problem solving

Question

Solve the following problems.

1. Using the numerals 1, 0, 8, 4, 7, 5, and 2, form a four-digit number and a three-digit number that will give the biggest and the smallest estimated products.

2. Estimate the product of 49 501 and 21 by rounding off the first number to the nearest thousand and the second number to the nearest ten.

3. A carton contains 16 895 buttons. If Arnold bought 8 such cartons, around how many buttons did he buy?

4. Find the estimated product of the largest four-digit number and the smallest five-digit number.

Answer 1

1. The largest product will be either 8 thousand something multiplied by 7 hundred something or 7 thousand something multiplied by 8 hundred something. To determine which one and what the "somethings" are, try a few:
2. 8542•710 = 6,064,820
3. 8421•750 = 6,315,750
4. 7542•810 = 6,109,020
5. 7420•851 = 6,314,420
6. 7520•841 = 6,324,320
7. 7521•840 = 6,317,640
8. 8520•741 = 6,313,320

Looks to me like 7520 is the 4-digit number and 841 is the 3-digit number. But you may wish to try a few more.

The smallest product would be 1 thousand something multiplied by 2 hundred something or visa-versa. Trying a few:

1. 1045•278 = 290,510
2. 2045•178 = 364,010
3. 1078•245 = 264,110
4. 1058•247 = 261,326
5. 1057•248 = 262,136
6. 1047•258 = 270,126

Looks to me like 1058 is the 4-digit number and 247 is the 3-digit number. But you may wish to try a few more.

2. 50,000 • 20 = 1,000,000

3. 17,000 • 8 = 136,000 so a bit less than that.

4. Largest 4 digit number = 9,999 and smallest 5 digit number is 100,000 To estimate, use 10,000•100,000 = 10⁴•10⁵ = 10⁹ = 1,000,000,000