https://file.aiquickdraw.com/mathbot/file/1726791782964g41gjvxv.jpg

Let's go over the math problems you shared in the image. Here are the solutions:

### 4. Use a calculator to evaluate each expression:
These problems require direct calculation using the given operators. I'll solve them step-by-step.

- **a) \( 332 - \frac{294}{49} \)**
  \[
  332 - \frac{294}{49} = 332 - 6 = 326
  \]
  
- **b) \( 209 \times 12 \div 4 \)**
  \[
  209 \times 12 = 2508 \quad \text{then} \quad 2508 \div 4 = 627
  \]
  
- **c) \( 312 \times 426 - 212 \times 158 \)**
  \[
  312 \times 426 = 132912, \quad 212 \times 158 = 33496
  \]
  \[
  132912 - 33496 = 99316
  \]
  
- **d) \( 2205 + 93 \div 3 - 1241 \)**
  \[
  93 \div 3 = 31, \quad 2205 + 31 = 2236, \quad 2236 - 1241 = 995
  \]
  
- **e) \( 156 \times 283 + 215 \times 132 \)**
  \[
  156 \times 283 = 44148, \quad 215 \times 132 = 28380
  \]
  \[
  44148 + 28380 = 72528
  \]
  
- **f) \( 245 \times 138 \div (7 + 23) \)**
  \[
  245 \times 138 = 33810, \quad 7 + 23 = 30, \quad 33810 \div 30 = 1127
  \]

- **g) \( (148 + 216) \times (351 - 173) \)**
  \[
  148 + 216 = 364, \quad 351 - 173 = 178
  \]
  \[
  364 \times 178 = 64892
  \]

- **h) \( 1258 + 341 \times 28 - 2357 \)**
  \[
  341 \times 28 = 9548, \quad 1258 + 9548 = 10806, \quad 10806 - 2357 = 8449
  \]

### 5. Use mental math to evaluate:
These problems involve simpler calculations, suitable for mental math.

- **a) \( 20000 - 4000 \times 2 \)**
  \[
  4000 \times 2 = 8000, \quad 20000 - 8000 = 12000
  \]

- **b) \( 6 + \frac{125}{25} \)**
  \[
  125 \div 25 = 5, \quad 6 + 5 = 11
  \]

- **c) \( (1000 + 6000) \times 3 \)**
  \[
  1000 + 6000 = 7000, \quad 7000 \times 3 = 21000
  \]

- **d) \( 60 \div 3 \times 9 \)**
  \[
  60 \div 3 = 20, \quad 20 \times 9 = 180
  \]

- **e) \( 5 \times (4 + 11) \)**
  \[
  4 + 11 = 15, \quad 5 \times 15 = 75
  \]

- **f) \( 50 + 50 \div 50 \)**
  \[
  50 \div 50 = 1, \quad 50 + 1 = 51
  \]

- **g) \( (50 + 50) \div 50 \)**
  \[
  50 + 50 = 100, \quad 100 \div 50 = 2
  \]

- **h) \( 9 \times 10 - (30 + 30) \)**
  \[
  9 \times 10 = 90, \quad 30 + 30 = 60, \quad 90 - 60 = 30
  \]

- **i) \( 16 \div 2 \times 9 \)**
  \[
  16 \div 2 = 8, \quad 8 \times 9 = 72
  \]

- **j) \( 200 - \frac{200}{20} \)**
  \[
  200 \div 20 = 10, \quad 200 - 10 = 190
  \]

### 6. Use mental math to evaluate:
These problems also involve simple arithmetic.

- **a) \( 4 \times 7 - 2 + 1 \)**
  \[
  4 \times 7 = 28, \quad 28 - 2 = 26, \quad 26 + 1 = 27
  \]

- **b) \( 4 \times (7 - 2) + 1 \)**
  \[
  7 - 2 = 5, \quad 4 \times 5 = 20, \quad 20 + 1 = 21
  \]

- **c) \( 4 \times 7 - (2 - 1) \)**
  \[
  2 - 1 = 1, \quad 4 \times 7 = 28, \quad 28 - 1 = 27
  \]

- **d) \( 4 \times (7 - 2 + 1) \)**
  \[
  7 - 2 + 1 = 6, \quad 4 \times 6 = 24
  \]

- **e) \( (4 \times 7 - 2) + 1 \)**
  \[
  4 \times 7 = 28, \quad 28 - 2 = 26, \quad 26 + 1 = 27
  \]

- **f) \( 4 \times 7 - (2 + 1) \)**
  \[
  2 + 1 = 3, \quad 4 \times 7 = 28, \quad 28 - 3 = 25
  \]

---

Would you like more details on any of these problems? Here are five related questions for further practice:

1. What is the result of \( 3 \times 25 + 150 - 100 \)?
2. Calculate \( 121 \times 11 \div (9 + 2) \).
3. Use mental math to evaluate \( 500 - 50 \div 2 + 10 \).
4. Solve \( (12 \times 5 - 20) + 18 \).
5. Find the value of \( 120 \div (6 \times 5) \).

### Tip:
When solving problems with mixed operations (addition, subtraction, multiplication, and division), always remember to follow the **order of operations** (PEMDAS: Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right)).

Solve the following math problems using mental math and calculators as per the image.

This problem set involves solving arithmetic expressions using calculators and mental math techniques. Concepts covered include PEMDAS, division, multiplication, and basic subtraction and addition, suitable for students in Grades 5-7.

Math Problem Statement

Solution

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Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

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