Q1.
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
Answer
Compare the two sides part by part, the way we compared Raja’s and Joy’s marbles.
(a) 245 + 289 > 246 + 285
245 is 1 less than 246, but 289 is 4 more than 285. Net gain = 4 – 1 = 3, so the left side is 3 more.
(Check: 534 and 531.)
(b) 273 – 145 = 272 – 144
273 is 1 more than 272, but we also take away 1 more (145 instead of 144). The extra and the loss cancel.
(Check: 128 and 128.)
(c) 364 + 587 < 363 + 589
364 is 1 more than 363, but 587 is 2 less than 589. Net = 1 – 2 = –1, so the left side is 1 less.
(Check: 951 and 952.)
(d) 124 + 245 < 129 + 245
The second number is the same on both sides; 124 < 129, so the left sum is 5 less.
(Check: 369 and 374.)
(e) 213 – 77 < 214 – 76
The right side starts 1 higher and takes away 1 less, so it is 2 more.
(Check: 136 and 138.)
245 is 1 less than 246, but 289 is 4 more than 285. Net gain = 4 – 1 = 3, so the left side is 3 more.
(Check: 534 and 531.)
(b) 273 – 145 = 272 – 144
273 is 1 more than 272, but we also take away 1 more (145 instead of 144). The extra and the loss cancel.
(Check: 128 and 128.)
(c) 364 + 587 < 363 + 589
364 is 1 more than 363, but 587 is 2 less than 589. Net = 1 – 2 = –1, so the left side is 1 less.
(Check: 951 and 952.)
(d) 124 + 245 < 129 + 245
The second number is the same on both sides; 124 < 129, so the left sum is 5 less.
(Check: 369 and 374.)
(e) 213 – 77 < 214 – 76
The right side starts 1 higher and takes away 1 less, so it is 2 more.
(Check: 136 and 138.)
Why it happens: Think of each expression as a story. In (b) Raja starts with 1 rupee more than Joy but also spends 1 rupee more — so both end with the same amount. Comparing the changes is far quicker than adding four-digit numbers.
Tip: When comparing a + b with c + d, ask “how much did the first number go up?” and “how much did the second number go down?” The bigger movement decides the sign.