer

$15$

Key Points to Remember

Essential concepts to master this topic

Sign Rule: Negative times negative equals positive
Technique: Rewrite -a as -1 × a for clarity: -1 × (-3) × 5
Check: Substitute back: -(-3) × 5 = 3 × 5 = 15 ✓

Common Mistakes

Avoid these frequent errors

Forgetting the negative sign in front of a
Don't calculate -a·b as just (-3)·5 = -15! This ignores the negative sign before the variable a. Always remember that -a means "the opposite of a", so when a = -3, then -a = -(-3) = +3.

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 -a equal positive 3 when a = -3?

The symbol -a means "the opposite of a". When a = -3, the opposite of -3 is +3. Think of it as: -a = -(negative number) = positive number.

Can I just multiply -3 × 5 directly?

No! The expression is -a·b, not a·b. You must first find what -a equals when a = -3. Since -a = -(-3) = +3, then multiply: 3 × 5 = 15.

How do I handle the negative sign before a variable?

Treat the negative sign as multiplying by -1. So -a becomes -1 × a. When a = -3: $-1 \times (-3) = +3$ .

What's the difference between -a·b and (-a)·b?

They're the same thing! Both mean "negative a times b". The parentheses in (-a)·b just make it clearer that the negative applies to the variable a.

How can I check if 15 is really correct?

Substitute back: -a·b where a = -3 and b = 5. Calculate: -(-3) × 5 = 3 × 5 = 15. Your answer matches!

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