Consider the expression (0.6) • (0.7). a) Write a related expression using whole number factors, then evaluate the expression. b) How many times greater is the product of your rela... Consider the expression (0.6) • (0.7). a) Write a related expression using whole number factors, then evaluate the expression. b) How many times greater is the product of your related expression from part a than the product of your original expression? Explain your thinking. c) Mai says the product of (0.6) • (0.7) is 4.2. Do you agree with Mai? Use the related expression from part a to help you determine whether Mai is correct. Read more

Steps to Solve

1. Rewrite Using Whole Number Factors

To rewrite $0.6$ and $0.7$ as whole number factors, we can express them as fractions:

$$ 0.6 = \frac{6}{10} \quad \text{and} \quad 0.7 = \frac{7}{10} $$

We can then write the original expression as:

$$ (0.6) \cdot (0.7) = \left(\frac{6}{10}\right) \cdot \left(\frac{7}{10}\right) $$

2. Evaluate the Expression

Next, we multiply the fractions:

$$ \left(\frac{6}{10}\right) \cdot \left(\frac{7}{10}\right) = \frac{6 \cdot 7}{10 \cdot 10} = \frac{42}{100} $$

Now, we convert this back to decimal:

$$ \frac{42}{100} = 0.42 $$

3. Determine Comparison

For part b, we need to compare this product with the original expression ($0.6 \cdot 0.7$). Since we have both equal to $0.42$, we can calculate how many times greater one product is compared to the other, which is:

$$ \frac{0.42}{0.42} = 1 $$

4. Evaluate Mai’s Claim

For part c, Mai claims the product is $4.2$. We need to check this claim against our previous result of $0.42$.

Since $4.2 \neq 0.42$, Mai is incorrect.