Solve: Adding 3/8 + 2/3 - Unlike Denominators Practice

Fraction Addition with Different Denominators

Solve the following exercise:

38+23= \frac{3}{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
00:07 Make sure to multiply both numerator and denominator
00:15 Calculate the multiplications
00:21 Add with the common denominator
00:24 Calculate the numerator
00:28 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:

38+23= \frac{3}{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

3×38×3+2×83×8=924+1624 \frac{3\times3}{8\times3}+\frac{2\times8}{3\times8}=\frac{9}{24}+\frac{16}{24}

Now we'll combine and get:

9+1624=2524 \frac{9+16}{24}=\frac{25}{24}

3

Final Answer

2524 \frac{25}{24}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Find LCD before adding fractions with different denominators
  • Technique: Convert 38 \frac{3}{8} to 924 \frac{9}{24} and 23 \frac{2}{3} to 1624 \frac{16}{24}
  • Check: Verify LCD is correct: 24 ÷ 8 = 3 and 24 ÷ 3 = 8 ✓

Common Mistakes

Avoid these frequent errors
  • Adding numerators and denominators separately
    Don't add 3 + 2 = 5 and 8 + 3 = 11 to get 5/11! This completely ignores fraction rules and gives a wrong answer. 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

How do I find the LCD of 8 and 3?

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Since 8 and 3 share no common factors, multiply them together: 8 × 3 = 24. For numbers that aren't relatively prime, find the smallest number both denominators divide into evenly.

Why can't I just add 3/8 + 2/3 directly?

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You can't add fractions with different denominators because they represent different-sized pieces! It's like trying to add 3 slices of pizza cut into 8 pieces with 2 slices cut into 3 pieces.

What if my answer is an improper fraction like 25/24?

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That's perfectly correct! 2524 \frac{25}{24} can be converted to 1124 1\frac{1}{24} if needed, but improper fractions are valid answers in mathematics.

How do I multiply 3/8 by 3 to get the same denominator?

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Multiply both the numerator and denominator by 3: 3×38×3=924 \frac{3 \times 3}{8 \times 3} = \frac{9}{24} . This keeps the fraction's value the same while changing its form.

Can I simplify 25/24 further?

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No! Since 25 and 24 share no common factors (25 = 5² and 24 = 2³ × 3), the fraction 2524 \frac{25}{24} is already in simplest form.

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