Answer :
To find the closest estimate for [tex]\(327 + 171\)[/tex], we will compare it to the given expressions and see which one is closest.
1. Calculate [tex]\(327 + 171\)[/tex]:
- The sum is [tex]\(498\)[/tex].
2. Evaluate each option:
a. Option [tex]\(300 + 175\)[/tex]:
- The sum is [tex]\(475\)[/tex].
- The difference from the actual sum [tex]\(498\)[/tex] is [tex]\(|498 - 475| = 23\)[/tex].
b. Option [tex]\(300 + 100\)[/tex]:
- The sum is [tex]\(400\)[/tex].
- The difference from [tex]\(498\)[/tex] is [tex]\(|498 - 400| = 98\)[/tex].
c. Option [tex]\(325 + 200\)[/tex]:
- The sum is [tex]\(525\)[/tex].
- The difference from [tex]\(498\)[/tex] is [tex]\(|498 - 525| = 27\)[/tex].
d. Option [tex]\(325 + 175\)[/tex]:
- The sum is [tex]\(500\)[/tex].
- The difference from [tex]\(498\)[/tex] is [tex]\(|498 - 500| = 2\)[/tex].
3. Determine the closest estimate:
- Comparing the differences, we have:
- 23 for the first option,
- 98 for the second option,
- 27 for the third option,
- 2 for the fourth option.
- The smallest difference is [tex]\(2\)[/tex], which comes from the option [tex]\(325 + 175\)[/tex].
Therefore, the expression [tex]\(325 + 175\)[/tex] gives the closest estimate of [tex]\(327 + 171\)[/tex].
1. Calculate [tex]\(327 + 171\)[/tex]:
- The sum is [tex]\(498\)[/tex].
2. Evaluate each option:
a. Option [tex]\(300 + 175\)[/tex]:
- The sum is [tex]\(475\)[/tex].
- The difference from the actual sum [tex]\(498\)[/tex] is [tex]\(|498 - 475| = 23\)[/tex].
b. Option [tex]\(300 + 100\)[/tex]:
- The sum is [tex]\(400\)[/tex].
- The difference from [tex]\(498\)[/tex] is [tex]\(|498 - 400| = 98\)[/tex].
c. Option [tex]\(325 + 200\)[/tex]:
- The sum is [tex]\(525\)[/tex].
- The difference from [tex]\(498\)[/tex] is [tex]\(|498 - 525| = 27\)[/tex].
d. Option [tex]\(325 + 175\)[/tex]:
- The sum is [tex]\(500\)[/tex].
- The difference from [tex]\(498\)[/tex] is [tex]\(|498 - 500| = 2\)[/tex].
3. Determine the closest estimate:
- Comparing the differences, we have:
- 23 for the first option,
- 98 for the second option,
- 27 for the third option,
- 2 for the fourth option.
- The smallest difference is [tex]\(2\)[/tex], which comes from the option [tex]\(325 + 175\)[/tex].
Therefore, the expression [tex]\(325 + 175\)[/tex] gives the closest estimate of [tex]\(327 + 171\)[/tex].
