Solve the Equation: a + 2½ = 4 | Mixed Number Addition

Q: Do I have to convert the mixed number to an improper fraction?

Converting to improper fractions like $ \frac{5}{2} $ makes subtraction much easier! You can work with mixed numbers directly, but fractions help avoid mistakes with borrowing.

Q: Should my final answer be a mixed number or improper fraction?

Either form is mathematically correct! However, mixed numbers like $ 1\frac{1}{2} $ are often preferred because they're easier to visualize and understand.

Q: What if I get confused about which operation to use?

Think about undoing what's happening to the variable. Since $ 2\frac{1}{2} $ is being added to a, you need to subtract it from both sides to isolate a.

Q: How can I check if my answer is correct?

Substitute your answer back into the original equation: $ 1\frac{1}{2} + 2\frac{1}{2} $. Adding these mixed numbers gives you $ 4 $, which matches the right side! ✓

Linear Equations with Mixed Number Terms

$a+2\frac{1}{2}=4$

$a=\text{?}$

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Step-by-step video solution

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00:00 Solve

00:03 Let's isolate variable A and calculate

00:07 And this is the solution to the question

Step-by-step written solution

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Understand the problem

$a+2\frac{1}{2}=4$

$a=\text{?}$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Convert the mixed number $2\frac{1}{2}$ to an improper fraction.
Step 2: Subtract $2\frac{1}{2}$ from both sides of the equation to isolate $a$ .
Step 3: Simplify the result to find the value of $a$ .

Now, let's work through each step:

Step 1: Convert $2\frac{1}{2}$ to an improper fraction. $2\frac{1}{2} = \frac{5}{2}$ .

Step 2: The equation becomes $a + \frac{5}{2} = 4$ . To isolate $a$ , subtract $\frac{5}{2}$ from both sides:

$a = 4 - \frac{5}{2}$

Step 3: Convert 4 into a fraction with the same denominator to perform the subtraction. $4 = \frac{8}{2}$ .

$a = \frac{8}{2} - \frac{5}{2} = \frac{3}{2}$ .

The improper fraction $\frac{3}{2}$ can be converted back to a mixed number, giving $a = 1\frac{1}{2}$ .

Therefore, the solution to the problem is $a = 1\frac{1}{2}$ .

Final Answer

$a=1\frac{1}{2}$

Key Points to Remember

Essential concepts to master this topic

Isolation Rule: Subtract mixed numbers from both sides to isolate the variable
Technique: Convert $2\frac{1}{2}$ to $\frac{5}{2}$ for easier subtraction
Check: Substitute: $1\frac{1}{2} + 2\frac{1}{2} = 4$ ✓

Common Mistakes

Avoid these frequent errors

Adding instead of subtracting to isolate the variable
Don't add $2\frac{1}{2}$ to both sides = $a = 6\frac{1}{2}$ ! This moves the variable further from isolation instead of solving for it. Always subtract the term that's being added to the variable.

Practice Quiz

Test your knowledge with interactive questions

$$ x+7=14 $$

$x=\text{?}$

FAQ

Everything you need to know about this question

Do I have to convert the mixed number to an improper fraction?

Converting to improper fractions like $\frac{5}{2}$ makes subtraction much easier! You can work with mixed numbers directly, but fractions help avoid mistakes with borrowing.

How do I subtract a mixed number from a whole number?

Convert both to improper fractions with the same denominator. Here: $4 = \frac{8}{2}$ and $2\frac{1}{2} = \frac{5}{2}$ , so $\frac{8}{2} - \frac{5}{2} = \frac{3}{2}$ .

Should my final answer be a mixed number or improper fraction?

Either form is mathematically correct! However, mixed numbers like $1\frac{1}{2}$ are often preferred because they're easier to visualize and understand.

What if I get confused about which operation to use?

Think about undoing what's happening to the variable. Since $2\frac{1}{2}$ is being added to a, you need to subtract it from both sides to isolate a.

How can I check if my answer is correct?

Substitute your answer back into the original equation: $1\frac{1}{2} + 2\frac{1}{2}$ . Adding these mixed numbers gives you $4$ , which matches the right side! ✓

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