Answer :
To determine which equations are true based on the given equation [tex]\( 83 \times 27 = 2,241 \)[/tex], let's go through each option step by step:
Option (A): [tex]\( 2,241 \div 83 = 27 \)[/tex]
- When you divide [tex]\( 2,241 \)[/tex] by [tex]\( 83 \)[/tex], you are checking if the division results in [tex]\( 27 \)[/tex].
- Since [tex]\( 83 \times 27 = 2,241 \)[/tex], dividing [tex]\( 2,241 \)[/tex] by [tex]\( 83 \)[/tex] should indeed give you [tex]\( 27 \)[/tex].
- Therefore, this equation is true.
Option (B): [tex]\( 27 \div 2,241 = 83 \)[/tex]
- Here, you’re dividing a smaller number [tex]\( 27 \)[/tex] by a larger number [tex]\( 2,241 \)[/tex].
- A division where the divisor is greater than the dividend (like this one) cannot result in a whole number like [tex]\( 83 \)[/tex].
- Thus, this equation is false.
Option (C): [tex]\( 83 \div 2,241 = 27 \)[/tex]
- Similar to option B, dividing [tex]\( 83 \)[/tex] by [tex]\( 2,241 \)[/tex] (a larger number) cannot equal a larger number like [tex]\( 27 \)[/tex].
- Therefore, this equation is false.
Option (D): [tex]\( 2,241 \div 27 = 83 \)[/tex]
- Dividing [tex]\( 2,241 \)[/tex] by [tex]\( 27 \)[/tex] checks if [tex]\( 83 \)[/tex] comes out as a result.
- This makes sense because if [tex]\( 83 \times 27 = 2,241 \)[/tex], then dividing [tex]\( 2,241 \)[/tex] by [tex]\( 27 \)[/tex] should yield [tex]\( 83 \)[/tex].
- So, this equation is true.
Option (E): [tex]\( 27 \times 83 = 2,241 \)[/tex]
- Since multiplication is commutative, switching the order of the factors does not change the product.
- Thus, [tex]\( 27 \times 83 \)[/tex] is the same as [tex]\( 83 \times 27 \)[/tex], and both equal [tex]\( 2,241 \)[/tex].
- Therefore, this equation is true.
So, the true equations are (A), (D), and (E).
Option (A): [tex]\( 2,241 \div 83 = 27 \)[/tex]
- When you divide [tex]\( 2,241 \)[/tex] by [tex]\( 83 \)[/tex], you are checking if the division results in [tex]\( 27 \)[/tex].
- Since [tex]\( 83 \times 27 = 2,241 \)[/tex], dividing [tex]\( 2,241 \)[/tex] by [tex]\( 83 \)[/tex] should indeed give you [tex]\( 27 \)[/tex].
- Therefore, this equation is true.
Option (B): [tex]\( 27 \div 2,241 = 83 \)[/tex]
- Here, you’re dividing a smaller number [tex]\( 27 \)[/tex] by a larger number [tex]\( 2,241 \)[/tex].
- A division where the divisor is greater than the dividend (like this one) cannot result in a whole number like [tex]\( 83 \)[/tex].
- Thus, this equation is false.
Option (C): [tex]\( 83 \div 2,241 = 27 \)[/tex]
- Similar to option B, dividing [tex]\( 83 \)[/tex] by [tex]\( 2,241 \)[/tex] (a larger number) cannot equal a larger number like [tex]\( 27 \)[/tex].
- Therefore, this equation is false.
Option (D): [tex]\( 2,241 \div 27 = 83 \)[/tex]
- Dividing [tex]\( 2,241 \)[/tex] by [tex]\( 27 \)[/tex] checks if [tex]\( 83 \)[/tex] comes out as a result.
- This makes sense because if [tex]\( 83 \times 27 = 2,241 \)[/tex], then dividing [tex]\( 2,241 \)[/tex] by [tex]\( 27 \)[/tex] should yield [tex]\( 83 \)[/tex].
- So, this equation is true.
Option (E): [tex]\( 27 \times 83 = 2,241 \)[/tex]
- Since multiplication is commutative, switching the order of the factors does not change the product.
- Thus, [tex]\( 27 \times 83 \)[/tex] is the same as [tex]\( 83 \times 27 \)[/tex], and both equal [tex]\( 2,241 \)[/tex].
- Therefore, this equation is true.
So, the true equations are (A), (D), and (E).
