Solve the Fraction Addition: 1/2.5 + 2/5 Step by Step

Q: Why can't I just add the numerators and denominators separately?

Fractions represent parts of a whole. You can only add parts when they're the same size! Think of it like adding 1/2 pizza slice + 2/5 pizza slice - you need equal-sized pieces first.

Q: How do I convert 2.5 to a fraction?

Since 2.5 = 2 + 0.5 = 2 + 1/2 = $ \frac{5}{2} $. So $ \frac{1}{2.5} = \frac{1}{\frac{5}{2}} = \frac{2}{5} $ by flipping and multiplying!

Q: What's the easiest way to find the LCD of fractions?

List the multiples of each denominator until you find the smallest common one. For 5/2 and 5: multiples of 2 are 2,4,6,8,10... and multiples of 5 are 5,10,15... So LCD = 10.

Q: Why does 1/2.5 equal 2/5?

When you have $ \frac{1}{2.5} $, convert 2.5 to fraction form: $ \frac{5}{2} $. Then $ \frac{1}{\frac{5}{2}} = 1 \times \frac{2}{5} = \frac{2}{5} $.

Q: How can I check if 4/5 is the right answer?

Convert everything to decimals: $ \frac{1}{2.5} = 0.4 $ and $ \frac{2}{5} = 0.4 $. So 0.4 + 0.4 = 0.8, and $ \frac{4}{5} = 0.8 $ ✓

Fraction Addition with Decimal Denominators

Solve the following exercise:

$\frac{1}{2.5}+\frac{2}{5}=\text{?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 We want to find the least common denominator

00:06 Therefore, multiply by 2 for the common denominator 5

00:09 Remember to multiply both numerator and denominator

00:15 Let's calculate the multiplications

00:22 Add under common denominator

00:27 Calculate the numerator

00:30 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following exercise:

$\frac{1}{2.5}+\frac{2}{5}=\text{?}$

Final Answer

$\frac{4}{5}$

Key Points to Remember

Essential concepts to master this topic

Conversion: Change decimal denominator to fraction: 2.5 = 5/2
Technique: Find LCD of 5/2 and 5: LCD = 10
Check: Verify 2/5 + 2/5 = 4/5 using common denominator ✓

Common Mistakes

Avoid these frequent errors

Adding fractions with different denominators directly
Don't add 1/2.5 + 2/5 = 3/7.5! This ignores the rule that fractions need common denominators before adding. Always convert to equivalent fractions with the same denominator first.

Practice Quiz

Test your knowledge with interactive questions

$$ $\frac{4}{5}+\frac{1}{5}=$

FAQ

Everything you need to know about this question

Why can't I just add the numerators and denominators separately?

Fractions represent parts of a whole. You can only add parts when they're the same size! Think of it like adding 1/2 pizza slice + 2/5 pizza slice - you need equal-sized pieces first.

How do I convert 2.5 to a fraction?

Since 2.5 = 2 + 0.5 = 2 + 1/2 = $\frac{5}{2}$ . So $\frac{1}{2.5} = \frac{1}{\frac{5}{2}} = \frac{2}{5}$ by flipping and multiplying!

What's the easiest way to find the LCD of fractions?

List the multiples of each denominator until you find the smallest common one. For 5/2 and 5: multiples of 2 are 2,4,6,8,10... and multiples of 5 are 5,10,15... So LCD = 10.

Why does 1/2.5 equal 2/5?

When you have $\frac{1}{2.5}$ , convert 2.5 to fraction form: $\frac{5}{2}$ . Then $\frac{1}{\frac{5}{2}} = 1 \times \frac{2}{5} = \frac{2}{5}$ .

How can I check if 4/5 is the right answer?

Convert everything to decimals: $\frac{1}{2.5} = 0.4$ and $\frac{2}{5} = 0.4$ . So 0.4 + 0.4 = 0.8, and $\frac{4}{5} = 0.8$ ✓

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