Answer :
To find which expression gives the closest estimate to [tex]\(327 + 171\)[/tex], we can compare the actual sum to each of the given expressions. Here’s a step-by-step explanation:
1. Calculate the Actual Sum:
- The actual sum of the numbers is [tex]\(327 + 171 = 498\)[/tex].
2. Evaluate Each Expression:
- First Expression: [tex]\(300 + 175 = 475\)[/tex]
- Difference from actual sum: [tex]\( |498 - 475| = 23\)[/tex]
- Second Expression: [tex]\(325 + 175 = 500\)[/tex]
- Difference from actual sum: [tex]\( |498 - 500| = 2\)[/tex]
- Third Expression: [tex]\(325 + 200 = 525\)[/tex]
- Difference from actual sum: [tex]\( |498 - 525| = 27\)[/tex]
- Fourth Expression: [tex]\(300 + 100 = 400\)[/tex]
- Difference from actual sum: [tex]\( |498 - 400| = 98\)[/tex]
3. Determine the Closest Estimate:
- We compare the differences to see which expression is closest to the actual sum of 498.
- The expression with the smallest difference is the closest estimate.
- Second Expression [tex]\(325 + 175 = 500\)[/tex] has the smallest difference of 2 from the actual sum.
Thus, the expression [tex]\(325 + 175\)[/tex] gives the closest estimate to [tex]\(327 + 171\)[/tex].
1. Calculate the Actual Sum:
- The actual sum of the numbers is [tex]\(327 + 171 = 498\)[/tex].
2. Evaluate Each Expression:
- First Expression: [tex]\(300 + 175 = 475\)[/tex]
- Difference from actual sum: [tex]\( |498 - 475| = 23\)[/tex]
- Second Expression: [tex]\(325 + 175 = 500\)[/tex]
- Difference from actual sum: [tex]\( |498 - 500| = 2\)[/tex]
- Third Expression: [tex]\(325 + 200 = 525\)[/tex]
- Difference from actual sum: [tex]\( |498 - 525| = 27\)[/tex]
- Fourth Expression: [tex]\(300 + 100 = 400\)[/tex]
- Difference from actual sum: [tex]\( |498 - 400| = 98\)[/tex]
3. Determine the Closest Estimate:
- We compare the differences to see which expression is closest to the actual sum of 498.
- The expression with the smallest difference is the closest estimate.
- Second Expression [tex]\(325 + 175 = 500\)[/tex] has the smallest difference of 2 from the actual sum.
Thus, the expression [tex]\(325 + 175\)[/tex] gives the closest estimate to [tex]\(327 + 171\)[/tex].
