I don't understand the rules for adding and subtracting postive and negative ,can you please explain it to me? im having a test
1) When adding numbers of the same sign, we add their absolute values, and give the result the same sign.
Examples:
2 + 5.7 = 7.7
(-7.3) + (-2.1) = -(7.3 + 2.1) = -9.4
(-100) + (-0.05) = -(100 + 0.05) =
-100.05
2) When adding numbers of the opposite signs, we take their absolute values, subtract the smaller from the larger, and give the result the sign of the number with the larger absolute value.
Example:
7 + (-3.4) = ?
Subtracting the smaller from the larger gives 7 - 3.4 = 3.6, and since the larger value was 7, we give the result the same sign as 7, so 7 + (-3.4) = 3.6.
Example:
8.5 + (-17) = ?
Subtracting the smaller from the larger gives 17 - 8.5 = 8.5, and since the larger value was 17, we give the result the same sign as -17, so
8.5 + (-17) = -8.5.
Example:
-2.2 + 1.1 = ?
Subtracting the smaller from the larger gives 2.2 - 1.1 = 1.1, and since the larger value was 2.2, we give the result the same sign as -2.2, so
-2.2 + 1.1 = -1.1.
Example:
6.93 + (-6.93) = ?
Subtracting the smaller from the larger gives 6.93 - 6.93 = 0. The sign in this case does not matter, since 0 and -0 are the same. Note that 6.93 and -6.93 are opposite numbers. All opposite numbers have this property that their sum is equal to zero. Two numbers that add up to zero are also called additive inverses.
Subtracting Positive and Negative Numbers
Subtracting a number is the same as adding its opposite.
Examples:
In the following examples, we convert the subtracted number to its opposite, and add the two numbers.
7 - 4.4 = 7 + (-4.4) = 2.6
22.7 - (-5) = 22.7 + (5) = 27.7
-8.9 - 1.7 = -8.9 + (-1.7) = -10.6
-6 - (-100.6) = -6 + (100.6) = 94.6
thank you
Of course! Understanding the rules for adding and subtracting positive and negative numbers is essential for solving mathematical problems. Let's break it down into three scenarios: adding positives and negatives, subtracting positives and negatives, and adding or subtracting numbers with the same sign.
1. Adding Positives and Negatives:
- If you have two positive numbers, simply add them together. For example, 5 + 3 = 8.
- If you have two negative numbers, again, add them together. For example, -4 + (-2) = -6.
- When you're adding a positive number and a negative number, subtract the smaller absolute value from the larger one, preserving the sign of the number with the larger absolute value. For example, 7 + (-3) = 4.
2. Subtracting Positives and Negatives:
- If you're subtracting a positive number from another positive number, you can proceed as you normally would using standard subtraction. For example, 9 - 5 = 4.
- If you're subtracting a negative number from another negative number, change the operation to addition and swap the signs of both numbers. For example, -6 - (-2) becomes -6 + 2 = -4.
- When you're subtracting a positive number from a negative number, again, change the operation to addition and change the sign of the positive number. For example, -3 - 2 becomes -3 + (-2) = -5.
3. Adding or Subtracting Numbers with the Same Sign:
- If you have two positive numbers, add them together and keep the positive sign. For example, 6 + 2 = 8.
- If you have two negative numbers, add them together and keep the negative sign. For example, -5 + (-3) = -8.
Remember to pay attention to the signs and absolute values of numbers when performing addition or subtraction operations. Practice with some examples to reinforce your understanding, and ask your teacher for further clarification if needed. Good luck on your test!