Certainly! Let's solve the division problem step-by-step.
We need to divide [tex]\( 334.4 \)[/tex] by [tex]\( 3.8 \)[/tex].
1. Remove the decimal points: To make the division simpler, we first convert [tex]\( 334.4 \)[/tex] and [tex]\( 3.8 \)[/tex] into whole numbers by multiplying both by 10. This changes the problem to dividing [tex]\( 3344 \)[/tex] by [tex]\( 38 \)[/tex].
2. Set up the long division: Arrange [tex]\( 3344 \)[/tex] inside the division bracket and [tex]\( 38 \)[/tex] outside.
3. Determine how many times 38 fits into the leading digits of 3344:
- First Digit: [tex]\( 38 \)[/tex] does not fit into [tex]\( 3 \)[/tex] or [tex]\( 33 \)[/tex], so we move to [tex]\( 334 \)[/tex].
- 334/38: [tex]\( 38 \times 8 = 304 \)[/tex], which is the largest multiple of 38 that is less than or equal to 334. Therefore, the first digit of our quotient is [tex]\( 8 \)[/tex].
4. Subtract and bring down the next digit:
- [tex]\( 334 - 304 = 30 \)[/tex]. Bring down the next digit, which is 4, making it 304.
- [tex]\( 304/38 = 8 \)[/tex] again, as [tex]\( 38 \times 8 = 304 \)[/tex].
5. Subtract once more:
- [tex]\( 304 - 304 = 0 \)[/tex].
At this point, we have no more digits to bring down and our division is complete.
6. Combine the quotient digits: From the steps above, our quotient is [tex]\( 88 \)[/tex].
7. Include the decimal: Since we multiplied both the dividend and divisor by [tex]\( 10 \)[/tex] at the beginning, we must adjust by placing the decimal correctly in our final quotient.
The resulting quotient is [tex]\( 88.0 \)[/tex].
So, the final answer to [tex]\( \frac{334.4}{3.8} \)[/tex] is [tex]\( 88.0 \)[/tex].
