Solve the Fraction Addition: 2/5 + 3/10 Step by Step

Fraction Addition with Common Denominators

Solve the following exercise:

25+310=? \frac{2}{5}+\frac{3}{10}=\text{?}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 Multiply the fraction by 2 to find a common denominator
00:09 Remember to multiply both numerator and denominator
00:20 Calculate the multiplications
00:26 Add under common denominator
00:29 Calculate the numerator
00:33 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

Solve the following exercise:

25+310=? \frac{2}{5}+\frac{3}{10}=\text{?}

2

Step-by-step solution

To solve this problem, we need to add the fractions 25 \frac{2}{5} and 310 \frac{3}{10} .

Firstly, we find a common denominator for the fractions. The denominators are 5 and 10. The least common multiple (LCM) of 5 and 10 is 10.

Next, we convert each fraction to an equivalent fraction with the denominator of 10:

  • The fraction 25 \frac{2}{5} is equivalent to 2×25×2=410 \frac{2 \times 2}{5 \times 2} = \frac{4}{10} .
  • The fraction 310 \frac{3}{10} is already expressed with the denominator of 10, so it remains as 310 \frac{3}{10} .

Now, we add both fractions: 410+310=4+310=710 \frac{4}{10} + \frac{3}{10} = \frac{4+3}{10} = \frac{7}{10} .

Therefore, the solution to the exercise is 710 \frac{7}{10} .

3

Final Answer

710 \frac{7}{10}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Find common denominator before adding numerators
  • Technique: Convert 2/5 to 4/10 by multiplying top and bottom by 2
  • Check: Verify 4/10 + 3/10 = 7/10 by adding numerators only ✓

Common Mistakes

Avoid these frequent errors
  • Adding denominators along with numerators
    Don't add 2/5 + 3/10 = 5/15! This creates a completely wrong fraction. The denominators represent the size of parts, not quantities to add. Always keep the common denominator and only add the numerators.

Practice Quiz

Test your knowledge with interactive questions

Complete the following exercise:

\( \frac{3}{4}:\frac{5}{6}=\text{?} \)

FAQ

Everything you need to know about this question

Why can't I just add 2/5 + 3/10 directly?

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You can't add fractions with different denominators directly because they represent different-sized pieces. Think of it like trying to add 2 slices of pizza cut into 5 pieces with 3 slices cut into 10 pieces - you need the same size pieces first!

How do I find the common denominator?

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Look for the Least Common Multiple (LCM) of the denominators. For 5 and 10, since 10 is already a multiple of 5, the LCM is 10. This makes your work easier!

What if my answer can be simplified further?

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Always check if your final answer can be reduced! For 710 \frac{7}{10} , since 7 and 10 share no common factors other than 1, it's already in simplest form.

Do I always use the larger denominator as the common denominator?

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Not always! Use the LCM instead. If adding 14+16 \frac{1}{4} + \frac{1}{6} , the LCM of 4 and 6 is 12, not 6. This ensures you find the smallest common denominator.

Why did 2/5 become 4/10?

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When you multiply both the numerator and denominator by the same number (2), you create an equivalent fraction: 2×25×2=410 \frac{2 \times 2}{5 \times 2} = \frac{4}{10} . This doesn't change the value, just the form!

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