Integers. a) Circle the positive integers from the following set: 18, -10, 25, 7, 30, 12, -5, 14, -2. b) Circle the negative integers from the following set: 19, -4, 0, 11, -7, -15, -3, 9, 6. 2. Peter

Here are the solutions to the problems. 1. Integers a) Circle the positive integers from the following set: \18, -10, 25, 7, 30, 12, -5, 14, -2\ The positive integers are numbers greater than zero. The numbers to be circled are: 18, 25, 7, 30, 12, 14. b) Circle the negative integers from the following set: \19, -4, 0, 11, -7, -15, -3, 9, 6\ The negative integers are numbers less than zero. The numbers to be circled are: -4, -7, -15, -3. 2. Petero used a ladder to climb an avocado tree. He made 8 steps up the ladder and 4 steps down the ladder. Use a number line to represent: a) The number of steps he made up the ladder. Moving up is represented by a positive integer. The number of steps up is +8. On a number line, this is a movement of 8 units to the right from 0. b) The number of steps he made down the ladder. Moving down is represented by a negative integer. The number of steps down is -4. On a number line, this is a movement of 4 units to the left from 0. 3. A grade 8 learner was carrying out a science experiment on heat change. The original temperature reading was 9^ C. The temperature fell by 9^ C. Using a number line, show the new reading of the new temperature. Step 1: Identify the initial temperature and the change. Original temperature = 9^ C. Temperature fell by 9^ C, which means a decrease of 9^ C. Step 2: Calculate the new temperature. New temperature = 9^ C - 9^ C = 0^ C. Step 3: Represent on a number line. Start at 9 on the number line and move 9 units to the left. This movement ends at 0. The new temperature reading is 0^ C. 4. Represent the following numbers on a number line: a) 9 Draw a straight line and mark a point as 0. Mark equal intervals to the right for positive numbers and to the left for negative numbers. Place a dot or mark at the position corresponding to 9 on the number line. 5. Fill in the following blank spaces: a) -8 + X = -15 Let the blank be x. -8 + x = -15 x = -15 - (-8) x = -15 + 8 x = -7 The blank is -7. b) X - (-4) = 8 Let the blank be y. y - (-4) = 8 y + 4 = 8 y = 8 - 4 y = 4 The blank is 4. c) 10 - X = -7 Let the blank be z. 10 - z = -7 -z = -7 - 10 -z = -17 z = 17 The blank is 17. 6. Complete the table below by identifying equivalent integers in the respective blank spaces in the table. | Description | Positive integer | Negative integer | | :-------------------------- | :--------------- | :--------------- | | 100 m below sea level | 100 | -100 | | 20 cm to the right of 0 on a number line | 20 | -20 | | Eight steps below a ladder | 8 | -8 | | 6 floors up | 6 | -6 | That's 2 down. 3 left today — send the next one.