How to Divide Integers

TenMarks teaches you all you need to know about dividing integers.

How to Divide Integers Now let's talk about dividing integers. We’re given three problems. Let's approach them one by one. The first one is 10 ÷ -5. Before we start, let me tell you the basic rules. If the signs of the numbers being divided, the signs of the numbers, if they are the same, then the quotient which is the end result is positive. If they are different, then the sign is negative. If the signs of the dividend and the divisor are the same, then it's positive and the quotient is what’s positive. So let's do this. 10 ÷ -5, 10 has got a sign of positive, 5 has got a sign of negative. 10 ÷ 5 is 2, but since the signs are different, the end result or the quotient will be a negative sign. The second problem is; evaluate the expression A x B ÷ C when a=-5, D=6 and C=-2. So let's take a little bit more space. A x B ÷ C, so A, B, and C are given to us. So let's substitute these values here. So we get A. Instead of A, I get -5 multiplied by B which is 6 ÷ C which is -2. Since A x B is one unit, we can put a parenthesis around it. So -5 x 6 is -30 because one is positive and one is negative, divided by -2. Since both signs are negative, which means the signs are the same, the end result will be a positive, 30÷ 2 is 15. So the answer to question two is positive 15. Now, let's change the color of our pen and do question three, problem three. The temperature of a place changes from 20º Celsius on Monday to 10º Celsius on Tuesday. So I'm going to actually start writing this down. So the temperature on Monday was 20º Celsius. The temperature on Tuesday was 10º Celsius. What is the average change in temperature? Well, before we do that let's find the change in temperature. What is the change in temperature? Change in temperature is the temperature on Tuesday minus the temperature on Monday. We want to know what it changed from to. So temperature on Tuesday was 10º Celsius minus temperature on Monday was 20º Celsius. So, what is the change? The change in temperature equals 10-20 is -10º Celsius. Change in temperature is -10º Celsius which makes sense because the change is a negative change, the temperature dropped from 20 to 10. So the change is a negative value. Now, that’s the change in temperature. The average change in temperature is defined as the total change in temperature over the number of days, number of days that we’re considering. In this case, since the number of days equals two, the average change will be -10º Celsius ÷ 2 = -5º Celsius. The key thing to remember is average change equals total change divided by the number of days, how many days are we talking about, two, which gives us -5º. Now what we’ve learned about dividing integers is again, if the signs of the two integers, the dividend and the divisor, dividend being the number that is being divided, the divisor is what’s dividing it is different. If the signs are different, the end result which is the quotient will be negative. If the signs are the same, then it will be positive. So for example, if we look at -30÷-2 the answer is positive because the signs are the same.