Solve: 2/5 - 2 + 3/5 | Fraction and Whole Number Operations

Q: Why should I rearrange the terms instead of solving left to right?

Rearranging helps you group like terms together! When you see $ \frac{2}{5}+\frac{3}{5} $, it's much easier to add these first since they have the same denominator.

Q: Can I convert the whole number 2 to a fraction instead?

Yes! You could write $ 2 = \frac{10}{5} $, then compute $ \frac{2}{5}-\frac{10}{5}+\frac{3}{5} = \frac{2-10+3}{5} = \frac{-5}{5} = -1 $. Both methods work!

Q: How do I know when fractions have the same denominator?

Look at the bottom numbers of each fraction. In this problem, both $ \frac{2}{5} $ and $ \frac{3}{5} $ have 5 as the denominator, so they're like fractions.

Q: What if I get confused about the order of operations?

Remember PEMDAS! Since we only have addition and subtraction here, work left to right. But rearranging using the commutative property can make it simpler.

Q: Why does 5/5 equal 1?

Any fraction where the numerator equals the denominator equals 1! Think of it as $ \frac{5}{5} = 5 \div 5 = 1 $. This is a fundamental fraction rule.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 We'll use the commutative law and arrange the exercise to make it easier to solve

00:14 We'll continue solving according to the correct order of operations, from left to right

00:16 When adding fractions, we'll be careful to add numerators while keeping the denominator

00:23 We'll convert from fraction to whole number and continue solving

00:28 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

$\frac{2}{5}-2+\frac{3}{5}=$

2

Step-by-step solution

We can use the substitutive property to reorder and make solving the equation simpler:

$\frac{2}{5}+\frac{3}{5}-2=$

We first add the fractions:

$\frac{2+3}{5}=\frac{5}{5}=1$

Now we obtain the exercise:

$1-2=-1$

3

Final Answer

$-1$

Key Points to Remember

Essential concepts to master this topic

Commutative Property: Rearrange terms to group like fractions together first
Technique: Add fractions with same denominator: $\frac{2}{5}+\frac{3}{5}=\frac{5}{5}=1$
Check: Verify by substituting: $\frac{2}{5}-2+\frac{3}{5}=1-2=-1$ ✓

Common Mistakes

Avoid these frequent errors

Adding fractions and whole numbers directly without proper conversion
Don't try to compute $\frac{2}{5}-2$ directly = confusion and wrong answers! This mixes different number forms incorrectly. Always group like fractions first, then handle whole number operations.

Practice Quiz

Test your knowledge with interactive questions

$$ 94+12+6= $$

FAQ

Everything you need to know about this question

Why should I rearrange the terms instead of solving left to right?

+

Rearranging helps you group like terms together! When you see $\frac{2}{5}+\frac{3}{5}$ , it's much easier to add these first since they have the same denominator.

Can I convert the whole number 2 to a fraction instead?

+

Yes! You could write $2 = \frac{10}{5}$ , then compute $\frac{2}{5}-\frac{10}{5}+\frac{3}{5} = \frac{2-10+3}{5} = \frac{-5}{5} = -1$ . Both methods work!

How do I know when fractions have the same denominator?

+

Look at the bottom numbers of each fraction. In this problem, both $\frac{2}{5}$ and $\frac{3}{5}$ have 5 as the denominator, so they're like fractions.

What if I get confused about the order of operations?

+

Remember PEMDAS! Since we only have addition and subtraction here, work left to right. But rearranging using the commutative property can make it simpler.

Why does 5/5 equal 1?

+

Any fraction where the numerator equals the denominator equals 1! Think of it as $\frac{5}{5} = 5 \div 5 = 1$ . This is a fundamental fraction rule.

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Solve: 2/5 - 2 + 3/5 | Fraction and Whole Number Operations

Mixed Operations with Like Fractions

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