Certainly! To solve [tex]\( 117.6 \div 4.9 \)[/tex], we follow these steps:
1. Simplify the Division: We can simplify the division by eliminating the decimal points. Multiply both the dividend (117.6) and the divisor (4.9) by 10 to get whole numbers:
[tex]\[
117.6 \times 10 = 1176 \quad \text{and} \quad 4.9 \times 10 = 49
\][/tex]
Therefore, the division problem is transformed to:
[tex]\[
1176 \div 49
\][/tex]
2. Long Division Setup: Set up the long division of 1176 by 49.
3. Division Process: Perform the long division step-by-step.
- First Digit: Determine how many times 49 goes into the first part of 1176. [tex]\(49\)[/tex] goes into [tex]\(117\)[/tex] twice (since [tex]\(49 \times 2 = 98\)[/tex] which is less than [tex]\(117\)[/tex]).
[tex]\[
2 \times 49 = 98
\][/tex]
Subtract [tex]\(98\)[/tex] from [tex]\(117\)[/tex]:
[tex]\[
117 - 98 = 19
\][/tex]
- Bring Down the Next Digit: Bring down the next digit of the dividend, which is 6, making it 196.
- Next Digits: Determine how many times 49 goes into 196. [tex]\(49\)[/tex] goes into [tex]\(196\)[/tex] exactly four times (since [tex]\(49 \times 4 = 196\)[/tex]).
[tex]\[
4 \times 49 = 196
\][/tex]
Subtract [tex]\(196\)[/tex] from [tex]\(196\)[/tex]:
[tex]\[
196 - 196 = 0
\][/tex]
So, the quotient from this long division process is 24 since there are no remainders.
Putting everything together:
[tex]\[
117.6 \div 4.9 = 24
\][/tex]
To summarize, the quotient of [tex]\( 117.6 \div 4.9 \)[/tex] is approximately [tex]\( 24 \)[/tex] (with high precision making the result very close to [tex]\( 23.999999999999996 \)[/tex]).
