Solve m/n + 3(-m): Algebraic Expression Evaluation with Given Values

Algebraic Expression Evaluation with Negative Values

Look at the following expression:

mn+3(m) \frac{m}{n}+3(-m)


Substitute and calculate:

  1. m=3,n=0.2 m=3,n=-0.2

  2. m=4,n=3 m=-4,n=-3

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Set up and calculate
00:03 Let's start by setting up the first option
00:07 Be careful with parentheses
00:16 Convert from decimal to fraction
00:25 Positive times negative always equals negative
00:33 Instead of dividing, multiply by the reciprocal
00:37 Positive times negative always equals negative
00:54 This is the solution for option A, now let's calculate option B
01:00 Let's set up according to the data for option B
01:03 Be careful with parentheses
01:07 Negative divided by negative always equals positive
01:11 Negative times negative always equals positive
01:24 Break down the fraction into whole number and remainder
01:35 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Look at the following expression:

mn+3(m) \frac{m}{n}+3(-m)


Substitute and calculate:

  1. m=3,n=0.2 m=3,n=-0.2

  2. m=4,n=3 m=-4,n=-3

2

Step-by-step solution

Let's start with the first option.

Let's substitute the given data into the expression:

30.2+3(3)= \frac{3}{-0.2}+3(-3)=

We'll next solve the exercise from left to right, first converting 0.2 into a simple fraction:

315+3(3)= \frac{3}{-\frac{1}{5}}+3(-3)=

Now let's solve the multiplication problem, remembering that when we multiply a positive number by a negative number, the result must be negative:

3×(3)=9 3\times(-3)=-9

Now we have the exercise:

315+(9)= \frac{3}{-\frac{1}{5}}+(-9)=

Let's convert the division problem to a multiplication problem, remembering to switch between the numerator and denominator of the fraction:

3×51+(9)= 3\times-\frac{5}{1}+(-9)=

Let's take -9 out of the parentheses and keep the appropriate sign:

3×(5)19= \frac{3\times(-5)}{1}-9=

3×(5)9= 3\times(-5)-9=

159=24 -15-9=-24

Let's continue with the second option.

First we'll substitute the given data into the expression:

43+3((4))= \frac{-4}{-3}+3(-(-4))=

Let's next solve the exercise from left to right.

Note that we are dividing a negative number by a negative number, so the result must be positive:

43+3((4))= \frac{4}{3}+3(-(-4))=

Let's open the parentheses and keep the appropriate sign:

43+3×(4)= \frac{4}{3}+3\times(4)=

Let's solve the multiplication problem:

43+12= \frac{4}{3}+12=

Let's break down the fraction into an addition problem:

3+13+12=33+13+12=1+13+12=1313 \frac{3+1}{3}+12=\frac{3}{3}+\frac{1}{3}+12=1+\frac{1}{3}+12=13\frac{1}{3}

Therefore, the final answer is:

1=24,2=1313 1=-24,2=13\frac{1}{3}

3

Final Answer

1=24,2=+1313 1=-24,2=+13\frac{1}{3}

Key Points to Remember

Essential concepts to master this topic
  • Order of Operations: Calculate division first, then multiplication, finally addition/subtraction
  • Technique: For 30.2 \frac{3}{-0.2} , convert to 3×(5)=15 3 \times (-5) = -15
  • Check: Substitute back: 30.2+3(3)=15+(9)=24 \frac{3}{-0.2} + 3(-3) = -15 + (-9) = -24

Common Mistakes

Avoid these frequent errors
  • Forgetting to apply signs correctly when substituting negative values
    Don't substitute m = -4 as 3(-4) = 3(4) = 12! This ignores the negative sign and gives positive results instead of negative. Always carefully track each negative sign: 3(-(-4)) = 3(4) = 12.

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

How do I handle division by a negative decimal like -0.2?

+

Convert the decimal to a fraction first! 0.2=15 -0.2 = -\frac{1}{5} , so 30.2=3÷(15)=3×(5)=15 \frac{3}{-0.2} = 3 \div (-\frac{1}{5}) = 3 \times (-5) = -15 .

What does 3(-m) mean when m is already negative?

+

When m = -4, then 3(-m) = 3(-(-4)) = 3(4) = 12. The double negative becomes positive! Always work from the inside out with parentheses.

Why is my answer different from the mixed number format?

+

Both forms are correct! 403=1313 \frac{40}{3} = 13\frac{1}{3} since 40 ÷ 3 = 13 remainder 1. Use whichever format the problem asks for.

How do I know which operation to do first?

+

Follow PEMDAS: Parentheses first, then division mn \frac{m}{n} , then multiplication 3(-m), finally addition. Work left to right within each step.

What if I get confused with all the negative signs?

+

Slow down and track each step! Write out what you're substituting: "m = 3, so -m = -3, so 3(-m) = 3(-3) = -9". Take it one substitution at a time.

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