Solve the Fraction Addition: 1/2 + 3/10 Step by Step

Fraction Addition with Different Denominators

Solve the following exercise:

12+310= \frac{1}{2}+\frac{3}{10}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:05 Let's solve this math problem step by step.
00:08 First, we'll multiply the fraction by 5 to get a common denominator. This will make it easier to work with.
00:16 Remember, when we multiply a fraction, we need to multiply both the top number (numerator) and bottom number (denominator).
00:24 Now, let's work out these multiplications carefully.
00:28 Great! Now we can add the fractions since they have the same denominator.
00:34 Let's add the numbers in the numerator while keeping the same denominator.
00:38 And there we have it! We've found our solution. Great job following along!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the following exercise:

12+310= \frac{1}{2}+\frac{3}{10}=

2

Step-by-step solution

Let's try to find the least common denominator between 2 and 10

To find the least common denominator, we need to find a number that is divisible by both 2 and 10

In this case, the common denominator is 10

Now we'll multiply each fraction by the appropriate number to reach the denominator 10

We'll multiply the first fraction by 5

We'll multiply the second fraction by 1

1×52×5+3×110×1=510+310 \frac{1\times5}{2\times5}+\frac{3\times1}{10\times1}=\frac{5}{10}+\frac{3}{10}

Now we'll combine and get:

5+310=810 \frac{5+3}{10}=\frac{8}{10}

3

Final Answer

810 \frac{8}{10}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Find the least common denominator before adding fractions
  • Technique: Convert 12 \frac{1}{2} to 510 \frac{5}{10} by multiplying by 5
  • Check: 510+310=810 \frac{5}{10} + \frac{3}{10} = \frac{8}{10} with same denominators ✓

Common Mistakes

Avoid these frequent errors
  • Adding numerators and denominators separately
    Don't add 1 + 3 = 4 and 2 + 10 = 12 to get 412 \frac{4}{12} ! This completely ignores fraction rules and gives wrong answers. Always find a common denominator first, then add only the numerators.

Practice Quiz

Test your knowledge with interactive questions

Without calculating, determine whether the quotient in the division exercise is less than 1 or not:

\( 5:6= \)

FAQ

Everything you need to know about this question

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

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Fractions represent parts of a whole. You can't combine 12 \frac{1}{2} (half) and 310 \frac{3}{10} (three tenths) until they represent parts of the same size whole!

How do I find the least common denominator?

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Look for the smallest number that both denominators divide into evenly. For 2 and 10: 10 ÷ 2 = 5 (evenly), so 10 is the LCD.

What if the LCD isn't obvious?

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List the multiples of each denominator until you find a match:

  • Multiples of 2: 2, 4, 6, 8, 10
  • Multiples of 10: 10, 20, 30...

The first common number is your LCD!

Do I need to simplify my final answer?

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Yes! Always check if you can simplify. 810 \frac{8}{10} can be simplified to 45 \frac{4}{5} by dividing both parts by 2.

Can I use any common denominator, not just the least one?

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Yes, but using the least common denominator keeps your numbers smaller and easier to work with. Any common denominator will give the same final answer!

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