Solve: 12 1/49 + 2 3/7 Mixed Number Addition Problem

Q: Why can't I just add the numerators and denominators separately?

Because fractions represent parts of different wholes! $ \frac{1}{49} $ means 1 part out of 49, while $ \frac{3}{7} $ means 3 parts out of 7. You need the same denominator to add them properly.

Q: How do I know which denominator to use as the common one?

Find the Least Common Denominator (LCD)! Since 49 = 7 × 7, and we already have 49 as one denominator, use 49 as the LCD. Convert $ \frac{3}{7} $ to forty-ninths.

Q: Do I need to simplify the final answer?

Always check if you can simplify! In this case, $ \frac{22}{49} $ cannot be simplified further because 22 and 49 share no common factors except 1.

Q: Can I convert everything to improper fractions instead?

Yes, that works too! Convert both mixed numbers to improper fractions: $ \frac{589}{49} + \frac{17}{7} $, find common denominator, add, then convert back to mixed number.

Mixed Number Addition with Unlike Denominators

$12\frac{1}{49}+2\frac{3}{7}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 The formula for converting a mixed number to a fraction

00:08 We will use this formula in our exercise and convert to fractions

00:27 Multiply to find the common denominator

00:42 Multiply by the common denominator

00:53 Now we'll convert back to a mixed number

00:59 Break down 708 into 686 plus 22

01:06 Break down the fraction into a whole number and remainder

01:12 Convert the whole fraction to a whole number

01:19 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

$12\frac{1}{49}+2\frac{3}{7}=$

Step-by-step solution

To solve the problem of adding $12\frac{1}{49} + 2\frac{3}{7}$ , we'll follow step-by-step procedures:

Step 1: Identify the whole numbers and fractions:
Whole numbers: 12 and 2.
Fractions: $\frac{1}{49}$ and $\frac{3}{7}$ .
Step 2: Convert $\frac{3}{7}$ to a fraction with a denominator of 49:
Multiply both the numerator and denominator by 7: $\frac{3 \times 7}{7 \times 7} = \frac{21}{49}$ .
Step 3: Add the fractions:
$\frac{1}{49} + \frac{21}{49} = \frac{1 + 21}{49} = \frac{22}{49}$ .
Step 4: Add the whole numbers:
12 + 2 = 14.
Step 5: Combine the whole number result and the fraction result:
The result is $14\frac{22}{49}$ .

Therefore, the solution to the problem $12\frac{1}{49} + 2\frac{3}{7}$ is $14\frac{22}{49}$ , which matches choice 4.

Final Answer

$14\frac{22}{49}$

Key Points to Remember

Essential concepts to master this topic

Rule: Convert all fractions to common denominator before adding
Technique: Convert $\frac{3}{7}$ to $\frac{21}{49}$ by multiplying by 7
Check: Verify $\frac{1}{49} + \frac{21}{49} = \frac{22}{49}$ and 12 + 2 = 14 ✓

Common Mistakes

Avoid these frequent errors

Adding fractions without finding common denominator
Don't add $\frac{1}{49} + \frac{3}{7} = \frac{4}{56}$ ! This gives wrong results because you can't add fractions with different denominators directly. Always find the LCD (49) and convert both fractions first.

Practice Quiz

Test your knowledge with interactive questions

$2\frac{2}{5}+2\frac{2}{5}=$

FAQ

Everything you need to know about this question

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

Because fractions represent parts of different wholes! $\frac{1}{49}$ means 1 part out of 49, while $\frac{3}{7}$ means 3 parts out of 7. You need the same denominator to add them properly.

How do I know which denominator to use as the common one?

Find the Least Common Denominator (LCD)! Since 49 = 7 × 7, and we already have 49 as one denominator, use 49 as the LCD. Convert $\frac{3}{7}$ to forty-ninths.

Do I need to simplify the final answer?

Always check if you can simplify! In this case, $\frac{22}{49}$ cannot be simplified further because 22 and 49 share no common factors except 1.

What if the whole numbers don't add up to a nice number?

No problem! Add the whole numbers separately (12 + 2 = 14), then add the fractions separately. Keep them as separate parts in your mixed number answer.

Can I convert everything to improper fractions instead?

Yes, that works too! Convert both mixed numbers to improper fractions: $\frac{589}{49} + \frac{17}{7}$ , find common denominator, add, then convert back to mixed number.

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