Math Problem Statement

Use inductive reasoning to predict the next line in the pattern: 4×4 = 16, 5×4 = 20, 6×4 = 24, 7×4 = 28.

Solution

The pattern in the image shows a series of multiplications involving 4:

4×4=164 \times 4 = 16 5×4=205 \times 4 = 20 6×4=246 \times 4 = 24 7×4=287 \times 4 = 28

To use inductive reasoning, we observe that the first factor is increasing by 1 in each line, while the second factor remains 4. Following this pattern, the next line would involve increasing the first factor by 1 again:

8×4=328 \times 4 = 32

So, the next line in the pattern is:

8×4=328 \times 4 = 32

Would you like further details or have any questions?

Here are some related questions to consider:

  1. What would be the 10th line in this pattern?
  2. Can we generalize this pattern for any number nn?
  3. How would the pattern change if we increased the second factor instead of the first?
  4. What role does inductive reasoning play in predicting patterns?
  5. Can we use this pattern to explain the distributive property of multiplication?

Tip: Inductive reasoning is a useful tool for identifying and predicting patterns based on specific examples or trends.

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Math Problem Analysis

Mathematical Concepts

Arithmetic
Patterns
Inductive Reasoning

Formulas

Multiplication: a × b = c

Theorems

Pattern Recognition
Inductive Reasoning

Suitable Grade Level

Grades 5-7