Sure, let's solve the division of [tex]\( 14,053 \)[/tex] by [tex]\( 8 \)[/tex] step-by-step.
1. Determine how many times 8 fits into the first digit(s) of the dividend (1).
- 8 does not fit into the first digit [tex]\( 1 \)[/tex].
- Combine the first two digits: [tex]\( 14 \)[/tex].
- [tex]\( 8 \)[/tex] fits into [tex]\( 14 \)[/tex] once (because [tex]\( 8 \times 1 = 8 \)[/tex]).
2. Subtract the product from the combined digits:
[tex]\[
14 - 8 = 6
\][/tex]
3. Bring down the next digit from the dividend (0) to get [tex]\( 60 \)[/tex], and determine how many times 8 fits into [tex]\( 60 \)[/tex]:
- [tex]\( 8 \times 7 = 56 \)[/tex]. So, 8 fits into [tex]\( 60 \)[/tex] seven times.
4. Subtract the product from [tex]\( 60 \)[/tex]:
[tex]\[
60 - 56 = 4
\][/tex]
5. Bring down the next digit from the dividend (5) to make [tex]\( 45 \)[/tex]:
- [tex]\( 8 \times 5 = 40 \)[/tex]. So, 8 fits into [tex]\( 45 \)[/tex] five times.
6. Subtract the product from [tex]\( 45 \)[/tex]:
[tex]\[
45 - 40 = 5
\][/tex]
7. Bring down the last digit from the dividend (3) to make [tex]\( 53 \)[/tex]:
- [tex]\( 8 \times 6 = 48 \)[/tex]. So, 8 fits into [tex]\( 53 \)[/tex] six times.
8. Subtract the product from [tex]\( 53 \)[/tex]:
[tex]\[
53 - 48 = 5
\][/tex]
The quotient is formed by the sequence of numbers obtained: [tex]\( 1, 7, 5, 6 \)[/tex].
Hence, the quotient is [tex]\( 1,756 \)[/tex] and the remainder is [tex]\( 5 \)[/tex].
So, the result of dividing [tex]\( 14,053 \)[/tex] by [tex]\( 8 \)[/tex] is:
[tex]\[
14,053 \div 8 = 1,756 \text{ R } 5
\][/tex]
Which means:
[tex]\[
14,053 = 8 \times 1,756 + 5
\][/tex]
Thus, the quotient is [tex]\( 1,756 \)[/tex] and the remainder is [tex]\( 5 \)[/tex].
