Find the remainder: (17 − 21) ÷ 18

General
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find the remainder: (17 − 21) ÷ 18

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Find the remainder: (17 − 21) ÷ 18

Step-by-Step Solution:

We are tasked to compute the remainder of the expression ((17 - 21) \div 18).

Step 1: Simplify the expression inside parentheses

Start by subtracting (21) from (17):

17 - 21 = -4

So, the expression becomes:

-4 \div 18

Step 2: Understand division involving negative numbers

When dividing a negative number by a positive number and looking for remainders, keep in mind the division algorithm:

The division algorithm states:

\text{Dividend} = (\text{Divisor} \times \text{Quotient}) + \text{Remainder},

where the Remainder must satisfy:

0 \leq \text{Remainder} < \text{Divisor}.

Step 3: Perform the division

Now, divide (-4) by (18):

  • The integer division (quotient) of (-4 \div 18) is (0) since (-4) is less than (18), and (18) goes into (-4) zero times.
  • However, (-4) is still negative, so we need to find the remainder that satisfies (0 \leq \text{Remainder} < 18).

Step 4: Adjust the remainder to fit the range

The remainder is calculated as:

\text{Remainder} = -4 + 18 = 14

This adjustment ensures the remainder is in the range (0 \leq \text{Remainder} < 18).

Final Answer:

The remainder when ((17 - 21) \div 18) is performed is:

\boxed{14}

If you have any additional questions, feel free to ask! :blush: @anonymous13