Final answer:
The remainder when 157 is divided by 5 is 2. To express this as a fraction of the divisor, the remainder fraction is ⅓.
Step-by-step explanation:
The question asks to determine the remainder when 157 is divided by 5. To find the remainder of the division, we can use the division algorithm, which states that a number can be expressed as the product of the divisor and the quotient plus the remainder. In mathematical terms, this is expressed as:
a = bq + r
where 'a' is the dividend, 'b' is the divisor, 'q' is the quotient, and 'r' is the remainder.
For the given problem:
- Dividend (a) = 157
- Divisor (b) = 5
- Quotient (q) = 31 (as provided)
Using the division algorithm: 157 = 5 × 31 + r
When we calculate 5 × 31, we get 155. Now, we subtract this number from the dividend:
157 - 155 = 2
Therefore, the remainder (r) is 2, and as a fraction of the divisor it is ⅓.