Answer :
To find which options have the same value as 40% of 84, let's break down what each option represents and check their equivalence:
1. Understanding 40% of 84:
To calculate 40% of 84, you convert the percentage to a decimal and multiply it by 84.
[tex]\[
40\% \text{ of } 84 = \frac{40}{100} \times 84
\][/tex]
This calculation gives us a value of 33.6.
2. Evaluating Each Option:
- Option A: [tex]\(40 \cdot 84\)[/tex]
- This calculates the product of 40 and 84, which is definitely more than 33.6, so it does not match 40% of 84.
- Option B: [tex]\(0.4 \div 84\)[/tex]
- This is dividing 0.4 by 84, which results in a very small number, much less than 33.6.
- Option C: [tex]\(\frac{40}{100} \cdot 84\)[/tex]
- This calculation exactly matches the way to find 40% of 84. Hence, it equals 33.6.
- Option D: [tex]\(84 \div 40\)[/tex]
- This divides 84 by 40, which does not equal 33.6, so it does not match.
- Option E: [tex]\(0.4 \cdot 84\)[/tex]
- This is another way to write the calculation for 40% of 84, as 0.4 is the decimal form of 40%. Multiplying 0.4 by 84 gives us 33.6.
3. Correct Options:
The options that give the same value as 40% of 84 (33.6) are:
- Option C: [tex]\(\frac{40}{100} \cdot 84\)[/tex]
- Option E: [tex]\(0.4 \cdot 84\)[/tex]
Both these options correctly calculate 40% of 84 and result in a value of 33.6.
1. Understanding 40% of 84:
To calculate 40% of 84, you convert the percentage to a decimal and multiply it by 84.
[tex]\[
40\% \text{ of } 84 = \frac{40}{100} \times 84
\][/tex]
This calculation gives us a value of 33.6.
2. Evaluating Each Option:
- Option A: [tex]\(40 \cdot 84\)[/tex]
- This calculates the product of 40 and 84, which is definitely more than 33.6, so it does not match 40% of 84.
- Option B: [tex]\(0.4 \div 84\)[/tex]
- This is dividing 0.4 by 84, which results in a very small number, much less than 33.6.
- Option C: [tex]\(\frac{40}{100} \cdot 84\)[/tex]
- This calculation exactly matches the way to find 40% of 84. Hence, it equals 33.6.
- Option D: [tex]\(84 \div 40\)[/tex]
- This divides 84 by 40, which does not equal 33.6, so it does not match.
- Option E: [tex]\(0.4 \cdot 84\)[/tex]
- This is another way to write the calculation for 40% of 84, as 0.4 is the decimal form of 40%. Multiplying 0.4 by 84 gives us 33.6.
3. Correct Options:
The options that give the same value as 40% of 84 (33.6) are:
- Option C: [tex]\(\frac{40}{100} \cdot 84\)[/tex]
- Option E: [tex]\(0.4 \cdot 84\)[/tex]
Both these options correctly calculate 40% of 84 and result in a value of 33.6.
