Add Mixed Numbers: Solving 1/4 + 2 3/4 Step-by-Step

Q: Why is the answer positive when I see a plus sign in parentheses?

The $ (+\frac{1}{4}) $ notation just emphasizes that $ \frac{1}{4} $ is positive. Since you're adding two positive numbers, your result will always be positive!

Q: Do I need to convert mixed numbers to improper fractions first?

Not necessarily! When denominators are the same, you can add the whole numbers together and the fractions together. But converting to improper fractions is a great way to double-check your answer.

Q: What if the fractions don't have the same denominator?

You'll need to find a common denominator first! Convert both fractions so they have the same bottom number, then add as usual.

Q: Can I use the number line method for all addition problems?

Absolutely! The number line helps you visualize addition. Start at the first number, then move right for positive additions. It's especially helpful for understanding why your answer makes sense.

Mixed Number Addition with Positive Results

$(+\frac{1}{4})+(2\frac{3}{4})=\text{ ?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Find the point on the axis

00:07 To add, we move in the right (positive) direction on the axis

00:15 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

$(+\frac{1}{4})+(2\frac{3}{4})=\text{ ?}$

Step-by-step solution

First, locate the number $\frac{1}{4}$ on the number line and move $2\frac{3}{4}$ steps to the right from it.

This means the resulting number will be positive:

Finally, solve the exercise:

$\frac{1}{4}+2\frac{3}{4}=3$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Add whole numbers and fractions separately when denominators match
Technique: $\frac{1}{4} + 2\frac{3}{4} = 0 + 2 + \frac{1+3}{4} = 3$
Check: Convert to improper fractions: $\frac{1}{4} + \frac{11}{4} = \frac{12}{4} = 3$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to add the whole number part
Don't just add the fractions $\frac{1}{4} + \frac{3}{4} = 1$ and ignore the 2! This gives you 1 instead of 3. Always remember that $2\frac{3}{4}$ means 2 + $\frac{3}{4}$ , so you must add all parts together.

Practice Quiz

Test your knowledge with interactive questions

a is negative number.

b is negative number.

What is the sum of a+b?

FAQ

Everything you need to know about this question

Why is the answer positive when I see a plus sign in parentheses?

The $(+\frac{1}{4})$ notation just emphasizes that $\frac{1}{4}$ is positive. Since you're adding two positive numbers, your result will always be positive!

Do I need to convert mixed numbers to improper fractions first?

Not necessarily! When denominators are the same, you can add the whole numbers together and the fractions together. But converting to improper fractions is a great way to double-check your answer.

What if the fractions don't have the same denominator?

You'll need to find a common denominator first! Convert both fractions so they have the same bottom number, then add as usual.

How do I know when my fraction answer should be a whole number?

If your numerator is divisible by your denominator, you have a whole number! Like $\frac{12}{4} = 3$ because 12 ÷ 4 = 3 exactly.

Can I use the number line method for all addition problems?

Absolutely! The number line helps you visualize addition. Start at the first number, then move right for positive additions. It's especially helpful for understanding why your answer makes sense.

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