Q1.
Some expressions are given in following three columns. In each column, one or more terms are changed from the first expression. Go through the example (in the first column) and fill the blanks, doing as little computation as possible.
Answer
Change one term by a little and the value changes by exactly the same little amount.
Column 1 — starting from 53 + (–16) = 37
54 + (–16) = 38 (54 is 1 more than 53, so the value is 1 more than 37)
53 + (–15) = 38 (–15 is 1 more than –16, so the value is 1 more than 37)
53 + (–15) = 38 (–15 is 1 more than –16, so the value is 1 more than 37)
Column 2 — starting from 53 + (–16) = 37
52 + (–16) = 36 (52 is 1 less than 53, so the value is 1 less than 37)
53 + (–17) = 36 (–17 is 1 less than –16, so the value is 1 less than 37)
53 + (–17) = 36 (–17 is 1 less than –16, so the value is 1 less than 37)
Column 3 — starting from –87 + (–16)
| Expression | Reasoning | Value |
|---|---|---|
| –87 + (–16) | 87 + 16 = 103, both negative | –103 |
| –88 + (–15) | first term 1 less, second term 1 more → no change | –103 |
| –86 + (–18) | first term 1 more, second term 2 less → 1 less | –104 |
| –97 + (–26) | first term 10 less, second term 10 less → 20 less than –103 | –123 |
Why it happens: Careful with the negative terms. –15 is greater than –16 (it is one step to the right on the number line), so replacing –16 by –15 increases the value. Similarly –17 is one less than –16, so it decreases the value.
Check it yourself: –86 + (–18) = –(86 + 18) = –104 ✓ and –97 + (–26) = –(97 + 26) = –123 ✓