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

Fraction Addition with Different Denominators

35+310= \frac{3}{5}+\frac{3}{10}=

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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 Multiply by 2 to find the common denominator
00:09 Remember to multiply both numerator and denominator
00:15 Calculate the products
00:20 Add under the 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
1

Understand the problem

35+310= \frac{3}{5}+\frac{3}{10}=

2

Step-by-step solution

To solve this problem, we'll follow these steps:

  • Step 1: Identify the given fractions, 35 \frac{3}{5} and 310 \frac{3}{10} .
  • Step 2: Find the least common denominator (LCD) of the denominators 5 and 10.
  • Step 3: Convert each fraction to have this common denominator.
  • Step 4: Add the fractions.

Now, let's work through each step:

Step 1: We have the fractions 35 \frac{3}{5} and 310 \frac{3}{10} .

Step 2: Check the denominators. The denominators are 5 and 10. The least common multiple of 5 and 10 is 10. Thus, our common denominator will be 10.

Step 3: Convert each fraction to an equivalent fraction with a denominator of 10:
35 \frac{3}{5} is equivalent to 3×25×2=610 \frac{3 \times 2}{5 \times 2} = \frac{6}{10} (since 510 \frac{5}{10} must equal 10, multiply both numerator and denominator by 2).

Step 4: The fraction 310 \frac{3}{10} already has the denominator of 10.
Thus, 35+310=610+310=6+310=910 \frac{3}{5} + \frac{3}{10} = \frac{6}{10} + \frac{3}{10} = \frac{6 + 3}{10} = \frac{9}{10} .

Therefore, the answer to the problem is 910 \frac{9}{10} , which corresponds to choice 1.

3

Final Answer

910 \frac{9}{10}

Key Points to Remember

Essential concepts to master this topic
  • Common Denominator: Find LCD before adding fractions with different denominators
  • Technique: Convert 35 \frac{3}{5} to 610 \frac{6}{10} by multiplying by 22 \frac{2}{2}
  • Check: Verify 610+310=910 \frac{6}{10} + \frac{3}{10} = \frac{9}{10} by adding numerators only ✓

Common Mistakes

Avoid these frequent errors
  • Adding numerators and denominators separately
    Don't add 35+310 \frac{3}{5} + \frac{3}{10} as 615 \frac{6}{15} ! This gives the wrong answer because you can't add fractions with different denominators directly. Always find a common denominator first, then add only 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 3+3=6 and 5+10=15?

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Because fractions represent parts of different wholes! 35 \frac{3}{5} means 3 parts out of 5, while 310 \frac{3}{10} means 3 parts out of 10. You need the same-sized pieces (common denominator) before adding.

How do I find the least common denominator?

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Look for the smallest number that both denominators divide into evenly. Since 5 goes into 10, and 10 goes into 10, the LCD of 5 and 10 is simply 10!

Do I always multiply the first fraction to get the common denominator?

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Not always! Sometimes the second fraction needs converting, sometimes both do. In this case, 310 \frac{3}{10} already has denominator 10, so only 35 \frac{3}{5} needs converting.

What if my answer is an improper fraction?

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That's perfectly fine! 910 \frac{9}{10} is a proper fraction, but if you got something like 1310 \frac{13}{10} , you could leave it as is or convert to 1310 1\frac{3}{10} .

How can I check if my answer is right?

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Convert both fractions to decimals and add: 35=0.6 \frac{3}{5} = 0.6 and 310=0.3 \frac{3}{10} = 0.3 , so 0.6 + 0.3 = 0.9 = 910 \frac{9}{10}

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