(a) 67 – 19 = 48 (b) 67 – 20 = 47 (c) 35 + 25 = 60 (d) 5 × 11 = 55 (e) 120 ÷ 3 = 40 Clearly, 40 < 47 < 48 < 55 < 60 Therefore, 120 ÷ 3 < 67 – 20 < 67 – 19 < 5 × 11 < 35 + 25 Thus, (e) < (b) < (a) < (d) < (c). Comparing Expressions NCERT In-Text Questions (Page 26) Use ‘>’ or ‘<’ or ‘=’ in each of the following expressions to compare them. Can you do it without complicated calculations? Explain your thinking in each case. (a) 245 + 289 246 + 285 (b) 273 – 145 272 – 144 (c) 364 + 587 363 + 589 (d) 124 + 245 129 + 245 (e) 213 – 77 214 – 76 Solution: Terms in Expressions NCERT In-Text Questions (Pages 28-29) Check if replacing subtraction by addition in this way does not change the value of the expression, by taking different examples. Solution: Let us take numbers 56 and 17. 56 – 17 = 39 Now, 56 + (-17) = 39 Hence, if we replace the subtraction sign with the addition sign in this way, the value of the expression does not change. (Answer may vary by taking the different numbers.) Can you explain why subtracting a number is the same as adding its inverse, using the Token Model of integers that we saw in the Class 6 textbook of mathematics? Solution: Do it yourself. In the following table, some expressions are given. Complete the table. Solution: Does changing the order in which the terms are added give different values? Solution: No. Since in the expression, each term is separated by a ‘+’ sign. So, changing the order in which the terms are added does not change the value. As, 4 + 15 +(-9) = 10 or (-9) + 15 + 4 = 10 Swapping and Grouping NCERT In-Text Questions (Pages 29-31) Will this also hold when there are terms having negative numbers as well? Take some more expressions and check. Solution: Yes, swapping the terms having negative numbers does not change the sum. As (-3) + (-2) = -5 or (-2) + (-3) = -5 (Answer may vary) Can you explain why this is happening using the Token Model of integers that we saw in the Class 6 textbook of mathematics? Solution: Yes Will this also hold when there are terms having negative numbers as well? Take some more expressions and check. Solution: Yes, while adding the terms having negative numbers, grouping them in any order gives the same result. As, Can you explain why this is happening using the Token Model of integers that we saw in the Class 6 textbook of mathematics? Solution: Yes Does adding the terms of an expression in any order give the same value? Take some more expressions and check. Consider expressions with more than 3 terms also. Solution: Can you explain why this is happening using the Token Model of integers that we saw in the Class 6 textbook of mathematics? Solution: Do it yourself. Manasa is adding a long list of numbers. It took her five minutes to add them all and she got the answer 11749. Then she realised that she had forgotten to include the fourth number 9055. Does she have to start all over again? Solution: No, there is no need to start all over again. She has to add fourth number that is 9055 to the sum she got (11749) to get the correct sum of the list of given numbers. That is 11749 + 9055 = 20804 More Expressions and Their Terms NCERT In-Text Questions (Pages 32-33) If the total number of friends goes up to 7 and the tip remains the same, how much will they have to pay? Write an expression for this situation and identify its terms. Solution: Since the total number of friends = 7 and the cost of each dosa = ₹ 23 Therefore, the total cost of 7 dosas = 7 × 23 As the tip remains the same, that is ₹ 5. So, the expression for describing the total cost is 7 × 23 + 5 = 7 × 23 + 5 = 161 + 5 = ₹ 166. The terms in the expression 7 × 23 + 5 are 7 × 23, 5. Think and discuss why she wrote this. The expression written as a sum of terms is- Solution: Do it yourself. For each of the cases below, write the expression and identify its terms: If the teacher had called out ‘4’, Ruby would write _________ If the teacher had called out ‘7’, Ruby would write _________ Solution: If the teacher had called our ‘4’, Ruby would write 8 × 4 + 1 Terms: 8 × 4, 1 If the teacher had called our ‘7’, Ruby would write 4 × 7 + 5 Terms: 4 × 7, 5 Write an expression like the above for your class size. Solution: Do it yourself. Identify the terms in the two expressions above. Solution: 432 = 4 × 100 + 1 × 20 + 1 × 10 + 2 × 1 Terms: 4 × 100, 1 × 20, 1 × 10, and 2 × 1 432 = 8 × 50 + 1 × 10 + 4 × 5 + 2 × 1 Terms: 8 × 50, 1 × 10, 4 × 5, and 2 × 1 Can you think of some more ways of giving ₹ 432 to someone? Solution: Do it yourself. Figure it Out (Pages 34-35)