Adding Integers The addition of integers can be done in a variety of ways, such as using number lines, manipulatives and a T-chart, calculators or shortcuts. Parentheses (or brackets) are often used around integers and their positive/negative signs to make things less confusing when doing mathematical operations. Adding Integers Using a Number Line Step 1: Draw a number line. Step 2: Locate the first number on the number line. Step 3: Move the number of spaces as shown by the second number. Move to the right if the second integer is positive. Move to the left if the second integer is negative. The number that you land on after moving the correct number of spaces to the left or right is the answer. Examples A) () + (+5) Step 1: Draw a number line. Step 2: Locate the first number on the number line. Step 3: From the first number, move five spaces to the right, because the second number is positive. Conclusion: () + (+5) = +2 Alberta Education, Alberta, Canada (www.learnalberta.ca) Adding Integers 1/12
B) () + () () + () = Move three places to the left of the first number, because the second number is negative. C) (+4) + ( 6) (+4) + ( 6) = Move six places to the left of the first number, because the second number is negative. D) () + (+3) () + (+3) = Move three places to the right of the first number, because the second number is positive. Alberta Education, Alberta, Canada (www.learnalberta.ca) Adding Integers 2/12
You can also use a vertical number line to help you think about adding integers. Think of a hot air balloon floating through the points on a vertical number line. Positive numbers are like puffs of air to lift the hot air balloon up. Negative numbers are like sandbags to weigh the hot air balloon down. To add integers, place the first number on the number line. Look at what the second number is (positive = a puff of air; negative = a sandbag). Move along the number line the number of spaces as shown by the second number. Examples A) ( 6) + (+4) = +1 0 You land here on (). Start the balloon here, at the first number. 4 6 The operation says to add a positive number (+4). This means you have 4 puffs of air lifting the balloon up. Conclusion: ( 6) + (+4) = () Alberta Education, Alberta, Canada (www.learnalberta.ca) Adding Integers 3/12
B) (+5) + ( 7) = What does this mean? Think of the second number as sandbags. Start with (+5) and ADD ( 7) or sandbags, which will bring down your hot air balloon. Look on the vertical number line. +5 + 4 +3 Start here with the balloon. +2 +1 0 The operation says to add a negative number ( 7). This means you have 7 sandbags weighing the balloon down. You land here on (). Conclusion: (+5) + ( 7) = () Alberta Education, Alberta, Canada (www.learnalberta.ca) Adding Integers 4/12
Adding Integers Using Manipulatives and a T-Chart Manipulatives are objects or shapes, such as coloured counters or chips, that are used to represent positive and negative numbers. Manipulatives can be created using a computer. For example, copy a simple shape onto a word processing document. Colour or shade the shape and make 10 copies. Each of these shapes will represent positive one (+1). Create another shape and shade it a different colour. Make 10 copies. Each of these shapes will represent negative one (). E.g., +1 One positive object and one negative object equal ZERO. E.g., + = 0 (+1) + () = 0 can be shown on the number line below. 0 +1 +2 +3 Alberta Education, Alberta, Canada (www.learnalberta.ca) Adding Integers 5/12
Placing manipulatives on a chart like the one below, or on opposite sides of a folded sheet of paper, helps in the addition of integers. E.g., + Negative objects are placed on this side of the chart. Positive objects are placed on this side of the chart. Examples A) () + (+7) + Step 1: Place objects on the chart to represent the value of each integer. + Step 2: Cross off or remove pairs of positive and negative objects. Remember: = 0 + The solution to the problem is the number of objects remaining. The sign is the same as the colour of the objects remaining and/or the sign of the column of the T-chart. () + (+7) = +3 Alberta Education, Alberta, Canada (www.learnalberta.ca) Adding Integers 6/12
B) The temperature was C, then dropped another 3 C. What is the final temperature now? () + () + Add objects to the chart to represent the value of each integer. There are no pairs of positive and negative integers, therefore the solution is the number of objects on the chart. () + () = 7 The temperature is now 7 C. C) A golfer scored +3 on one hole and then on the next hole. What is her score so far? () + (+3) + Add objects to the chart to represent the value of each integer. Cross off or remove pairs of positive and negative objects. + The solution to the addition problem is the number of objects remaining on the chart, with the sign of the integer matching the colour of the counters/chips left. (+3) + () = +2 The golfer s score so far is +2. Alberta Education, Alberta, Canada (www.learnalberta.ca) Adding Integers 7/12
Adding Integers Using a Calculator Calculators can be used to add integers if the calculator has an integer button. On many models, the integer button looks like this: + Addition of integers using a calculator can be done using one of two methods, depending on the model of calculator. Calculator Method #1 Example (3) + (+32) 1. Enter the value of the first integer, followed by the + / key only if the integer is negative. 1 3 + / 3 2. Press the + key. 3. Enter the value of the second integer, followed by the + / key only if the integer is negative. In this example, the second number is not negative, so the + / key is not pushed. 3 2 32 4. Press the = key to display the answer. 19 (3) + (+32) = +19 Alberta Education, Alberta, Canada (www.learnalberta.ca) Adding Integers 8/12
Calculator Method #2 Example () + (+12) 1. If the first integer is negative, press the + / key, then enter the value of the first integer. 3 2. Press the + key. 3. If the second integer is negative, press the + / key then enter the value of the second integer. In this example, the second integer is positive, so the key + / is not pushed. 1 2 12 4. Press the = key to display the answer. 9 () + (+12) = +9 Example Check out this example of adding integers using a calculator. (8) + (+12) Method #1 2 8 + / + 1 2 = 6 Method #2 + / 2 8 + 1 2 = 6 (8) + (+12) = 6 Alberta Education, Alberta, Canada (www.learnalberta.ca) Adding Integers 9/12
Adding Integers Using Shortcuts Two shortcuts can be applied to help with the addition of integers. Adding integers with different signs Example (+5) + () Ignore the positive and negative signs for the moment and subtract the numbers. 5 2 = 3 The sign of the answer is the sign of the largest number in the question. 5 > 2 The sign of the answer will be the sign in front of the 5 in the question. (+5) + () = +3 Proof: Adding integers with the same signs Example () + () If both numbers are positive or negative, add the numbers. 1 + 3 = 4 The sign of the numbers in the question becomes the sign of the answer. The signs of both numbers in the question were negative, so the sign of the answer will also be negative. () + () = Proof: Alberta Education, Alberta, Canada (www.learnalberta.ca) Adding Integers 10/12
Practice: Adding Integers 1. What is the opposite integer? The first one is done for you. a) Integer Opposite b) Integer Opposite +13 3 3 c) Integer Opposite d) Integer Opposite +40 5 2. Find the missing integer. a) (+4) + ( ) = +10 b) (+6) + ( ) = +4 c) () + ( ) = 9 d) ( 7) + ( ) = e) (+9) + ( ) = +3 f) () + ( ) = 1 3. Use a number line or manipulatives to solve the following. a) (+2) + (+6) + () = b) () + (+8) + (+2) = c) ( 6) + () + ( 7) = d) (+9) + ( 6) + (+4) = e) (+1) + ( 7) + (+5) = f) ( 7) + (+4) + (2) = Alberta Education, Alberta, Canada (www.learnalberta.ca) Adding Integers 11/12
4. Write each problem in mathematical terms using integers. Choose a method to solve for the unknown, such as a number line, manipulatives or a calculator. The first one is done for you. Imran has $500.00 in his bank account. He purchased a personal CD player for $295.00. How much money does Imran have left in his account? (+$500.00) + ( $295.00) = $205.00 Imran has $205.00 left in his account. a) Chong woke up in the morning and checked the thermometer outside her window. It was 0 C. Four hours later, the temperature dropped 7 C. What is the outside temperature now? b) David cuts and rakes grass in the neighbourhood. He earned $40.00 on Monday, spent $10.00 on Tuesday, spent $5.00 on Wednesday, earned $20.00 on Thursday, and earned $10.00 on Friday. How much money did David have at the end of the week? c) A submarine starts at sea level and dives 50 m below the surface, then rises 20 m, and then finally dives 84 m. What is the submarine s final depth? d) Nina and her friends took up the sport of golf. They played their best on hole 8. Their scores for hole 8 were: +5,, 0, +4,,, +3. What was their combined score on the eighth hole? Alberta Education, Alberta, Canada (www.learnalberta.ca) Adding Integers 12/12