Solve 2-(1/1+1/2): Unit Fraction Addition and Subtraction Problem

Q: Why do I need to solve the parentheses first?

The order of operations (PEMDAS) requires you to solve expressions inside parentheses before doing any other operations. Ignoring this rule completely changes your answer!

Q: How do I add fractions with different denominators?

Find the least common denominator (LCD). For $ \frac{1}{1} + \frac{1}{2} $, the LCD is 2. Convert $ \frac{1}{1} $ to $ \frac{2}{2} $, then add: $ \frac{2}{2} + \frac{1}{2} = \frac{3}{2} $.

Q: Can I just write 1/1 as 1 instead of converting it?

Absolutely! Since $ \frac{1}{1} = 1 $, you can write the expression as $ 2 - (1 + \frac{1}{2}) $. Just remember to still find a common denominator when adding.

Q: How do I subtract a fraction from a whole number?

Convert the whole number to a fraction with the same denominator. Here, write $ 2 = \frac{4}{2} $, then subtract: $ \frac{4}{2} - \frac{3}{2} = \frac{1}{2} $.

Q: What if I get a different answer like 3½?

Double-check your order of operations! Getting $ 3\frac{1}{2} $ usually means you added instead of subtracting, or didn't solve the parentheses first. The correct answer is $ \frac{1}{2} $.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:04 When opening parentheses, minus times plus always equals minus

00:10 Let's use this formula in our exercise

00:14 Let's solve according to the order of operations from left to right

00:17 We'll convert from fraction to number, and solve

00:21 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$2-(\frac{1}{1}+\frac{1}{2})=$

2

Step-by-step solution

We will solve the expression $2 - \left(\frac{1}{1} + \frac{1}{2}\right)$ step by step:

Step 1: Calculate the expression inside the parentheses first.

We have $\frac{1}{1} + \frac{1}{2}$ .

The simplest way to add fractions is to find a common denominator. The denominators here are 1 and 2, so the least common denominator is 2.

Convert $\frac{1}{1}$ to $\frac{2}{2}$ for easy addition:

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

Now add $\frac{2}{2} + \frac{1}{2}$ :

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

Step 2: Subtract this result from 2.

Write 2 as a fraction with a denominator of 2 to facilitate subtraction:

$2 = \frac{4}{2}$

Now perform the subtraction:

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

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

3

Final Answer

$\frac{1}{2}$

Key Points to Remember

Essential concepts to master this topic

Rule: Solve expressions inside parentheses before subtracting from main number
Technique: Convert $\frac{1}{1}$ to $\frac{2}{2}$ when adding to $\frac{1}{2}$
Check: Verify $2 - \frac{3}{2} = \frac{4}{2} - \frac{3}{2} = \frac{1}{2}$ ✓

Common Mistakes

Avoid these frequent errors

Subtracting each fraction separately from 2
Don't calculate 2 - 1/1 - 1/2 = wrong answer! This ignores the parentheses and violates order of operations. Always solve what's inside parentheses first, then subtract that result from 2.

Practice Quiz

Test your knowledge with interactive questions

$$ 100-(5+55)= $$

FAQ

Everything you need to know about this question

Why do I need to solve the parentheses first?

+

The order of operations (PEMDAS) requires you to solve expressions inside parentheses before doing any other operations. Ignoring this rule completely changes your answer!

How do I add fractions with different denominators?

+

Find the least common denominator (LCD). For $\frac{1}{1} + \frac{1}{2}$ , the LCD is 2. Convert $\frac{1}{1}$ to $\frac{2}{2}$ , then add: $\frac{2}{2} + \frac{1}{2} = \frac{3}{2}$ .

Can I just write 1/1 as 1 instead of converting it?

+

Absolutely! Since $\frac{1}{1} = 1$ , you can write the expression as $2 - (1 + \frac{1}{2})$ . Just remember to still find a common denominator when adding.

How do I subtract a fraction from a whole number?

+

Convert the whole number to a fraction with the same denominator. Here, write $2 = \frac{4}{2}$ , then subtract: $\frac{4}{2} - \frac{3}{2} = \frac{1}{2}$ .

What if I get a different answer like 3½?

+

Double-check your order of operations! Getting $3\frac{1}{2}$ usually means you added instead of subtracting, or didn't solve the parentheses first. The correct answer is $\frac{1}{2}$ .

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Solve 2-(1/1+1/2): Unit Fraction Addition and Subtraction Problem

Order of Operations with Unit Fractions

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