Integers

In daily life we often need numbers less than zero. A temperature of 5 degrees below zero, a loss of Rs 200, a depth of 30 m below sea level or a withdrawal from a bank account can all be shown using negative numbers. In this chapter you will learn that the collection of numbers ..., -3, -2, -1, 0, 1, 2, 3, ... is called integers. Positive integers lie to the right of zero on the number line and negative integers to the left. You will use the number line to compare and order integers: a number on the right is always greater, so -2 is greater than -7. The chapter then teaches addition of integers using the number line and positive and negative counters, where one positive and one negative counter together make zero. You will learn that the sum of an integer and its additive inverse, such as 6 and -6, is zero, and that subtracting an integer is the same as adding its additive inverse, so 5 - (-3) = 5 + 3 = 8.

Detailed Worksheet: Integers Section A - Definitions (10 marks) 1. What are integers? Write the integers between -4 and 3. (2 marks) 2. What is a negative integer? Give two real-life situations where negative integers are used. (2 marks) 3. Define the additive inverse of an integer. Write the additive inverses of 9, -14 and 0. (2 marks) 4. What is the predecessor and successor of an integer? Write the predecessor and successor of -10. (2 marks) 5. State the rule for subtraction of integers. Use it to find 7 - (-4). (2 marks) Section B - Calculations and Applications (15 marks) 6. Find: (i) -11 + 7 (ii) -20 + (-15) (iii) 35 + (-35) (iv) -8 + 18 (v) 90 + (-62) (vi) -7 + (-3) + 12. (3 marks) 7. Find: (i) 35 - (20) (ii) 72 - (90) (iii) -15 - (-18) (iv) -20 - (13) (v) 23 - (-12) (vi) -32 - (-40). (3 marks) 8. Arrange in ascending order: (i) -7, 10, -5, -2, 9 (ii) -18, 0, 4, -12, 25 (iii) -1, -100, 50, -50, 1. (3 marks) 9. The temperatures of four cities on a winter day were: Siachen -10 degrees C, Shimla 5 degrees C, Srinagar -2 degrees C and Delhi 15 degrees C. (i) Which city is the coldest? (ii) Which is the hottest? (iii) Find the difference between the temperatures of Delhi and Siachen. (3 marks) 10. A submarine is at 120 m below sea level. It rises 45 m and then dives 30 m. (i) Represent the positions as integers. (ii) Find its final position. (iii) How far is it from the surface? (3 marks) Section C - Diagrams (10 marks) 11. Draw a number line from -6 to 6. Use it to find (i) 3 + (-5) (ii) -2 + (-3). Show each jump with an arrow drawn on the line. Explain the direction of movement for adding a negative integer. (4 marks) 12. Draw positive and negative counters to find (i) (+5) + (-3) (ii) (-4) + (+4). Explain why one positive and one negative counter cancel each other. (3 marks) 13. Draw a vertical number line like a thermometer from -10 to 10. Mark the temperatures -8, -3, 0, 4 and 9. Which temperature is the lowest, and how many degrees is 9 above -3? (3 marks) Section D - Analysis and Higher-order Thinking (15 marks) 14. In a quiz, positive marks are given for correct answers and negative marks for incorrect answers. Team A scored 25, -5, -10, 15, 10 in five rounds and Team B scored -10, 10, 15, 5, -5. (i) Find the total score of each team. (ii) Which team won? (iii) Can we add the scores in any order? Explain. (5 marks) 15. Sunita says, "The sum of two integers is always greater than each of them." (i) Test her statement with 5 and 3, and with -5 and -3. (ii) Is her statement correct? (iii) Write a pair of integers whose sum is less than both. (iv) Write a pair whose sum is 0. (5 marks) 16. A shopkeeper marks profit as a positive integer and loss as a negative integer. Over a week, he had: Monday profit Rs 150, Tuesday loss Rs 200, Wednesday profit Rs 300, Thursday loss Rs 75, Friday loss Rs 50. (i) Write the daily results as integers. (ii) Find his net result for the week. (iii) Was it a profit or a loss? (iv) How much profit on Saturday would make the week's total Rs 500? (5 marks) Instructions: Time allowed 2 hours. Attempt all sections. Draw all number lines with a ruler and mark equal distances for each unit.