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101-02: arithmetic

This is lesson 101-02 of CU-101.2, checked against cint 0.2.0.

You will have the computer do arithmetic inside printed text, and find out what it does with a remainder.

the program

"minutes in a week: {7 * 24 * 60}\n";
"2 + 3 * 4 = {2 + 3 * 4}\n";
"(2 + 3) * 4 = {(2 + 3) * 4}\n";
"17 / 5 = {17 / 5}, remainder {17 % 5}\n";
"-17 / 5 = {-17 / 5}, remainder {-17 % 5}\n";

Run this program in ced

Run it:

minutes in a week: 10080
2 + 3 * 4 = 14
(2 + 3) * 4 = 20
17 / 5 = 3, remainder 2
-17 / 5 = -4, remainder 3

what happened

Braces make a hole in the text. cint works out what is inside { and } and prints the answer in its place. Outside the braces, 2 + 3 * 4 is printed just as it is written; inside them, it is worked out.

These signs are called operators. + adds, - subtracts and * multiplies. / divides and % gives the remainder of a division.

Multiplying and dividing come before adding and subtracting, as in school arithmetic. So 2 + 3 * 4 is 2 + 12, which is 14. Parentheses go first, so (2 + 3) * 4 is 5 * 4, which is 20.

Division gives a whole number. cint works with whole numbers only, so 17 / 5 is 3, not 3.4. % gives what is left over: 17 is three 5s and 2 more.

Division rounds down. The last line divides a negative number. On a number line, -17 divided by 5 is -3.4, and "down" means toward the left, so the answer is -4, not -3. The remainder is then 3, because five times -4 is -20, and -20 plus 3 is -17. For every division that gives an answer, the answer times the number you divided by, plus the remainder, gives back the number you started with.

   -5     -4     -3     -2     -1      0
    |------|------|------|------|------|
               ^
             -3.4 rounds down to -4

change it

1. Print how many hours are in a year of 365 days.
2. Print how many days old you are, roughly: your age times 365.
3. What is 100 / 7, and what is 100 % 7? Check the rule from above: the answer times 7, plus the remainder, is 100.

hours in a year: 8760

when it goes wrong

In school, many people write x for times. Try it:

"minutes in a week: {7 x 24 x 60}\n";

Run this program in ced

error[C1035]: invalid character or string literal
  --> minutes.ci:1:22
   |
 1 | "minutes in a week: {7 x 24 x 60}\n";
   |                      ^
   |

The ^ points into the hole: what is inside the braces is not something cint can work out, because x is not an operator. Write * for times.

new words

operator, remainder, rounding down

Next: lesson 101-03, names for values.