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

Convert $\frac{7}{2}$ into its reciprocal form:

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

Algebraic Substitution with Variable Cancellation

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

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

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

How do I add -1/3 + 4?

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

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

🌟 Unlock Your Math Potential

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