MPM1D Adding and Subtracting Integers Þ the ordinary counting numbers 1, 2, 3, Þ they sometimes include zero Þ include negative and positive numbers Þ -4, -3, -2, -1, 0, 1, 2, 3, 4 Þ a positive or negative Þ could mean multiplication sign ( ), division sign ( ), addition sign (+) or minus sign ( ) Number Line Number sense Explain why 2 < 1, even though +2 > +1 Is zero a negative number, a positive number, or neither? Is zero an even number, an odd number, or neither? Write the following numbers in order from least to greatest: 6, 8, 2, 2, 10, 1 Give an example of a negative number in real life. Two opposite integers are 16 apart on a number line. What are the numbers? Does zero have an opposite integer?
*The sign always goes with the number directly after it *When no sign is written in front, it means the number is positive! 2 + 7 The 2 is negative The 7 is positive 3 + ( 4) The 3 is negative The 4 is also negative 8 5 The 8 is positive The 5 is negative *If you write two signs together, put a bracket around the second one. We do NOT write 3 + 4 ßBad Form! Addition & Subtraction: Example 1 Evaluate. a) 100 30 b) 8 6 c) 14 20 d) 14 + 20 Example 2 Evaluate. a) 4 9 b) 3 10 c) 2 + 4 d) 114 120 e) 60 35 f) 2 6 8 + 6 + 10 g) 5 + 4 + 3 1 8 h) 18 23 + 11 26 + 8
How do we deal with two mathematical signs next to each other? Simplifying two signs to one sign: If we have (+) then we can write it as just eg. 3 (+1) = 3 If we have + ( ) then we can write it as just eg. 3 + ( 1) = If we have + (+) then we can write it as just eg. 3 + (+1) = If we have ( ) then we can write it as just eg. 3 ( 1) = Whenever we have two signs next to each other that cannot be rewritten as one sign, we write the second one in brackets. Good Form: 3 + ( 6) or 2 ( 4) Bad Form! 3 + 6 or 2 4 Example 3 Evaluate. a) 2 ( 4) STEPS: 1. Get rid of double signs 2. Collect all the positives first and negatives next b) 3 + 8 + ( 5) 3. Add the positives. Add the negatives. And then add or subtract the remaining two values using the integer rules. c) 20 10 + 35 ( 20) CHALLENGE: In a magic square, each row, column, and diagonal has the same sum. Find the integers to complete the square. d) 6 + 3 3 (+10) +4 +1 +2-2
1. List four possible values to make the statement true or explain why it is not possible. a. An integer greater than 2 and greater than 8 b. An integer greater than 12 and less than 2 c. An integer greater than 2 and less than 12 2. The sum of two integers is between 20 and 4. If you subtract these two integers, the difference is a negative number close to 0. List four possible pairs of integers. 3. Complete the statement to make it true. a. If you subtract a positive integer from a negative one, the result b. If you subtract a negative integer from a positive one, the result c. If you subtract a negative integer from a negative one, the result is negative if d. If you subtract a positive integer from a positive one, the result is negative if
Integer Worksheet Pre-Practice (Optional) 1. True or false: 4 is less than 6. Explain. 2. Ms. Kueh spent $10 when she only had $5 in her account. How much does she have now? How was this possible? 3. Evaluate 3 6 4. Change double signs to single signs, then evaluate: a. 7 + ( 2) b. 8 ( 1) c. 5 +4 d. 3 ( 2) 5. The temperature outside was 6 C in the morning. During the day it rose 8. At night it dropped by 11 C. What was the temperature that night? Mandatory Work: Evaluate. Show all work. Don t use a calculator. 6. 7 3 + 5 2 + 8 + 14 5 7. 4 + 3 1 (+5). Remember to change double signs to single signs before evaluating. 8. 5 + 3 7 ( 8) 9. 9 2 + 5 2 + +5 10. 1 1 + 2 + 5 ( 6) 11. Fill in the blanks with plus or minus signs to make the statement true. Show your work. 5 3 7 3 2 = 6 12. Order the following numbers from least to greatest: 9, 15, 16, 4, 2, 7, 20, 21 13. The temperature is +5 degrees. As a storm approaches, it drops by 7 degrees. As evening comes on, it drops another 3 degrees. What is the final temperature? 14. A submarine is at a depth of 30 m. It descends another 20 m, then rises 40 m. What was its final depth? 15. the items on a company balance sheet show these entries for income and expenses. income, $ 25,000; wage expense $ 22,000, taxes $ 4000; proceeds from sales $5000. the profit is the difference between the income and the expenses. What is the profit?
Answers: 1. False. On a number line, 4 is to the right of 6. Also in terms of money, having $4 is better than having $6. 2. She has $5. If she used credit card, she could spend $10 even when she had only $5. 3. 9 4. a. 5 b. 9 c. 1 d. 5 5. 9 C 6. 10 7. 11 8. 3 9. 9 10. 1 11. Answers may vary 12. 20, 15, 9, 7, 1, 2, 4, 16, 21 13. 5 degrees 14. depth of 10 m 15. $4000 Extra word problems (Optional) Put each of the following into an Algebraic Expression and then solve. a) A gain of $ 3 followed by a loss of $ 2 b) A gain of $3 followed by a loss of $ 9 c) A drop of 4 degrees followed by a rise of 5 degrees d) Descending 3 floors, then ascending 2 floors then descending 3 floors e) The temperature is -3 degrees. As the day progresses, the temperature increases by 8 degrees, then drops 6 degrees. f) Kerri's father kept a weekly journal during his dieting. His mass at the beginning of his dieting was 96 kg. The results are shown below. Write an expression to show the gains and losses and then use your expression to find his final mass. Week 1 gained 2 kg Week 2 lost 4 kg Week 3 gained 2 kg Week 4 lost 1 kg Week 5 lost 3 kg Answers: a) $1 b) $-6 c) rose 1 degree d) descended 4 floors e)-1 degree f) 92 kg