To solve the division problem [tex]\(\frac{978}{37}\)[/tex] and determine the quotient and remainder, follow these steps:
1. Identify the Dividend and Divisor:
- Dividend (numerator) = 978
- Divisor (denominator) = 37
2. Calculate the Quotient:
- The quotient of dividing 978 by 37 is the number of times 37 can go into 978 completely without exceeding it.
[tex]\[
978 \div 37 = 26
\][/tex]
3. Calculate the Remainder:
- After determining how many times 37 fits into 978 without exceeding it, we must find what is left over. This is called the remainder.
To find the remainder, multiply the quotient by the divisor and subtract this product from the dividend:
[tex]\[
\text{Remainder} = 978 - (37 \times 26) = 978 - 962 = 16
\][/tex]
So, when you divide 978 by 37, you get a quotient of 26 and a remainder of 16. Therefore, the correct representation of the division is:
[tex]\[
\frac{978}{37} = 26 \text{ R } 16
\][/tex]
Thus, the correct answer from the given choices is:
26 R16
