TenMarks teaches you how the subtraction of integers.
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Learn about Subtracting Integers This lesson is about subtracting integers using a number line and absolute values. Let's do the problems one by one. The first one wants us to take away or subtract from four the value -3 using a number line. Now, a key to remember is that if we’re subtracting a number using a number line, this is the same as adding the opposite of that number. What’s the opposite of -3? Four minus -3 is the same as add the opposite of -3 which is +3. So, this is the same as 4 + 3. So what do we do? We start with zero and we first move four spaces to the right which is +4. Then from here, the next value is a positive. So, we continue moving to the right three spaces. We end up at +7, so the answer is +7. 4-(-3)=7. That’s what we were looking for. Now let's try the second one. I'm going to take some more space and we will solve using absolute values. So problem 2A is -13, -10. If the signs are the same, we are essentially adding. If the integers are the same signs, if the signs are the same, we add the absolute values. So in this case, the absolute value of -13 is 13. The absolute value of -10 equals 10. So we add the two. So we go 13 + 10 = 23. That’s the value. Now, we still need to determine the sign. What’s the sign? Well the sign, this is one. Step two is the resign of the result is same as the sign of the numbers. Since both numbers have the same sign anyway, which is the reason we added. So, 23 is the value and since of these are negative, the sign is also a negative. So (-13)-10=-23, (-13)-10=-23 and we just sued the absolute value concept to show that. Let's try one more, which is (-24)-(-15). Now if we’re subtracting two values, this is the same as -24, adding the opposite of this which is positive 15. If we’re subtracting a negative number, we can add a positive number. So, this is what we are trying to determine,-24+15. So this is -24 and +15, each signs are different. So step one; we determine is the sign the same or different between the two numbers? If the signs are different, we subtract. So we take the larger number which is 24. From that, we take away 15, which means the end result is nine. That’s step one. Step two is the resulting sign is the sign of the greater number? Not greater in value but greater in quantity. Here, between 24 and 15, 24 is bigger. So whatever the sign of 24 was will be the sign of the result. 24 had a negative sign, so the result nine will have a negative sign as well. So -24 - 15 is the same as -24+15 which is equal to -9. That’s what we were looking for. A key to remember, if we are subtracting a negative number, that’s the same as adding the opposite of that number. If we were subtracting any number for that mater, we can change that to addition of the opposite of that number and makes it a little easier to do.