Here are six integer cards: (+1), (+7), (+18), (−5), (−2), (−9). You can pick any of these and make an expression using addition(s) and subtraction(s). Here is an expression: (+18) + (+1) − (+7) − (−2) which gives a value (+14). Now, pick cards and make an expression such that its value is closer to (−30).
One possible expression: (−9) + (−5) + (−2) − (+1) − (+7) + (+18) = −9 − 5 − 2 − 1 − 7 + 18 = −6 Another expression closer to −30: (−9) + (−5) − (+1) − (+7) + (+18) − (−2) = −9 − 5 − 1 − 7 + 18 + 2 = −2 To get closer to −30: Use all negative cards and subtract positive cards. (−9) + (−5) + (−2) − (+1) − (+7) − (+18) = −9 − 5 − 2 − 1 − 7 − 18 = −42 This is close to −30.
Explanation
The chapter provides integer cards for creating expressions. To get a value close to −30, we should maximize negative contributions and minimize positive contributions. Using all negative cards and subtracting positive cards gives the most negative result.
Solution Steps
Step 1: List available cards: +1, +7, +18, −5, −2, −9
Step 2: To get close to −30, use negative cards and subtract positive cards
Step 3: Try: (−9) + (−5) + (−2) − (+1) − (+7) − (+18)
Step 4: Calculate: −9 − 5 − 2 − 1 − 7 − 18 = −42
Step 5: This is close to −30