Answer :

When 157 is divided by 5, the quotient is 31 and the remainder is 2. The remainder as a fraction of the divisor is [tex]\( \frac{2}{5} \)[/tex].

To express the remainder as a fraction, we take the remainder and place it over the divisor. Therefore, the fraction representing the remainder is [tex]\( \frac{2}{5} \).[/tex]

However, the question seems to imply that the quotient (which is 31) should be expressed as a fraction along with the remainder. In this case, we can write the entire division as a mixed number, which is a whole number (the quotient) plus a proper fraction (the remainder over the divisor). So, the mixed number would be [tex]\( 31 + \frac{2}{5} \)[/tex], which can also be written as an improper fraction by multiplying the whole number by the divisor and adding the remainder:

[tex]\[ 31 \times 5 + 2 = 155 + 2 = 157 \][/tex]

As a fraction, this is [tex]\( \frac{157}{5} \)[/tex]. But since we are looking for the remainder as a fraction, we subtract the whole number part (which is [tex]\( 31 \times 5 = 155 \)[/tex]) from the total:

[tex]\[ \frac{157}{5} - \frac{155}{5} = \frac{157 - 155}{5} = \frac{2}{5} \][/tex]

So, the remainder expressed as a fraction is indeed [tex]\( \frac{2}{5} \)[/tex].

To summarize, when 157 is divided by 5, the quotient is 31 and the remainder is 2. The remainder as a fraction of the divisor is [tex]\( \frac{2}{5} \)[/tex].

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Rewritten by : Barada

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.

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.