2\left(\dfrac{1}{5}m-\dfrac{2}{5}\right)+\dfrac{3}5

Let's simplify the given expression step by step:

\[
2\left(\dfrac{1}{5}m - \dfrac{2}{5}\right) + \dfrac{3}{5}
\]

### Step 1: Distribute the 2 across the terms inside the parentheses.
We multiply \( 2 \) by both \( \dfrac{1}{5}m \) and \( \dfrac{2}{5} \):

\[
2 \cdot \dfrac{1}{5}m = \dfrac{2}{5}m
\]
\[
2 \cdot \dfrac{2}{5} = \dfrac{4}{5}
\]

Now, the expression becomes:

\[
\dfrac{2}{5}m - \dfrac{4}{5} + \dfrac{3}{5}
\]

### Step 2: Combine like terms.
The constants \( -\dfrac{4}{5} \) and \( \dfrac{3}{5} \) are like terms, so we combine them:

\[
-\dfrac{4}{5} + \dfrac{3}{5} = -\dfrac{1}{5}
\]

Now, the simplified expression is:

\[
\dfrac{2}{5}m - \dfrac{1}{5}
\]

### Final Answer:
The simplified form of the expression is:

\[
\dfrac{2}{5}m - \dfrac{1}{5}
\]

Would you like a more detailed explanation of any step or have any other questions?

Here are 5 related questions you might find helpful:
1. How do you factor out common terms from algebraic expressions?
2. Can you solve an equation if \( \dfrac{2}{5}m - \dfrac{1}{5} = 0 \)?
3. How do you handle fractions when solving algebraic equations?
4. What are the general steps for simplifying expressions involving distribution?
5. How do you solve for a variable when fractions are involved?

**Tip:** When simplifying, always combine like terms (such as constants or variables) to make your expression as simple as possible.

2\left(\dfrac{1}{5}m - \dfrac{2}{5}\right) + \dfrac{3}{5}

Explore how to simplify the algebraic expression 2(1/5m - 2/5) + 3/5 using distribution and combining like terms. This step-by-step guide is suitable for students in Grades 6-8.

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