Question
\( 8+4 \times 3 \) 3) \( (10+5) \div 3+4 \times 2 \) \( 8 \times[6-(4)] \) \( 50-10 \div 2-6 \frac{3}{3} \)
Ask by Lynch Daniels. in South Africa
Jan 21,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
1. \( 8 + 4 \times 3 = 20 \)
2. \( (10 + 5) \div 3 + 4 \times 2 = 13 \)
3. \( 8 \times [6 - (4)] = 16 \)
4. \( 50 - 10 \div 2 - 6 \times \frac{3}{3} = 39 \)
Solution
Sure, let's evaluate each of the given mathematical expressions step by step.
---
### 1. \( 8 + 4 \times 3 \)
**Order of Operations (PEMDAS/BODMAS):**
- **P**arentheses/**B**rackets
- **E**xponents/**O**rders
- **M**ultiplication and **D**ivision (from left to right)
- **A**ddition and **S**ubtraction (from left to right)
**Steps:**
1. **Multiplication first:**
\[
4 \times 3 = 12
\]
2. **Then addition:**
\[
8 + 12 = 20
\]
**Answer:** \( 20 \)
---
### 2. \( (10 + 5) \div 3 + 4 \times 2 \)
**Steps:**
1. **Parentheses first:**
\[
10 + 5 = 15
\]
2. **Division:**
\[
15 \div 3 = 5
\]
3. **Multiplication:**
\[
4 \times 2 = 8
\]
4. **Then addition:**
\[
5 + 8 = 13
\]
**Answer:** \( 13 \)
---
### 3. \( 8 \times [6 - (4)] \)
**Steps:**
1. **Innermost Parentheses:**
\[
6 - 4 = 2
\]
2. **Then multiplication:**
\[
8 \times 2 = 16
\]
**Answer:** \( 16 \)
---
### 4. \( 50 - 10 \div 2 - 6 \times \frac{3}{3} \)
**Steps:**
1. **Division:**
\[
10 \div 2 = 5
\]
2. **Simplify the fraction:**
\[
\frac{3}{3} = 1
\]
3. **Multiplication:**
\[
6 \times 1 = 6
\]
4. **Now, perform subtraction from left to right:**
\[
50 - 5 = 45
\]
\[
45 - 6 = 39
\]
**Answer:** \( 39 \)
---
**Summary of Results:**
1. \( 8 + 4 \times 3 = 20 \)
2. \( (10 + 5) \div 3 + 4 \times 2 = 13 \)
3. \( 8 \times [6 - (4)] = 16 \)
4. \( 50 - 10 \div 2 - 6 \times \frac{3}{3} = 39 \)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
One fun fact about order of operations is that it’s often remembered by the acronym PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). Think of it as the chef's secret recipe for solving math problems without any mix-ups! Now, when calculating expressions, a common mistake is to perform operations strictly from left to right instead of following the correct order. For instance, in \( 8 + 4 \times 3 \), many might mistakenly add first, but remember that multiplication wins the race! Always prioritize multiplication and division over addition and subtraction to get the right results.
