Solve the Fraction Addition: 4/8 + 5/12

Q: Why can't I just add 4/8 + 5/12 directly?

You can't add fractions with different denominators because they represent different-sized pieces! It's like trying to add 4 slices of pizza cut into 8 pieces with 5 slices cut into 12 pieces - you need the same size pieces first.

Q: How do I find the LCD of 8 and 12?

List multiples of each number: 8: 8, 16, 24, 32... 12: 12, 24, 36... The first number that appears in both lists is your LCD: 24!

Q: What do I multiply each fraction by?

Divide the LCD by each denominator: 24÷8=3, so multiply $ \frac{4}{8} $ by $ \frac{3}{3} $. And 24÷12=2, so multiply $ \frac{5}{12} $ by $ \frac{2}{2} $.

Q: Should I simplify 22/24?

Yes! Always simplify your final answer. Since both 22 and 24 are divisible by 2, $ \frac{22}{24} = \frac{11}{12} $ in lowest terms.

Q: Can I simplify the original fractions first?

Absolutely! Notice that $ \frac{4}{8} = \frac{1}{2} $. So you could solve $ \frac{1}{2} + \frac{5}{12} $ instead, which might be easier to work with.

Fraction Addition with Different Denominators

Solve the following equation:

$\frac{4}{8}+\frac{5}{12}=$

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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 3 and 2 respectively to find the common denominator

00:07 Make sure to multiply both numerator and denominator

00:22 Calculate the multiplications

00:34 Add with the common denominator

00:39 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following equation:

$\frac{4}{8}+\frac{5}{12}=$

Step-by-step solution

Let's first identify the lowest common denominator between 8 and 12.

In order to identify the lowest common denominator, we need to find a number that is divisible by both 8 and 12.

In this case, the common denominator is 24.

Let's proceed to 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 2

$\frac{4\times3}{8\times3}+\frac{5\times2}{12\times2}=\frac{12}{24}+\frac{10}{24}$

Now let's add:

$\frac{12+10}{24}=\frac{22}{24}$

Final Answer

$\frac{22}{24}$

Key Points to Remember

Essential concepts to master this topic

LCD Rule: Find least common denominator to add fractions with different denominators
Technique: Convert $\frac{4}{8}$ to $\frac{12}{24}$ and $\frac{5}{12}$ to $\frac{10}{24}$
Check: Verify LCD 24 divides evenly by both 8 and 12: 24÷8=3, 24÷12=2 ✓

Common Mistakes

Avoid these frequent errors

Adding denominators and numerators separately
Don't add 4+5=9 and 8+12=20 to get 9/20! This ignores that fractions represent parts of different wholes. Always find the LCD first, convert both fractions to equivalent fractions with the same denominator, 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 4/8 + 5/12 directly?

You can't add fractions with different denominators because they represent different-sized pieces! It's like trying to add 4 slices of pizza cut into 8 pieces with 5 slices cut into 12 pieces - you need the same size pieces first.

How do I find the LCD of 8 and 12?

List multiples of each number: 8: 8, 16, 24, 32... 12: 12, 24, 36... The first number that appears in both lists is your LCD: 24!

What do I multiply each fraction by?

Divide the LCD by each denominator: 24÷8=3, so multiply $\frac{4}{8}$ by $\frac{3}{3}$ . And 24÷12=2, so multiply $\frac{5}{12}$ by $\frac{2}{2}$ .

Should I simplify 22/24?

Yes! Always simplify your final answer. Since both 22 and 24 are divisible by 2, $\frac{22}{24} = \frac{11}{12}$ in lowest terms.

Can I simplify the original fractions first?

Absolutely! Notice that $\frac{4}{8} = \frac{1}{2}$ . So you could solve $\frac{1}{2} + \frac{5}{12}$ instead, which might be easier to work with.

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Solve the Fraction Addition: 4/8 + 5/12

Fraction Addition with Different Denominators

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why can't I just add 4/8 + 5/12 directly?

How do I find the LCD of 8 and 12?

What do I multiply each fraction by?

Should I simplify 22/24?

Can I simplify the original fractions first?

🌟 Unlock Your Math Potential

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