Evaluate -3m+4: Substituting m=2 and m=-1/2

Q: Why does m = 2 give the same answer as m = -1/2?

Because the variable m cancels out completely in the fraction! When you simplify $ \frac{m}{-3m} $, the m's cancel to give $ \frac{1}{-3} $, which is just a number.

Q: What if m = 0? Can I still cancel the variables?

No! When m = 0, you get $ \frac{0}{0} $ which is undefined. Variable cancellation only works when the variable is not zero.

Q: How do I add -1/3 + 4?

Convert 4 to thirds: $ 4 = \frac{12}{3} $. Then: $ -\frac{1}{3} + \frac{12}{3} = \frac{11}{3} = 3\frac{2}{3} $

Q: Why is the answer positive when we have -3m in the denominator?

After canceling m, we get $ -\frac{1}{3} + 4 $. The +4 is much larger than the $ -\frac{1}{3} $, so the final result is positive!

Algebraic Substitution with Variable Cancellation

Look at the following algebraic expression:

$m:-3m+4$

Calculate when: $m=2$

Calculate when: $m=-\frac{1}{2}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:09 First, let's set it up and calculate.

00:13 Let's begin by simplifying the expression, step by step.

00:18 We'll reduce whatever we can. Just take it slowly.

00:24 A positive number divided by a negative one is always negative.

00:35 In our simplified expression, the variable M isn't needed.

00:40 And there you have it! That's the solution to our question.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Look at the following algebraic expression:

$m:-3m+4$

Calculate when: $m=2$

Calculate when: $m=-\frac{1}{2}$

Step-by-step solution

Let's start with the first option.

Let's write the division exercise in the expression as a simple fraction:

$\frac{m}{-3m}+4=$

Note that we can reduce the m in both the numerator and denominator of the fraction to get:

$\frac{1}{-3}+4=$

Since we are dividing a negative number by a positive number, we will get a negative result:

$-\frac{1}{3}+4=3\frac{2}{3}$

Let's continue with the second option.

Since in the previous exercise we saw that we can reduce the m in the numerator and denominator of the fraction, we'll do the same thing here and therefore reach the same result:

$3\frac{2}{3}$

Therefore, the final answer is that for any m the expression will equal -3 and two thirds.

Final Answer

For each m the value of the expression will be $+3\frac{2}{3}$ .

Key Points to Remember

Essential concepts to master this topic

Rule: When variables cancel out, result is constant for all values
Technique: For m/(-3m), cancel m to get 1/(-3) = -1/3
Check: Substitute any m value: result always equals 3⅔ ✓

Common Mistakes

Avoid these frequent errors

Not recognizing when variables cancel completely
Don't substitute specific values into m/(-3m) without simplifying first = missing the pattern! This leads to thinking different m values give different answers. Always cancel common variables in fractions before substituting.

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 m = 2 give the same answer as m = -1/2?

Because the variable m cancels out completely in the fraction! When you simplify $\frac{m}{-3m}$ , the m's cancel to give $\frac{1}{-3}$ , which is just a number.

What if m = 0? Can I still cancel the variables?

No! When m = 0, you get $\frac{0}{0}$ which is undefined. Variable cancellation only works when the variable is not zero.

How do I add -1/3 + 4?

Convert 4 to thirds: $4 = \frac{12}{3}$ . Then: $-\frac{1}{3} + \frac{12}{3} = \frac{11}{3} = 3\frac{2}{3}$

Is this expression really the same for ANY value of m?

Yes! (except m = 0). Since the variable cancels out, the expression becomes a constant. Try any non-zero value and you'll always get $3\frac{2}{3}$ .

Why is the answer positive when we have -3m in the denominator?

After canceling m, we get $-\frac{1}{3} + 4$ . The +4 is much larger than the $-\frac{1}{3}$ , so the final result is positive!

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