Solve the Fraction Addition: 1/3 + 4/9 Step-by-Step

Fraction Addition with Unlike Denominators

Solve the following equation:

13+49= \frac{1}{3}+\frac{4}{9}=

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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 together.
00:08 First, multiply the fraction by 3, to find a common denominator.
00:13 Remember, multiply both the numerator and the denominator.
00:21 Now, calculate what you get from these multiplications.
00:30 Next, add the fractions using the common denominator.
00:35 Finally, calculate the new numerator.
00:39 Great job! That's how we find the solution.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the following equation:

13+49= \frac{1}{3}+\frac{4}{9}=

2

Step-by-step solution

We must first identify the lowest common denominator between 3 and 9.

In order to determine 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.

We will then proceed to 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+4×19×1=39+49 \frac{1\times3}{3\times3}+\frac{4\times1}{9\times1}=\frac{3}{9}+\frac{4}{9}

Finally we'll combine and obtain the following:

3+49=79 \frac{3+4}{9}=\frac{7}{9}

3

Final Answer

79 \frac{7}{9}

Key Points to Remember

Essential concepts to master this topic
  • LCD Rule: Find the least common denominator before adding fractions
  • Technique: Convert 13 \frac{1}{3} to 39 \frac{3}{9} by multiplying by 3
  • Check: Verify 39+49=79 \frac{3}{9} + \frac{4}{9} = \frac{7}{9} by adding numerators ✓

Common Mistakes

Avoid these frequent errors
  • Adding numerators and denominators separately
    Don't add 1+4=5 and 3+9=12 to get 5/12! This ignores the fundamental rule that fractions need common denominators. Always find the LCD first, convert both fractions, 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 straight across?

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Fractions represent parts of a whole, and you can only add parts when they're the same size! Think of it like adding 1 slice of a 3-piece pizza to 4 slices of a 9-piece pizza - you need equal-sized pieces first.

How do I know if 9 is really 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, and there's no smaller number that works, 9 is the LCD.

What if both fractions need to be converted?

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Sometimes both fractions need converting! For example, with 14+16 \frac{1}{4} + \frac{1}{6} , the LCD is 12, so you'd convert both: 312+212 \frac{3}{12} + \frac{2}{12} .

Do I need to simplify my final answer?

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Always check if you can simplify! In this problem, 79 \frac{7}{9} is already in lowest terms since 7 and 9 share no common factors besides 1.

Can I use a different common denominator besides the LCD?

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You could use any common multiple, but the LCD makes the math easiest. Using 18 instead of 9 would work but create unnecessarily large numbers to work with.

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