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Answer :
To find which expressions are equal to [tex]\(66 \times 7,250\)[/tex], let's go through each expression one by one.
1. Expression 1: [tex]\((725 \times 10^2) \times 66\)[/tex]
- Here, [tex]\(725 \times 10^2\)[/tex] is the same as multiplying 725 by 100, which equals [tex]\(72,500\)[/tex].
- Then, [tex]\(72,500 \times 66\)[/tex] should be calculated to match the original expression. However, this calculation results in a different value than [tex]\(66 \times 7,250\)[/tex].
2. Expression 2: [tex]\((725 \times 10) \times 60 \times 6\)[/tex]
- First, [tex]\(725 \times 10 = 7,250\)[/tex].
- Then, multiply by 60: [tex]\(7,250 \times 60\)[/tex].
- Finally, multiply the result by 6. However, when we complete this calculation, it does not equal the original expression, due to the sequence and grouping of the multiplications differing.
3. Expression 3: [tex]\(7,250 \times (60 + 6)\)[/tex]
- First, calculate the sum inside the parentheses: [tex]\(60 + 6 = 66\)[/tex].
- Then, multiply [tex]\(7,250 \times 66\)[/tex].
- This results in the same value as the original expression, hence this expression is equal.
4. Expression 4: [tex]\(7,250 \times 66\)[/tex]
- This expression directly mirrors the original expression [tex]\(66 \times 7,250\)[/tex].
- Hence, they are definitely equal.
5. Expression 5: [tex]\(66 \times (7,000 + 200)\)[/tex]
- Calculate the sum inside the parentheses: [tex]\(7,000 + 200 = 7,200\)[/tex].
- Then, multiply [tex]\(66 \times 7,200\)[/tex].
- This results in a different value than the original expression.
From this analysis, the expressions equal to [tex]\(66 \times 7,250\)[/tex] are:
- [tex]\(7,250 \times (60 + 6)\)[/tex]
- [tex]\(7,250 \times 66\)[/tex]
1. Expression 1: [tex]\((725 \times 10^2) \times 66\)[/tex]
- Here, [tex]\(725 \times 10^2\)[/tex] is the same as multiplying 725 by 100, which equals [tex]\(72,500\)[/tex].
- Then, [tex]\(72,500 \times 66\)[/tex] should be calculated to match the original expression. However, this calculation results in a different value than [tex]\(66 \times 7,250\)[/tex].
2. Expression 2: [tex]\((725 \times 10) \times 60 \times 6\)[/tex]
- First, [tex]\(725 \times 10 = 7,250\)[/tex].
- Then, multiply by 60: [tex]\(7,250 \times 60\)[/tex].
- Finally, multiply the result by 6. However, when we complete this calculation, it does not equal the original expression, due to the sequence and grouping of the multiplications differing.
3. Expression 3: [tex]\(7,250 \times (60 + 6)\)[/tex]
- First, calculate the sum inside the parentheses: [tex]\(60 + 6 = 66\)[/tex].
- Then, multiply [tex]\(7,250 \times 66\)[/tex].
- This results in the same value as the original expression, hence this expression is equal.
4. Expression 4: [tex]\(7,250 \times 66\)[/tex]
- This expression directly mirrors the original expression [tex]\(66 \times 7,250\)[/tex].
- Hence, they are definitely equal.
5. Expression 5: [tex]\(66 \times (7,000 + 200)\)[/tex]
- Calculate the sum inside the parentheses: [tex]\(7,000 + 200 = 7,200\)[/tex].
- Then, multiply [tex]\(66 \times 7,200\)[/tex].
- This results in a different value than the original expression.
From this analysis, the expressions equal to [tex]\(66 \times 7,250\)[/tex] are:
- [tex]\(7,250 \times (60 + 6)\)[/tex]
- [tex]\(7,250 \times 66\)[/tex]
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