Solve the Fraction Addition: 1/3 + 5/9 Step-by-Step

Fraction Addition with Common Denominators

Solve the following exercise:

13+59= \frac{1}{3}+\frac{5}{9}=

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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 3 to find the common denominator
00:07 Make sure to multiply both numerator and denominator
00:11 Calculate the products
00:17 Add with the common denominator
00:21 Calculate the numerator
00:25 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:

13+59= \frac{1}{3}+\frac{5}{9}=

2

Step-by-step solution

Let's try to find the lowest common denominator between 3 and 9

To find the lowest common denominator, we need to find a number that is divisible by both 3 and 9

In this case, the common denominator is 9

Now we'll multiply each fraction by the appropriate number to reach the denominator 9

We'll multiply the first fraction by 3

We'll multiply the second fraction by 1

1×33×3+5×19×1=39+59 \frac{1\times3}{3\times3}+\frac{5\times1}{9\times1}=\frac{3}{9}+\frac{5}{9}

Now we'll combine and get:

3+59=89 \frac{3+5}{9}=\frac{8}{9}

3

Final Answer

89 \frac{8}{9}

Key Points to Remember

Essential concepts to master this topic
  • LCD Rule: Find lowest common denominator to add fractions properly
  • Technique: Convert 13 \frac{1}{3} to 39 \frac{3}{9} by multiplying by 3
  • Check: Verify 39+59=89 \frac{3}{9} + \frac{5}{9} = \frac{8}{9} by adding numerators ✓

Common Mistakes

Avoid these frequent errors
  • Adding numerators and denominators separately
    Don't add 1+5=6 and 3+9=12 to get 6/12! This completely ignores the fraction rules and gives wrong results. 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 1+5 and 3+9 to get 6/12?

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Fractions represent parts of a whole. You can only add fractions when they have the same denominator (same-sized pieces). Adding across both parts gives a meaningless result!

How do I know 9 is the LCD of 3 and 9?

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The LCD is the smallest number that both denominators divide into evenly. Since 9 ÷ 3 = 3 and 9 ÷ 9 = 1, nine works perfectly as our common denominator.

Do I always multiply the first fraction to get the LCD?

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Not always! Look at each fraction individually. Here, 59 \frac{5}{9} already has denominator 9, so we multiply it by 11 \frac{1}{1} (which doesn't change it).

Can I simplify 8/9 further?

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No, 89 \frac{8}{9} is already in simplest form! Since 8 and 9 share no common factors except 1, this fraction cannot be reduced.

What if the LCD was a bigger number like 18?

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You could use 18, but it's not the lowest common denominator. Using the LCD keeps your numbers smaller and makes the arithmetic easier to handle.

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