Solve for Y in y - 4⅔ = 8: Mixed Number Equation Guide

Q: Why do I need to convert mixed numbers to improper fractions?

Converting makes addition much easier! When you have $ 8 + 4\frac{2}{3} $, converting gives you $ \frac{24}{3} + \frac{14}{3} = \frac{38}{3} $, which is simpler than trying to add mixed numbers directly.

Q: Can I solve this without converting to improper fractions?

Yes! You can add the whole numbers first: 8 + 4 = 12, then add the fraction $ \frac{2}{3} $ to get $ 12\frac{2}{3} $. Both methods work!

Q: How do I know which operation cancels out the subtraction?

Addition cancels subtraction! Since we have $ y - 4\frac{2}{3} $, we add $ 4\frac{2}{3} $ to both sides. Remember: opposite operations undo each other.

Q: How do I verify my answer is correct?

Substitute your answer back into the original equation: $ 12\frac{2}{3} - 4\frac{2}{3} = 8 $. Since $ 12\frac{2}{3} - 4\frac{2}{3} = 8\frac{0}{3} = 8 $, your answer is correct!

Linear Equations with Mixed Number Operations

$y-4\frac{2}{3}=8$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 Let's find Y!

00:10 We need to rearrange the equation so Y is by itself on one side.

00:15 Next, let's gather similar terms together.

00:18 And there you have it! That's how we solve the problem.

Step-by-step written solution

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Understand the problem

$y-4\frac{2}{3}=8$

Step-by-step solution

To solve the equation $y - 4\frac{2}{3} = 8$ , follow these steps:

Step 1: Identify the given equation:
$y - 4\frac{2}{3} = 8$ .
Step 2: Solve for $y$ by eliminating the subtraction of $4\frac{2}{3}$ . We do this by adding $4\frac{2}{3}$ to both sides of the equation:
$y - 4\frac{2}{3} + 4\frac{2}{3} = 8 + 4\frac{2}{3}$ .
Step 3: Simplify the left side:
Since $4\frac{2}{3} - 4\frac{2}{3} = 0$ , the left side simplifies to just $y$ .
Thus, $y = 8 + 4\frac{2}{3}$ .
Step 4: Simplify the right side by converting the mixed number to an improper fraction:
Convert $4\frac{2}{3}$ to an improper fraction: Multiply 4 by 3 and add 2, giving $\frac{14}{3}$ .
Therefore, add $8 + \frac{14}{3}$ . Convert 8 to a fraction with denominator 3, which is $\frac{24}{3}$ .
Now, add these fractions:
$\frac{24}{3} + \frac{14}{3} = \frac{38}{3}$ .
Step 5: Convert back to a mixed number (if desired):
$\frac{38}{3} = 12\frac{2}{3}$ .

Therefore, the solution to the problem is $y = 12\frac{2}{3}$ .

Final Answer

$12\frac{2}{3}$

Key Points to Remember

Essential concepts to master this topic

Rule: Add the same mixed number to both sides to isolate variable
Technique: Convert mixed numbers to improper fractions: $4\frac{2}{3} = \frac{14}{3}$
Check: Substitute back: $12\frac{2}{3} - 4\frac{2}{3} = 8$ ✓

Common Mistakes

Avoid these frequent errors

Adding fractions incorrectly when working with mixed numbers
Don't add mixed numbers like whole numbers = wrong final answer! Many students try 8 + 4⅔ = 12⅔ without proper fraction conversion. Always convert to improper fractions first: 8 = 24/3, then add 24/3 + 14/3 = 38/3 = 12⅔.

Practice Quiz

Test your knowledge with interactive questions

$$ -16+a=-17 $$

FAQ

Everything you need to know about this question

Why do I need to convert mixed numbers to improper fractions?

Converting makes addition much easier! When you have $8 + 4\frac{2}{3}$ , converting gives you $\frac{24}{3} + \frac{14}{3} = \frac{38}{3}$ , which is simpler than trying to add mixed numbers directly.

Can I solve this without converting to improper fractions?

Yes! You can add the whole numbers first: 8 + 4 = 12, then add the fraction $\frac{2}{3}$ to get $12\frac{2}{3}$ . Both methods work!

How do I know which operation cancels out the subtraction?

Addition cancels subtraction! Since we have $y - 4\frac{2}{3}$ , we add $4\frac{2}{3}$ to both sides. Remember: opposite operations undo each other.

What if I get a different mixed number answer?

Double-check your fraction addition! The most common error is incorrectly adding $\frac{24}{3} + \frac{14}{3}$ . Make sure you get $\frac{38}{3}$ , which converts to $12\frac{2}{3}$ .

How do I verify my answer is correct?

Substitute your answer back into the original equation: $12\frac{2}{3} - 4\frac{2}{3} = 8$ . Since $12\frac{2}{3} - 4\frac{2}{3} = 8\frac{0}{3} = 8$ , your answer is correct!

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