Complete addition and subtraction sentences with integers
Key note :–
1. Understanding Integers:
- Integers are whole numbers that include positive numbers, negative numbers, and zero.
- Example: -3, -2, -1, 0, 1, 2, 3.
2. Addition of Integers:
- Same sign addition: When adding two integers with the same sign, add their absolute values and keep the sign.
- Example: 5 + 3 = 8, -5 + (-3) = -8.
- Different sign addition: When adding integers with different signs, subtract the smaller absolute value from the larger absolute value and use the sign of the number with the larger absolute value.
- Example: 7 + (-4) = 3, -7 + 4 = -3.
3. Subtraction of Integers:
- Subtraction rule: To subtract an integer, add its opposite.
- Example: 5 – 3 = 5 + (-3) = 2, -5 – 3 = -5 + (-3) = -8.
- When subtracting negative integers: Remember that subtracting a negative number is the same as adding the positive version of that number.
- Example: 6 – (-4) = 6 + 4 = 10.
4. Examples of Completing Sentences:
- Addition: Complete the sentence:
5 + (-3) = ?
Solution: 5 + (-3) = 2 (add the absolute values and keep the sign of the number with the larger absolute value). - Subtraction: Complete the sentence:
-7 – 4 = ?
Solution: -7 – 4 = -11 (subtract and keep the negative sign).
Learn with an example
➡️ Type the integer that makes the following addition number sentence true:
_____+ -5 = -9
You want to find the number that makes the addition number sentence true.
Later on, you’ll learn another way of solving problems like this, but for now, there is a helpful shortcut that you can use. Look at the two numbers and ignore their signs. They are 5 and 9. Now find their sum and difference. To find the sum, add 5 and 9 to get 14. To compute the difference, subtract the smaller number, 5, from the larger number, 9, to get 4.
Now you have two numbers to try: 14 and 4. If you make these two numbers negative, you’ll have another two numbers to try: -14 and -4. The correct answer will be one of these four numbers.
Try 14:
14 + -5 = 9
Try 4:
4 + -5 = -1
Try -14:
-14 + -5 = -19
Try -4:
-4 + -5 = -9
The number -4 makes the number sentence true, so the correct answer is -4.
➡️ Type the integer that makes the following subtraction number sentence true:
-7 −____= -15
You want to find the number that makes the subtraction number sentence true.
Later on, you’ll learn another way of solving problems like this, but for now, there is a helpful shortcut that you can use. Look at the two numbers and ignore their signs. They are 7 and 15. Now find their sum and difference. To find the sum, add 7 and 15 to get 22. To compute the difference, subtract the smaller number, 7, from the larger number, 15, to get 8.
Now you have two numbers to try: 22 and 8. If you make these two numbers negative, you’ll have another two numbers to try: -22 and -8. The correct answer will be one of these four numbers.
Try 22:
-7 − 22 = -29
Try 8:
-7 − 8 = -15
Try -22:
–7 − –22 = 15
Try -8:
-7 − -8 = 1
The number 8 makes the number sentence true, so the correct answer is 8.
➡️ Type the integer that makes the following addition number sentence true:
____+ -6 = -8
You want to find the number that makes the addition number sentence true.
Later on, you’ll learn another way of solving problems like this, but for now, there is a helpful shortcut that you can use. Look at the two numbers and ignore their signs. They are 6 and 8. Now find their sum and difference. To find the sum, add 6 and 8 to get 14. To compute the difference, subtract the smaller number, 6, from the larger number, 8, to get 2.
Now you have two numbers to try: 14 and 2. If you make these two numbers negative, you’ll have another two numbers to try: -14 and -2. The correct answer will be one of these four numbers.
Try 14:
14 + -6 = 8
Try 2:
2 + -6 = -4
Try -14:
-14 + -6 = -20
Try -2:
-2 + -6 = -8
The number -2 makes the number sentence true, so the correct answer is -2.
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