Why is celsius = 5 * (fahr - 32) / 9 ?

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There is a program
to print Fahrenheit-Celsius table as below.

#include <stdio.h>

/* print Fahrenheit-Celsius table
    for fahr = 0, 20, ..., 300 */
int main()
{
	int fahr, celsius;
	int lower, upper, step;

	lower = 0;    /* lower limit of temperature table */
	upper = 300;  /* upper limit */
	step = 20;    /* step size */

	fahr = lower;
	while (fahr <= upper)  {
		celsius = 5 * (fahr - 32) / 9;
		printf("%d\t%d\n", fahr, celsius);
		fahr = fahr + step;
	}
}

The right part of the
figure is the output of this program. The Celsius temperature is computed and assigned to the variable celsius by
the statement

celsius = 5 * (fahr - 32) / 9;

The reason for multiplying by 5 and then dividing by 9 instead of just multiplying by 5/9 is that in C, as in many other languages, integer
division truncates: any fractional part is discarded. Since 5 and 9 are integers, 5/9 would be truncated to zero and so all the Celsius temperatures would be reported as zero.

Reference

The C Programming Language