Solve: 10 - (4/2 + 3/2) Order of Operations with Fractions

Q: Why can't I just work from left to right?

The order of operations (PEMDAS) requires you to solve parentheses first! Working left to right would give you the wrong answer because you'd be changing the mathematical meaning of the expression.

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

Convert the whole number to a fraction with the same denominator. For example: $ 10 = \frac{20}{2} $, so $ 10 - \frac{7}{2} = \frac{20}{2} - \frac{7}{2} = \frac{13}{2} $.

Q: Should I convert the mixed number answer to an improper fraction?

Either form is correct! $ 6\frac{1}{2} $ and $ \frac{13}{2} $ are the same value. Mixed numbers are often easier to understand, while improper fractions are better for further calculations.

Q: What if I get confused adding fractions with the same denominator?

When denominators are the same, just add the numerators and keep the denominator: $ \frac{4}{2} + \frac{3}{2} = \frac{4+3}{2} = \frac{7}{2} $. The bottom number stays the same!

Q: How do I know when to use mixed numbers vs improper fractions?

Use mixed numbers for final answers when they're easier to visualize (like $ 6\frac{1}{2} $). Use improper fractions during calculations because they're easier to work with mathematically.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 When opening parentheses, minus times plus always equals minus

00:09 Let's use this formula in our exercise

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

00:20 Let's convert from fraction to number, and substitute in our exercise

00:29 Let's convert from fraction to number, and substitute in our exercise

00:33 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

$10-(\frac{4}{2}+\frac{3}{2})=$

2

Step-by-step solution

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

Step 1: Evaluate the expression inside the parentheses.
Step 2: Subtract the result from 10.

Now, let's work through each step:
Step 1: Inside the parentheses, we have $\frac{4}{2} + \frac{3}{2}$ . First, simplify $\frac{4}{2}$ to 2 and $\frac{3}{2}$ remains as $\frac{3}{2}$ .
The sum is $2 + \frac{3}{2} = \frac{4}{2} + \frac{3}{2} = \frac{7}{2}$ .
Step 2: Now, subtract $\frac{7}{2}$ from 10.
Express 10 as a fraction: $\frac{20}{2} - \frac{7}{2} = \frac{13}{2}$ .
Convert the fraction back to a mixed number: $\frac{13}{2} = 6\frac{1}{2}$ .

Therefore, the solution to the problem is $6\frac{1}{2}$ .

3

Final Answer

$6\frac{1}{2}$

Key Points to Remember

Essential concepts to master this topic

Rule: Always solve expressions inside parentheses first following PEMDAS
Technique: Convert whole numbers to fractions: $10 = \frac{20}{2}$
Check: Verify $10 - \frac{7}{2} = 6\frac{1}{2}$ by adding back: $6\frac{1}{2} + \frac{7}{2} = 10$ ✓

Common Mistakes

Avoid these frequent errors

Working left to right without respecting parentheses
Don't solve 10 - 4/2 first = 8, then try to add 3/2! This ignores order of operations and gives 9½ instead of 6½. Always solve everything inside parentheses completely before moving to the next operation.

Practice Quiz

Test your knowledge with interactive questions

$$ 100-(30-21)= $$

FAQ

Everything you need to know about this question

Why can't I just work from left to right?

+

The order of operations (PEMDAS) requires you to solve parentheses first! Working left to right would give you the wrong answer because you'd be changing the mathematical meaning of the expression.

How do I subtract a fraction from a whole number?

+

Convert the whole number to a fraction with the same denominator. For example: $10 = \frac{20}{2}$ , so $10 - \frac{7}{2} = \frac{20}{2} - \frac{7}{2} = \frac{13}{2}$ .

Should I convert the mixed number answer to an improper fraction?

+

Either form is correct! $6\frac{1}{2}$ and $\frac{13}{2}$ are the same value. Mixed numbers are often easier to understand, while improper fractions are better for further calculations.

What if I get confused adding fractions with the same denominator?

+

When denominators are the same, just add the numerators and keep the denominator: $\frac{4}{2} + \frac{3}{2} = \frac{4+3}{2} = \frac{7}{2}$ . The bottom number stays the same!

How do I know when to use mixed numbers vs improper fractions?

+

Use mixed numbers for final answers when they're easier to visualize (like $6\frac{1}{2}$ ). Use improper fractions during calculations because they're easier to work with mathematically.

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Solve: 10 - (4/2 + 3/2) Order of Operations with Fractions

Order of Operations with Mixed Number Results

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