Solve 5/9 + 4/9: Adding Fractions with Same Denominators

Fraction Addition with Identical Denominators

59+49= \frac{5}{9}+\frac{4}{9}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 Let's color the appropriate number of squares according to the given data
00:17 Now let's count and add to the numerator in the new fraction
00:22 The denominator equals the number of cells we divided
00:27 Any number divided by itself always equals 1
00:31 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

59+49= \frac{5}{9}+\frac{4}{9}=

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Step-by-step solution

To solve this problem, we will follow these steps:

  • Step 1: Identify that both fractions have the same denominator.
  • Step 2: Use the formula for adding fractions with like denominators.
  • Step 3: Calculate the sum of the numerators and keep the denominator unchanged.

Now, let’s work through each step:
Step 1: We observe that the fractions 59 \frac{5}{9} and 49 \frac{4}{9} both have the denominator of 9.
Step 2: We'll apply the formula for adding fractions: ac+bc=a+bc \frac{a}{c} + \frac{b}{c} = \frac{a+b}{c} .
Step 3: Add the numerators 5 and 4 while keeping the denominator as 9:
59+49=5+49=99=1 \frac{5}{9} + \frac{4}{9} = \frac{5 + 4}{9} = \frac{9}{9} = 1 .

Therefore, the solution to the problem is 1 1 .

3

Final Answer

1 1

Key Points to Remember

Essential concepts to master this topic
  • Same Denominator Rule: Add numerators, keep denominator unchanged
  • Calculation: 59+49=5+49=99 \frac{5}{9} + \frac{4}{9} = \frac{5+4}{9} = \frac{9}{9}
  • Simplification Check: 99=1 \frac{9}{9} = 1 because any number divided by itself equals 1 ✓

Common Mistakes

Avoid these frequent errors
  • Adding both numerators and denominators
    Don't add denominators: 59+49=918 \frac{5}{9} + \frac{4}{9} = \frac{9}{18} = wrong answer! This breaks the fundamental rule of fraction addition and gives an incorrect result. Always keep the denominator the same and only add the numerators.

Practice Quiz

Test your knowledge with interactive questions

\( \)\( \frac{4}{5}+\frac{1}{5}= \)

FAQ

Everything you need to know about this question

Why don't I add the denominators together?

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The denominator tells you what size pieces you're working with. Since both fractions are ninths, you're adding pieces of the same size. Adding denominators would change the piece size, which doesn't make sense!

How do I know when 99 \frac{9}{9} equals 1?

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Any fraction where the numerator equals the denominator is equal to 1! Think of it as having 9 pieces out of 9 total pieces - that's the whole thing, which is 1.

What if the numerators don't add up to equal the denominator?

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That's totally normal! Most fraction additions don't result in 1. For example, 29+39=59 \frac{2}{9} + \frac{3}{9} = \frac{5}{9} , and 59 \frac{5}{9} is already in simplest form.

Do I always need to simplify my answer?

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Yes, always simplify! Look for common factors in the numerator and denominator. In this case, 99 \frac{9}{9} simplifies to 1, which is much cleaner than leaving it as a fraction.

Can I use this method for any fractions with the same denominator?

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Absolutely! This same denominator rule works for any fractions: ac+bc=a+bc \frac{a}{c} + \frac{b}{c} = \frac{a+b}{c} . Just add the numerators and keep the denominator the same.

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