Solve the Fraction Addition: 2/6 + 3/7 Step-by-Step

Q: How do I find the LCD of 6 and 7?

Since 6 and 7 share no common factors (they're relatively prime), their LCD is simply 6 × 7 = 42. For other pairs, find the smallest number both denominators divide into evenly.

Q: Why can't I just add the fractions as they are?

You can only add fractions when they have the same denominator. Think of it like adding different units - you can't add 2 apples and 3 oranges directly. You need a common "unit" first!

Q: Do I need to simplify the final answer?

Yes! Always check if your answer can be simplified. For $ \frac{32}{42} $, find the GCD of 32 and 42. Since GCD(32,42) = 2, you get $ \frac{16}{21} $.

Q: What if the denominators are harder numbers like 12 and 18?

Use the prime factorization method: 12 = 2² × 3 and 18 = 2 × 3². The LCD takes the highest power of each prime: 2² × 3² = 36.

Q: Can I use cross-multiplication here?

No! Cross-multiplication only works for equations with one fraction on each side. For addition like this problem, you must use the LCD method.

Fraction Addition with Different Denominators

Solve the following exercise:

$\frac{2}{6}+\frac{3}{7}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:08 Let's solve this problem.

00:11 First, multiply each fraction by the other's denominator to find a common denominator.

00:17 When you multiply, remember to do it to both the numerator and the denominator.

00:23 Next, calculate the products.

00:28 Now, add the fractions using the common denominator.

00:35 Calculate the numerator by adding.

00:39 And that's how you find the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following exercise:

$\frac{2}{6}+\frac{3}{7}=$

Step-by-step solution

Let's try to find the lowest common denominator between 6 and 7

To find the lowest common denominator, we need to find a number that is divisible by both 6 and 7

In this case, the common denominator is 42

Now we'll multiply each fraction by the appropriate number to reach the denominator 42

We'll multiply the first fraction by 7

We'll multiply the second fraction by 6

$\frac{2\times7}{6\times7}+\frac{3\times6}{7\times6}=\frac{14}{42}+\frac{18}{42}$

Now we'll combine and get:

$\frac{14+18}{42}=\frac{32}{42}$

Final Answer

$\frac{32}{42}$

Key Points to Remember

Essential concepts to master this topic

LCD Rule: Find the least common denominator to add fractions
Technique: $\frac{2}{6} \times \frac{7}{7} = \frac{14}{42}$ and $\frac{3}{7} \times \frac{6}{6} = \frac{18}{42}$
Check: Add numerators: $14 + 18 = 32$ , so $\frac{32}{42}$ ✓

Common Mistakes

Avoid these frequent errors

Adding numerators and denominators separately
Don't add $\frac{2}{6} + \frac{3}{7}$ as $\frac{2+3}{6+7} = \frac{5}{13}$ ! This ignores the fraction rules and gives completely wrong results. 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 6 and 7?

Since 6 and 7 share no common factors (they're relatively prime), their LCD is simply 6 × 7 = 42. For other pairs, find the smallest number both denominators divide into evenly.

Why can't I just add the fractions as they are?

You can only add fractions when they have the same denominator. Think of it like adding different units - you can't add 2 apples and 3 oranges directly. You need a common "unit" first!

Do I need to simplify the final answer?

Yes! Always check if your answer can be simplified. For $\frac{32}{42}$ , find the GCD of 32 and 42. Since GCD(32,42) = 2, you get $\frac{16}{21}$ .

What if the denominators are harder numbers like 12 and 18?

Use the prime factorization method: 12 = 2² × 3 and 18 = 2 × 3². The LCD takes the highest power of each prime: 2² × 3² = 36.

Can I use cross-multiplication here?

No! Cross-multiplication only works for equations with one fraction on each side. For addition like this problem, you must use the LCD method.

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