Let's provide a detailed, step-by-step solution to justify Mariah's statement.
Mariah states that the expression [tex]\( 5\left(-\frac{1}{3}\right)\left(-\frac{1}{5}\right)(-9) \)[/tex] is equivalent to [tex]\(-1 \times 3\)[/tex]. Let's see if her statement holds true.
Step-by-Step Solution:
1. Rewrite the expression: Start with the given expression:
[tex]\[
5 \left( -\frac{1}{3} \right) \left( -\frac{1}{5} \right) (-9)
\][/tex]
2. Combine the fractions: We want to simplify step by step. First, consider the product of the fractions:
[tex]\[
-\frac{1}{3} \times -\frac{1}{5} = \frac{1}{15}
\][/tex]
3. Incorporate the 5:
[tex]\[
5 \times \frac{1}{15} = \frac{5}{15} = \frac{1}{3}
\][/tex]
So the expression becomes:
[tex]\[
\frac{1}{3} \times (-9)
\][/tex]
4. Multiply by -9:
[tex]\[
\frac{1}{3} \times (-9) = -3
\][/tex]
5. Relate this to [tex]\(-1 \times 3\)[/tex]: Notice:
[tex]\[
-3 \text{ is the same as } -1 \times 3
\][/tex]
Now, let's fill in the blanks as per the required format:
Sentence 1:
- You can multiply 5 by [tex]\(\boxed{-\frac{1}{5}}\)[/tex] to get -1.
Why? Because [tex]\(5 \times -\frac{1}{5} = -1\)[/tex].
Sentence 2:
- You can multiply [tex]\(\boxed{-\frac{1}{3}}\)[/tex] by [tex]\(\boxed{-3}\)[/tex] to get 3.
Why? Because [tex]\(-\frac{1}{3} \times -3 = 1\)[/tex]. Since we incorporate the product with 9 in the next step, think of the combined multiplication.
Sentence 3:
- The final product is [tex]\( -1 \times 3 = \boxed{-3} \)[/tex].
Putting it all together, Mariah's statement is correctly justified. The product of [tex]\(5\left(-\frac{1}{3}\right)\left(-\frac{1}{5}\right)(-9)\)[/tex] indeed simplifies to [tex]\(-3\)[/tex], which is equivalent to [tex]\(-1 \times 3\)[/tex].
