Evaluate -2m:(m+8):1/m with m=1 and m=-1: Sequential Division Challenge

Q: What does the colon (:) mean in this expression?

The colon (:) represents division. So $ -2m:(m+8):\frac{1}{m} $ means $ -2m ÷ (m+8) ÷ \frac{1}{m} $.

Q: Why do I get different answers for m=1 and m=-1?

Because the variable m appears in multiple places in the expression! When m changes, it affects $ -2m $, $ (m+8) $, and $ \frac{1}{m} $ differently.

Q: How do I handle dividing by a fraction like 1/m?

Dividing by a fraction is the same as multiplying by its reciprocal. So dividing by $ \frac{1}{m} $ means multiplying by $ m $.

Q: Do I work left to right or follow PEMDAS?

For sequential operations of the same type (like multiple divisions), work left to right. First do $ -2m ÷ (m+8) $, then divide that result by $ \frac{1}{m} $.

Q: Why is the answer negative for both values of m?

Look at the signs carefully! For m=1: $ -2 $ (negative) divided by positive numbers stays negative. For m=-1: even though $ -2(-1) = +2 $, the final division by $ -1 $ makes it negative again.

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

00:14 Negative times positive is always negative

00:22 Calculate parentheses

00:28 Any number divided by itself always equals 1

00:39 This is the solution for option A, now let's calculate option B

00:42 Let's substitute according to option B's data

00:49 Pay attention to parentheses

00:57 Negative times negative is always positive

01:01 Calculate parentheses

01:08 Positive divided by negative is always negative

01:16 Write division as a fraction

01:21 Positive divided by negative is always negative

01:26 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 expression below:

$-2m:(m+8):\frac{1}{m}$

Substitue and calculate:

$m=1$

$m=-1$

2

Step-by-step solution

Let's start with the first option.

Let's substitute the data in the expression:

$-2\times(1):(1+8):\frac{1}{1}=$

We'll solve the multiplication (a negative number multiplied by a positive number gives a negative result), then solve what's in parentheses, and finally the simple fraction:

$-2:9:1=$

We'll solve from left to right.

Let's write the division as a simple fraction:

$-\frac{2}{9}:1=-\frac{2}{9}$

Let's continue with the second option.

Let's substitute the data in the expression:

$-2\times(-1):(-1+8):\frac{1}{-1}=$

First, we'll solve the multiplication (we're multiplying two negative numbers so the result will be positive), then the parentheses, and finally the fraction (we're dividing a positive number by a negative number so the result will be negative):

$2:7:-1=$

We'll solve from left to right, let's write the division as a simple fraction:

$+\frac{2}{7}:(-1)=$

Since we're dividing a positive number by a negative number, the result must be negative:

$-\frac{2}{7}$

Therefore, the final answer is:

$1=-\frac{2}{9},2=-\frac{2}{7}$

3

Final Answer

$-\frac{2}{7},-\frac{2}{9}$

Key Points to Remember

Essential concepts to master this topic

Order: Evaluate divisions from left to right sequentially
Technique: For $-2:9:1$ , first calculate $-\frac{2}{9}$ , then divide by 1
Check: Substitute both m values and verify $-\frac{2}{9}$ and $-\frac{2}{7}$ ✓

Common Mistakes

Avoid these frequent errors

Combining all divisions into one fraction
Don't write $-2:(m+8):\frac{1}{m}$ as $\frac{-2m}{m+8}$ = wrong structure! Sequential division means divide step-by-step from left to right, not create one big fraction. Always perform each division operation separately in order.

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

What does the colon (:) mean in this expression?

+

The colon (:) represents division. So $-2m:(m+8):\frac{1}{m}$ means $-2m ÷ (m+8) ÷ \frac{1}{m}$ .

Why do I get different answers for m=1 and m=-1?

+

Because the variable m appears in multiple places in the expression! When m changes, it affects $-2m$ , $(m+8)$ , and $\frac{1}{m}$ differently.

How do I handle dividing by a fraction like 1/m?

+

Dividing by a fraction is the same as multiplying by its reciprocal. So dividing by $\frac{1}{m}$ means multiplying by $m$ .

Do I work left to right or follow PEMDAS?

+

For sequential operations of the same type (like multiple divisions), work left to right. First do $-2m ÷ (m+8)$ , then divide that result by $\frac{1}{m}$ .

Why is the answer negative for both values of m?

+

Look at the signs carefully! For m=1: $-2$ (negative) divided by positive numbers stays negative. For m=-1: even though $-2(-1) = +2$ , the final division by $-1$ makes it negative again.

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Evaluate -2m:(m+8):1/m with m=1 and m=-1: Sequential Division Challenge

Sequential Division with Variable Substitution

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