Sure! Let's go through each problem step-by-step.
### Problem 9:
Question: 32 is 40 percent of what number?
Solution:
1. Step 1: Let the unknown number be [tex]\( N \)[/tex].
2. Step 2: We know that 32 is 40% of [tex]\( N \)[/tex]. This can be written mathematically as:
[tex]\[
32 = 0.40 \times N
\][/tex]
3. Step 3: To find [tex]\( N \)[/tex], we need to isolate [tex]\( N \)[/tex] on one side of the equation:
[tex]\[
N = \frac{32}{0.40}
\][/tex]
4. Step 4: Perform the division:
[tex]\[
N = 80.0
\][/tex]
Thus, the number [tex]\( N \)[/tex] is 80.
### Problem 10:
Question: All of the following are ways to write 25% of [tex]\( N \)[/tex] EXCEPT
Solution:
1. Step 1: Write down several ways to represent 25% of [tex]\( N \)[/tex].
- 25% of [tex]\( N \)[/tex] can be written as [tex]\( 0.25 \times N \)[/tex].
- 25% of [tex]\( N \)[/tex] can also be written as [tex]\( \frac{N}{4} \)[/tex].
- Another way to represent 25% of [tex]\( N \)[/tex] is [tex]\( N \times \frac{1}{4} \)[/tex].
- Yet another equivalent expression is [tex]\( \frac{1}{4} \times N \)[/tex].
These are all correct representations.
2. Step 2: Identify an expression that does NOT correctly represent 25% of [tex]\( N \)[/tex].
- Consider the option [tex]\( \frac{N \times 1}{5} \)[/tex]. This represents 20% of [tex]\( N \)[/tex], because:
[tex]\[
\frac{1}{5} = 0.20
\][/tex]
- Clearly, [tex]\( \frac{N \times 1}{5} \)[/tex] is not equal to 25% of [tex]\( N \)[/tex].
So, the incorrect representation of 25% of [tex]\( N \)[/tex] is [tex]\( \frac{1}{5} \times N \)[/tex].
Thus, the answer is the option that denotes [tex]\( \frac{1}{5} \times N \)[/tex] as a representation of 25% of [tex]\( N \)[/tex].
