Whole Numbers

The counting numbers 1, 2, 3, ... are called natural numbers. When zero is included, we get the whole numbers 0, 1, 2, 3, .... In this chapter you will learn that every whole number has a successor, obtained by adding 1, and every whole number except 0 has a predecessor, obtained by subtracting 1. You will represent whole numbers on a number line and use it to show addition as moving right, subtraction as moving left and multiplication as making equal jumps from zero. The chapter then studies the properties of whole numbers. They are closed under addition and multiplication but not under subtraction and division. Addition and multiplication are commutative and associative, multiplication distributes over addition, as in 6 x 105 = 6 x 100 + 6 x 5, zero is the additive identity and 1 is the multiplicative identity. Division by zero is not defined. You will use these properties for quick mental calculations and explore patterns, such as arranging numbers as dots in lines, rectangles, squares and triangles.

Detailed Worksheet: Whole Numbers Section A - Definitions (10 marks) 1. What are whole numbers? How are they different from natural numbers? (2 marks) 2. Define successor and predecessor. Which whole number has no predecessor? (2 marks) 3. State the closure property for whole numbers. Under which operations are whole numbers closed? (2 marks) 4. What is the additive identity and the multiplicative identity for whole numbers? Give one example of each. (2 marks) 5. State the distributive property of multiplication over addition with an example. (2 marks) Section B - Calculations and Applications (15 marks) 6. Find the sum by suitable rearrangement: (i) 837 + 208 + 363 (ii) 1962 + 453 + 1538 + 647 (iii) 2 x 1768 x 50. (3 marks) 7. Find the product using the distributive property: (i) 738 x 103 (ii) 854 x 102 (iii) 258 x 1008. (3 marks) 8. Find using suitable properties: (i) 4 x 166 x 25 (ii) 8 x 291 x 125 (iii) 625 x 279 x 16. (3 marks) 9. A taxi driver filled his car petrol tank with 40 litres of petrol on Monday. The next day, he filled the tank with 50 litres. If the petrol costs Rs 44 per litre, how much did he spend in all? Use the distributive property. (3 marks) 10. A vendor supplies 32 litres of milk to a hotel in the morning and 68 litres in the evening. If the milk costs Rs 45 per litre, how much money is due to the vendor per day? Show the use of a property in your working. (3 marks) Section C - Diagrams (10 marks) 11. Draw a number line from 0 to 12. Show (i) 3 + 5 (ii) 9 - 4 (iii) 3 x 4 on it using jumps. Explain the direction of movement in each case. (4 marks) 12. Draw dot patterns to show which of the numbers 6, 9, 10 and 12 can be arranged as a rectangle, a square or a triangle. (3 marks) 13. Draw a number line and mark the successor and predecessor of 7 and of 10. Which of the two numbers 7 and 10 lies to the left? (3 marks) Section D - Analysis and Higher-order Thinking (15 marks) 14. Study the pattern: 9 x 9 = 81, 99 x 99 = 9801, 999 x 999 = 998001. (i) Write the next two steps. (ii) Describe the pattern. (iii) Find 9 x 11, 99 x 11 and 999 x 11 and describe their pattern. (5 marks) 15. Check whether each statement is true or false with examples: (i) whole numbers are closed under subtraction (ii) division of a whole number by zero gives zero (iii) the product of a whole number and zero is zero (iv) subtraction is commutative (v) 1 is the identity for multiplication. (5 marks) 16. Lalita says, "Every number greater than 1 can be shown as a line of dots, but only some can be shown as rectangles." (i) Is she right? (ii) Which numbers can be shown only as a line? (iii) Which numbers can be shown as squares? Give three examples. (iv) Show that every square number is also a rectangle number. (5 marks) Instructions: Time allowed 2 hours. Attempt all sections. Name the property you use in each calculation and draw number lines with equal spacing.