Math Problem Statement

if 24 = 8, 53 = 13, 3* = 11, then find the value of 7 * 5.

Solution

The given pattern suggests that the multiplication sign ( * ) does not represent standard multiplication. Let's look closely at the equations and try to uncover a relationship.

  1. 24=82 * 4 = 8
  2. 53=135 * 3 = 13
  3. 3?=113 * ? = 11

For the first equation, 24=82 * 4 = 8, this matches normal multiplication (2 × 4 = 8).

For the second equation, 53=135 * 3 = 13, normal multiplication gives 15, but the result is 13, so we can assume there is an adjustment. Perhaps we subtract 2 from the product:
5×3=155 \times 3 = 15, and 152=1315 - 2 = 13.

Next, for 3?=113 * ? = 11, using the same logic, we need to find what number multiplied by 3 gives 11 after subtracting 2:
3×4=123 \times 4 = 12, and 122=1112 - 2 = 11. So, ?=4? = 4.

Now, to find 757 * 5, we use the same method: 7×5=357 \times 5 = 35, and subtract 2:
352=3335 - 2 = 33.

Thus, the value of 75=337 * 5 = 33.


Would you like more details on how the pattern works, or do you have other questions? Here are some related questions you can explore:

  1. How can we represent this pattern as a general rule for any numbers?
  2. What if the pattern involved addition or division instead of subtraction?
  3. Could this pattern be extended to higher numbers, like 10 * 8 or 6 * 9?
  4. How can you test if a pattern follows consistency across various operations?
  5. Can you create a new pattern that uses different operations, like exponentiation?

Tip: Always check for consistency in any pattern, and consider simple operations like addition or subtraction to spot the rule!

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Math Problem Analysis

Mathematical Concepts

Patterns
Arithmetic Operations
Modified Multiplication

Formulas

Multiplication
Subtraction Adjustment

Theorems

Pattern Recognition in Arithmetic

Suitable Grade Level

Grades 4-6