Answer :
To find which options have the same value as 40% of 84, we first need to calculate what 40% of 84 is.
1. Calculate 40% of 84:
To calculate 40% of a number, you can multiply the number by 0.4 (since 40% = 0.4 in decimal form).
[tex]\[
40\% \text{ of } 84 = 0.4 \times 84 = 33.6
\][/tex]
So, 40% of 84 is 33.6.
2. Evaluate each option:
- Option (A): [tex]\( 40 \cdot 84 \)[/tex]
This calculates the product of 40 and 84, which is not equal to 33.6.
- Option (B): [tex]\( 0.4 \div 84 \)[/tex]
This represents 0.4 divided by 84, which is much smaller than 33.6.
- Option (C): [tex]\( \frac{40}{100} \cdot 84 \)[/tex]
This is equivalent to finding 40% of 84 as a fraction, which equals 33.6.
- Option (D): [tex]\( 84 \div 40 \)[/tex]
This represents 84 divided by 40, which is not equal to 33.6.
- Option (E): [tex]\( 0.4 \times 84 \)[/tex]
This method also multiplies 0.4 by 84, which is the same operation as Option C, resulting in 33.6.
3. Identify the correct options:
When we compare these values to 33.6, Options (C) and (E) have the same value as 40% of 84, which is 33.6.
So, the correct answers are Option (C): [tex]\(\frac{40}{100} \cdot 84\)[/tex] and Option (E): [tex]\(0.4 \times 84\)[/tex].
1. Calculate 40% of 84:
To calculate 40% of a number, you can multiply the number by 0.4 (since 40% = 0.4 in decimal form).
[tex]\[
40\% \text{ of } 84 = 0.4 \times 84 = 33.6
\][/tex]
So, 40% of 84 is 33.6.
2. Evaluate each option:
- Option (A): [tex]\( 40 \cdot 84 \)[/tex]
This calculates the product of 40 and 84, which is not equal to 33.6.
- Option (B): [tex]\( 0.4 \div 84 \)[/tex]
This represents 0.4 divided by 84, which is much smaller than 33.6.
- Option (C): [tex]\( \frac{40}{100} \cdot 84 \)[/tex]
This is equivalent to finding 40% of 84 as a fraction, which equals 33.6.
- Option (D): [tex]\( 84 \div 40 \)[/tex]
This represents 84 divided by 40, which is not equal to 33.6.
- Option (E): [tex]\( 0.4 \times 84 \)[/tex]
This method also multiplies 0.4 by 84, which is the same operation as Option C, resulting in 33.6.
3. Identify the correct options:
When we compare these values to 33.6, Options (C) and (E) have the same value as 40% of 84, which is 33.6.
So, the correct answers are Option (C): [tex]\(\frac{40}{100} \cdot 84\)[/tex] and Option (E): [tex]\(0.4 \times 84\)[/tex].
