Solve the Fraction Addition: 1/6 + 3/7 Step by Step

Q: Why can't I just add 1/6 + 3/7 directly?

You can only add fractions when they have the same denominator. Think of it like adding 1 apple slice out of 6 pieces plus 3 orange slices out of 7 pieces - you need equal-sized pieces first!

Q: Is there a faster way than multiplying 6 × 7?

You could find the least common multiple (LCM) of 6 and 7, but since they share no common factors, their LCM is still 42. For simple problems like this, multiplying works great!

Q: How do I know if 25/42 can be simplified?

Check if the numerator and denominator share any common factors. Since 25 = 5×5 and 42 = 2×3×7, they share no common factors, so $ \frac{25}{42} $ is already simplified.

Q: Can I convert to decimals instead?

You could, but $ \frac{1}{6} $ and $ \frac{3}{7} $ create repeating decimals that are messy to work with. Fractions are cleaner for this type of problem!

Fraction Addition with Different Denominators

Solve the following exercise:

$\frac{1}{6}+\frac{3}{7}=\text{?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 Let's solve this problem together.

00:09 First, multiply each fraction by the other fraction's denominator. This will give us a common denominator.

00:19 Remember to multiply both the top number, called the numerator, and the bottom number, the denominator.

00:31 Now, do the multiplications for each fraction.

00:39 Add the numerators together under the common denominator.

00:44 Calculate the total for the numerator.

00:48 And there you have it. That's 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 exercise:

$\frac{1}{6}+\frac{3}{7}=\text{?}$

Step-by-step solution

To solve the problem of $\frac{1}{6} + \frac{3}{7}$ , we will use the following steps:

Step 1: Find the common denominator for 6 and 7 by multiplying them. The common denominator is $6 \times 7 = 42$ .
Step 2: Express each fraction with this common denominator:
- $\frac{1}{6} = \frac{1 \times 7}{6 \times 7} = \frac{7}{42}$
- $\frac{3}{7} = \frac{3 \times 6}{7 \times 6} = \frac{18}{42}$
Step 3: Add the adjusted fractions:
$\frac{7}{42} + \frac{18}{42} = \frac{7 + 18}{42} = \frac{25}{42}$
Step 4: Check if the fraction can be simplified further. In this case, $\frac{25}{42}$ is already in its simplest form.

The sum of $\frac{1}{6} + \frac{3}{7}$ is $\frac{25}{42}$ .

The correct answer is choice 4: $\frac{25}{42}$ .

Final Answer

$\frac{25}{42}$

Key Points to Remember

Essential concepts to master this topic

Rule: Find common denominator by multiplying both denominators together
Technique: Convert $\frac{1}{6} = \frac{7}{42}$ and $\frac{3}{7} = \frac{18}{42}$
Check: Verify $\frac{7}{42} + \frac{18}{42} = \frac{25}{42}$ is simplified ✓

Common Mistakes

Avoid these frequent errors

Adding numerators and denominators separately
Don't add 1+3=4 and 6+7=13 to get 4/13! This ignores that fractions need equal denominators before adding. Always find a common denominator first, then add only the numerators.

Practice Quiz

Test your knowledge with interactive questions

Complete the following exercise:

$\frac{3}{4}:\frac{5}{6}=\text{?}$

FAQ

Everything you need to know about this question

Why can't I just add 1/6 + 3/7 directly?

You can only add fractions when they have the same denominator. Think of it like adding 1 apple slice out of 6 pieces plus 3 orange slices out of 7 pieces - you need equal-sized pieces first!

Is there a faster way than multiplying 6 × 7?

You could find the least common multiple (LCM) of 6 and 7, but since they share no common factors, their LCM is still 42. For simple problems like this, multiplying works great!

How do I know if 25/42 can be simplified?

Check if the numerator and denominator share any common factors. Since 25 = 5×5 and 42 = 2×3×7, they share no common factors, so $\frac{25}{42}$ is already simplified.

What if I get a different common denominator?

Any common multiple of 6 and 7 works (like 84, 126, etc.), but using the smallest one makes calculations easier and keeps numbers manageable.

Can I convert to decimals instead?

You could, but $\frac{1}{6}$ and $\frac{3}{7}$ create repeating decimals that are messy to work with. Fractions are cleaner for this type of problem!

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Solve the Fraction Addition: 1/6 + 3/7 Step by Step

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 1/6 + 3/7 directly?

Is there a faster way than multiplying 6 × 7?

How do I know if 25/42 can be simplified?

What if I get a different common denominator?

Can I convert to decimals instead?

🌟 Unlock Your Math Potential

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