Answer :
To solve the problem of finding which options have the same value as [tex]\(40\%\)[/tex] of 84, let's break down the steps:
1. Calculate [tex]\(40\%\)[/tex] of 84:
- To find [tex]\(40\%\)[/tex] of any number, you can multiply the number by 0.4 (since [tex]\(40\% = \frac{40}{100} = 0.4\)[/tex]).
- So, [tex]\(40\%\)[/tex] of 84 can be calculated as:
[tex]\[
0.4 \times 84
\][/tex]
2. Evaluate each option:
- Option (A): [tex]\(40 \times 84\)[/tex]
- This is not the same as [tex]\(40\%\)[/tex] of 84 because this suggests multiplying 84 directly by 40, not by 0.4.
- Option (B): [tex]\(0.4 \div 84\)[/tex]
- This option is performing division, which is not what we want for multiplication by a percentage.
- Option (C): [tex]\(\frac{40}{100} \cdot 84\)[/tex]
- This is another way to represent [tex]\(40\%\)[/tex] of 84 mathematically. It simplifies to [tex]\(0.4 \times 84\)[/tex], which matches our target calculation.
- Option (D): [tex]\(84 \div 40\)[/tex]
- This is also a division operation and does not represent a percentage calculation.
- Option (E): [tex]\(0.4 \cdot 84\)[/tex]
- This is directly multiplying 84 by 0.4, which is exactly what we calculated for [tex]\(40\%\)[/tex] of 84.
3. Conclusion:
- The options that yield the same value as [tex]\(40\%\)[/tex] of 84 are (C) [tex]\(\frac{40}{100} \cdot 84\)[/tex] and (E) [tex]\(0.4 \cdot 84\)[/tex].
Therefore, the correct answers are option C and option E.
1. Calculate [tex]\(40\%\)[/tex] of 84:
- To find [tex]\(40\%\)[/tex] of any number, you can multiply the number by 0.4 (since [tex]\(40\% = \frac{40}{100} = 0.4\)[/tex]).
- So, [tex]\(40\%\)[/tex] of 84 can be calculated as:
[tex]\[
0.4 \times 84
\][/tex]
2. Evaluate each option:
- Option (A): [tex]\(40 \times 84\)[/tex]
- This is not the same as [tex]\(40\%\)[/tex] of 84 because this suggests multiplying 84 directly by 40, not by 0.4.
- Option (B): [tex]\(0.4 \div 84\)[/tex]
- This option is performing division, which is not what we want for multiplication by a percentage.
- Option (C): [tex]\(\frac{40}{100} \cdot 84\)[/tex]
- This is another way to represent [tex]\(40\%\)[/tex] of 84 mathematically. It simplifies to [tex]\(0.4 \times 84\)[/tex], which matches our target calculation.
- Option (D): [tex]\(84 \div 40\)[/tex]
- This is also a division operation and does not represent a percentage calculation.
- Option (E): [tex]\(0.4 \cdot 84\)[/tex]
- This is directly multiplying 84 by 0.4, which is exactly what we calculated for [tex]\(40\%\)[/tex] of 84.
3. Conclusion:
- The options that yield the same value as [tex]\(40\%\)[/tex] of 84 are (C) [tex]\(\frac{40}{100} \cdot 84\)[/tex] and (E) [tex]\(0.4 \cdot 84\)[/tex].
Therefore, the correct answers are option C and option E.
