https://file.aiquickdraw.com/mathbot/file/1726194235820knzwf0y9.jpg

Let's break down the math problems in the image step-by-step:

1. **Example (ex)**: 
   - "To find 12 times 17, I multiply 10 times 17 and 2 times 17 and add the two products together."
   - The expression is:  
     \[
     (10 \times 17) + (2 \times 17)
     \]
   - This simplifies to:  
     \[
     170 + 34 = 204
     \]

2. **Problem a**:
   - "To find 79 times 24, I multiply 80 times 24 and take off one group of 24."
   - The expression is:  
     \[
     (80 \times 24) - (1 \times 24)
     \]
   - This simplifies to:  
     \[
     1920 - 24 = 1896
     \]

3. **Problem b**:
   - "To find 12 times 13, I double 13 and halve 12 and then multiply."
   - The expression is:  
     \[
     (2 \times 13) \times (12 \div 2)
     \]
   - This simplifies to:  
     \[
     26 \times 6 = 156
     \]

4. **Challenge (c)**:
   - "To find 1,188 divided by 12, I think about 1,200 divided by 12—that’s 100 groups of 12. 1,188 has 1 fewer group of 12."
   - The expression is:  
     \[
     (1200 \div 12) - 1
     \]
   - This simplifies to:  
     \[
     100 - 1 = 99
     \]

Would you like further details on any of the expressions or simplifications?

Here are some related questions to deepen understanding:
1. What is another method to simplify \(79 \times 24\)?
2. Can you express \(12 \times 13\) using the distributive property?
3. How can rounding help when dividing large numbers, like in problem (c)?
4. Can you break down \(12 \times 17\) using different factor pairs instead of \(10\) and \(2\)?
5. What happens if you use a different approximation than \(1,200\) for dividing 1,188 by 12?

**Tip**: When dealing with large numbers, rounding or breaking them into smaller, more manageable parts is a helpful strategy for mental math!

To find 12 times 17, 79 times 24, 12 times 13, and 1,188 divided by 12 using specific mental math strategies.

Explore efficient mental math strategies for multiplying and dividing large numbers. Learn how to calculate 12 x 17, 79 x 24, and 1,188 ÷ 12 step by step using algebraic expressions and rounding techniques. Suitable for students in Grades 5-7.

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