Answer :
To solve the problem of dividing [tex]\( 1658 \)[/tex] by [tex]\( 25 \)[/tex] using long division, follow these steps:
1. Setup: Write [tex]\( 1658 \)[/tex] as the dividend and [tex]\( 25 \)[/tex] as the divisor, and position them for long division.
2. Divide: Begin by examining how many times [tex]\( 25 \)[/tex] fits into the leading part of the dividend:
- [tex]\( 25 \)[/tex] goes into [tex]\( 165 \)[/tex] 6 times (since [tex]\( 25 \times 6 = 150 \)[/tex]).
- Write [tex]\( 6 \)[/tex] atop the division bar.
3. Subtract and Bring Down:
- Subtract [tex]\( 150 \)[/tex] from [tex]\( 165 \)[/tex] which leaves [tex]\( 15 \)[/tex].
- Next, bring down the next digit (which is [tex]\( 8 \)[/tex]) to get [tex]\( 158 \)[/tex].
4. Repeat the Process:
- Now, [tex]\( 25 \)[/tex] fits into [tex]\( 158 \)[/tex] also 6 times (since [tex]\( 25 \times 6 = 150 \)[/tex]).
- Write another [tex]\( 6 \)[/tex] next to the previous [tex]\( 6 \)[/tex] on the quotient line, making the whole number part of the quotient [tex]\( 66 \)[/tex].
5. Subtract:
- Subtract [tex]\( 150 \)[/tex] from [tex]\( 158 \)[/tex] which leaves [tex]\( 8 \)[/tex]. This [tex]\( 8 \)[/tex] is the remainder.
So, our quotient as a whole number is [tex]\( 66 \)[/tex], with a remainder of [tex]\( 8 \)[/tex].
6. Convert to a Decimal and Fraction:
- To express the final quotient as a decimal, divide the remainder by the divisor:
- [tex]\( \frac{8}{25} = 0.32 \)[/tex].
- Add this decimal to the whole number part: [tex]\( 66 + 0.32 = 66.32 \)[/tex].
- Therefore, the quotient is [tex]\( 66.32 \)[/tex].
- To express the remainder as a fraction:
- The full quotient is [tex]\( 66 \frac{8}{25} \)[/tex].
By following these steps, we conclude that:
The quotient is [tex]\( 66 \)[/tex], the decimal result is [tex]\( 66.32 \)[/tex], and the quotient with the fraction remainder is [tex]\( 66 \frac{8}{25} \)[/tex].
Final Result:
- Quotient (whole number): [tex]\( 66 \)[/tex]
- Decimal representation: [tex]\( 66.32 \)[/tex]
- Fraction representation: [tex]\( 66 \frac{8}{25} \)[/tex]
1. Setup: Write [tex]\( 1658 \)[/tex] as the dividend and [tex]\( 25 \)[/tex] as the divisor, and position them for long division.
2. Divide: Begin by examining how many times [tex]\( 25 \)[/tex] fits into the leading part of the dividend:
- [tex]\( 25 \)[/tex] goes into [tex]\( 165 \)[/tex] 6 times (since [tex]\( 25 \times 6 = 150 \)[/tex]).
- Write [tex]\( 6 \)[/tex] atop the division bar.
3. Subtract and Bring Down:
- Subtract [tex]\( 150 \)[/tex] from [tex]\( 165 \)[/tex] which leaves [tex]\( 15 \)[/tex].
- Next, bring down the next digit (which is [tex]\( 8 \)[/tex]) to get [tex]\( 158 \)[/tex].
4. Repeat the Process:
- Now, [tex]\( 25 \)[/tex] fits into [tex]\( 158 \)[/tex] also 6 times (since [tex]\( 25 \times 6 = 150 \)[/tex]).
- Write another [tex]\( 6 \)[/tex] next to the previous [tex]\( 6 \)[/tex] on the quotient line, making the whole number part of the quotient [tex]\( 66 \)[/tex].
5. Subtract:
- Subtract [tex]\( 150 \)[/tex] from [tex]\( 158 \)[/tex] which leaves [tex]\( 8 \)[/tex]. This [tex]\( 8 \)[/tex] is the remainder.
So, our quotient as a whole number is [tex]\( 66 \)[/tex], with a remainder of [tex]\( 8 \)[/tex].
6. Convert to a Decimal and Fraction:
- To express the final quotient as a decimal, divide the remainder by the divisor:
- [tex]\( \frac{8}{25} = 0.32 \)[/tex].
- Add this decimal to the whole number part: [tex]\( 66 + 0.32 = 66.32 \)[/tex].
- Therefore, the quotient is [tex]\( 66.32 \)[/tex].
- To express the remainder as a fraction:
- The full quotient is [tex]\( 66 \frac{8}{25} \)[/tex].
By following these steps, we conclude that:
The quotient is [tex]\( 66 \)[/tex], the decimal result is [tex]\( 66.32 \)[/tex], and the quotient with the fraction remainder is [tex]\( 66 \frac{8}{25} \)[/tex].
Final Result:
- Quotient (whole number): [tex]\( 66 \)[/tex]
- Decimal representation: [tex]\( 66.32 \)[/tex]
- Fraction representation: [tex]\( 66 \frac{8}{25} \)[/tex]
