To solve [tex]\(51 \div 11\)[/tex], you need to divide 51 by 11. Here’s a step-by-step breakdown of how the division works:
1. Identify the Dividend and Divisor:
[tex]\[
\text{Dividend} = 51, \quad \text{Divisor} = 11
\][/tex]
2. Set Up the Division:
[tex]\[
\frac{51}{11}
\][/tex]
3. Perform the Division:
We need to see how many times 11 fits into 51.
- 11 goes into 51 four times because [tex]\(11 \times 4 = 44\)[/tex].
- Subtract 44 from 51: [tex]\(51 - 44 = 7\)[/tex]. This leaves a remainder of 7.
4. Expressing the Quotient and Remainder:
Our intermediate result is that 51 divided by 11 is 4 with a remainder 7, which can be written as:
[tex]\[
51 \div 11 = 4 \quad \text{remainder} \quad 7
\][/tex]
5. Convert the Remainder to a Decimal:
To get a more precise result, we need to convert the remainder 7 into a decimal fraction. We do this by continuing the division:
- Take the remainder 7 and divide by 11, so we get [tex]\( \frac{7}{11} \)[/tex].
To convert [tex]\( \frac{7}{11} \)[/tex] to a decimal:
- Use long division or recognize it as approximately 0.636363636363636..., which is a repeating decimal.
6. Combine the Whole Number and Decimal Parts:
When you add the decimal fraction to the whole number part of the quotient:
[tex]\[
4 + 0.636363636363636... = 4.636363636363637
\][/tex]
Therefore, [tex]\( 51 \div 11 = 4.636363636363637 \)[/tex].
