Solve the Fraction Addition: 2/8 + 2/3 Step by Step

Fraction Addition with Different Denominators

Solve the following exercise:

28+23= \frac{2}{8}+\frac{2}{3}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 Multiply each fraction by the second denominator to find the common denominator
00:08 Make sure to multiply both numerator and denominator
00:19 Calculate the multiplications
00:26 Add with the common denominator
00:30 Calculate the numerator
00:33 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:

28+23= \frac{2}{8}+\frac{2}{3}=

2

Step-by-step solution

Let's try to find the least common multiple (LCM) between 8 and 3

To find the least common multiple, we need to find a number that is divisible by both 8 and 3

In this case, the common multiple is 24

Now we'll multiply each fraction by the appropriate number to reach the denominator 24

We'll multiply the first fraction by 3

We'll multiply the second fraction by 8

2×38×3+2×83×8=624+1624 \frac{2\times3}{8\times3}+\frac{2\times8}{3\times8}=\frac{6}{24}+\frac{16}{24}

Now we'll combine and get:

6+1624=2224 \frac{6+16}{24}=\frac{22}{24}

3

Final Answer

2224 \frac{22}{24}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Find the least common denominator before adding fractions
  • Technique: Convert 28 \frac{2}{8} to 624 \frac{6}{24} and 23 \frac{2}{3} to 1624 \frac{16}{24}
  • Check: Verify LCD is correct: 24 ÷ 8 = 3, 24 ÷ 3 = 8 ✓

Common Mistakes

Avoid these frequent errors
  • Adding numerators and denominators separately
    Don't add 2+2=4 and 8+3=11 to get 4/11! This ignores that fractions represent parts of different wholes. Always find the LCD first to make denominators equal, then add only the numerators.

Practice Quiz

Test your knowledge with interactive questions

\( \frac{2}{4}+\frac{1}{4}= \)\( \)

FAQ

Everything you need to know about this question

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

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Because 28 \frac{2}{8} and 23 \frac{2}{3} represent different-sized pieces! It's like adding 2 slices from a pizza cut into 8 pieces with 2 slices from a pizza cut into 3 pieces - you need equal-sized pieces first.

How do I find the LCD of 8 and 3?

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List multiples of each number: 8: 8, 16, 24, 32... and 3: 3, 6, 9, 12, 15, 18, 21, 24... The first number that appears in both lists is your LCD, which is 24.

Do I need to simplify my final answer?

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It's good practice to check if you can simplify! 2224 \frac{22}{24} can be simplified by dividing both parts by 2 to get 1112 \frac{11}{12} , but many problems accept either form.

What if the denominators have no common factors?

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When denominators share no common factors (like 5 and 7), simply multiply them together to get your LCD. For example, LCD of 5 and 7 would be 35.

Can I convert to decimals instead?

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Yes, but be careful with repeating decimals! 23=0.666... \frac{2}{3} = 0.666... which might lead to rounding errors. Fraction form keeps your answer exact.

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