Answer :
To solve the division problem [tex]\(\frac{1658}{25}\)[/tex], we need to find both the quotient and the remainder. Let's go through the steps:
1. Perform the Division:
- Divide [tex]\(1658\)[/tex] by [tex]\(25\)[/tex].
- When you divide, the integer part of the quotient is [tex]\(66\)[/tex].
- To find the remainder, multiply [tex]\(66\)[/tex] by [tex]\(25\)[/tex] and subtract from [tex]\(1658\)[/tex]:
[tex]\[
1658 - (66 \times 25) = 1658 - 1650 = 8
\][/tex]
So the quotient is [tex]\(66\)[/tex] and the remainder is [tex]\(8\)[/tex].
2. Convert to Decimal Form:
- To get the decimal form of the quotient, divide [tex]\(8\)[/tex] (the remainder) by [tex]\(25\)[/tex]:
[tex]\[
8 \div 25 = 0.32
\][/tex]
- Therefore, the decimal quotient is:
[tex]\[
66 + 0.32 = 66.32
\][/tex]
3. Match the Choices:
- 66.32: This matches the decimal quotient we calculated.
- 66.8: This does not match our calculation.
- 62.32: This does not match our calculation.
- [tex]\(62 \frac{8}{25}\)[/tex]: This does not match our quotient.
- [tex]\(66 \frac{8}{25}\)[/tex]: This matches our quotient. [tex]\(66 \frac{8}{25}\)[/tex] is the fractional form, which can also be written as [tex]\(66 + \frac{8}{25} = 66 + 0.32 = 66.32\)[/tex].
From these calculations, the correct answers are:
- 66.32
- [tex]\(66 \frac{8}{25}\)[/tex]
These are the right choices that represent the quotient and remainder of the given division.
1. Perform the Division:
- Divide [tex]\(1658\)[/tex] by [tex]\(25\)[/tex].
- When you divide, the integer part of the quotient is [tex]\(66\)[/tex].
- To find the remainder, multiply [tex]\(66\)[/tex] by [tex]\(25\)[/tex] and subtract from [tex]\(1658\)[/tex]:
[tex]\[
1658 - (66 \times 25) = 1658 - 1650 = 8
\][/tex]
So the quotient is [tex]\(66\)[/tex] and the remainder is [tex]\(8\)[/tex].
2. Convert to Decimal Form:
- To get the decimal form of the quotient, divide [tex]\(8\)[/tex] (the remainder) by [tex]\(25\)[/tex]:
[tex]\[
8 \div 25 = 0.32
\][/tex]
- Therefore, the decimal quotient is:
[tex]\[
66 + 0.32 = 66.32
\][/tex]
3. Match the Choices:
- 66.32: This matches the decimal quotient we calculated.
- 66.8: This does not match our calculation.
- 62.32: This does not match our calculation.
- [tex]\(62 \frac{8}{25}\)[/tex]: This does not match our quotient.
- [tex]\(66 \frac{8}{25}\)[/tex]: This matches our quotient. [tex]\(66 \frac{8}{25}\)[/tex] is the fractional form, which can also be written as [tex]\(66 + \frac{8}{25} = 66 + 0.32 = 66.32\)[/tex].
From these calculations, the correct answers are:
- 66.32
- [tex]\(66 \frac{8}{25}\)[/tex]
These are the right choices that represent the quotient and remainder of the given division.
