Answer :
Sure, I'll provide a detailed, step-by-step solution to the division of 38.2 by 6.
1. Set up the division problem:
We want to divide 38.2 by 6. Let's write it as [tex]\( 38.2 \div 6 \)[/tex].
2. Perform the division:
- First, consider 38.2 as a whole number, and we'll convert it to a manageable quotient later.
- Take the whole number part of 38.2, which is 38.
3. Divide the integer part:
- 38 divided by 6 equals 6, because [tex]\( 6 \times 6 = 36 \)[/tex], and this is the largest multiple of 6 that is less than or equal to 38.
- So, the quotient so far is 6.
4. Calculate the remainder after dividing the integer part:
- Subtract [tex]\( 36 \)[/tex] from [tex]\( 38 \)[/tex]:
[tex]\( 38 - 36 = 2 \)[/tex].
5. Incorporate the decimal part:
- Now, bring down the 0 from the decimal part of 38.2 to make it 20.
- Divide 20 by 6 to get the next portion of the quotient.
- 20 divided by 6 is approximately 3.333 when reduced, but we'll just note the division as 3 for now, again because [tex]\( 6 \times 3 = 18 \)[/tex].
6. Calculate the new remainder:
- Subtract [tex]\( 18 \)[/tex] from [tex]\( 20 \)[/tex]:
[tex]\( 20 - 18 = 2 \)[/tex].
7. Continue the division for precision:
- Bring down another 0 making it 20 again:
- 20 divided by 6 is 3, repeat.
- The next digit is again 3.
- Continue in the same manner to build the decimal quotient [tex]\( 0.333... \)[/tex] recurring.
8. Combine the results:
- When we take into account the quotient from step 4 (integer part 6) and the fractional part from the continued division, we find the total quotient as approximately 6.3667.
- Therefore, when expressing the quotient in terms of its integer and decimal parts:
- The integer part is 6.
- The decimal (fractional) part continues as 0.36666666666666714.
9. Final quotient:
- So, [tex]\( \frac{38.2}{6} = 6.366666666666667 \)[/tex].
Hence, we have:
- The integer part is [tex]\( 6 \)[/tex],
- The decimal part is approximately [tex]\(0.36666666666666714 \)[/tex],
- And the total quotient is [tex]\( 6.366666666666667 \)[/tex].
1. Set up the division problem:
We want to divide 38.2 by 6. Let's write it as [tex]\( 38.2 \div 6 \)[/tex].
2. Perform the division:
- First, consider 38.2 as a whole number, and we'll convert it to a manageable quotient later.
- Take the whole number part of 38.2, which is 38.
3. Divide the integer part:
- 38 divided by 6 equals 6, because [tex]\( 6 \times 6 = 36 \)[/tex], and this is the largest multiple of 6 that is less than or equal to 38.
- So, the quotient so far is 6.
4. Calculate the remainder after dividing the integer part:
- Subtract [tex]\( 36 \)[/tex] from [tex]\( 38 \)[/tex]:
[tex]\( 38 - 36 = 2 \)[/tex].
5. Incorporate the decimal part:
- Now, bring down the 0 from the decimal part of 38.2 to make it 20.
- Divide 20 by 6 to get the next portion of the quotient.
- 20 divided by 6 is approximately 3.333 when reduced, but we'll just note the division as 3 for now, again because [tex]\( 6 \times 3 = 18 \)[/tex].
6. Calculate the new remainder:
- Subtract [tex]\( 18 \)[/tex] from [tex]\( 20 \)[/tex]:
[tex]\( 20 - 18 = 2 \)[/tex].
7. Continue the division for precision:
- Bring down another 0 making it 20 again:
- 20 divided by 6 is 3, repeat.
- The next digit is again 3.
- Continue in the same manner to build the decimal quotient [tex]\( 0.333... \)[/tex] recurring.
8. Combine the results:
- When we take into account the quotient from step 4 (integer part 6) and the fractional part from the continued division, we find the total quotient as approximately 6.3667.
- Therefore, when expressing the quotient in terms of its integer and decimal parts:
- The integer part is 6.
- The decimal (fractional) part continues as 0.36666666666666714.
9. Final quotient:
- So, [tex]\( \frac{38.2}{6} = 6.366666666666667 \)[/tex].
Hence, we have:
- The integer part is [tex]\( 6 \)[/tex],
- The decimal part is approximately [tex]\(0.36666666666666714 \)[/tex],
- And the total quotient is [tex]\( 6.366666666666667 \)[/tex].