Question

1. a rectangular pasture measures 618 feet long and 32 feet wide. about how much is the area of the pasture?
2. there are 126 fifth - graders at lucille elementary. for a jump - a - thon, 68 students jumped for 50 minutes, 17 students jumped for 30 minutes, and the rest of the fifth - graders jumped for 40 minutes. how many minutes did the fifth - graders jump?
3. which sum shows how to calculate 648×26 using partial products?

a. 12,000
800
160
3,600
240
+ 48
16,848
b. 12
8
16
36
24
+ 48
144
c. 600
40
8
20
+ 6
674

1. which product is correct? choose all that apply.

a. 296
× 3
678
b. 548
× 8
4,384
c. 416
× 7
28,742
d. 473
× 5
2,365

Explanation:

Step1: Calculate the area of the rectangular pasture

The area formula for a rectangle is $A = l\times w$, where $l = 618$ and $w = 32$. So $A=618\times32=(600 + 18)\times32=600\times32+18\times32=19200+576 = 19776$ square - feet.

Step2: Calculate the number of students who jumped for 40 minutes

There are 126 fifth - graders. 68 students jumped for 50 minutes and 17 students jumped for 30 minutes. The number of students who jumped for 40 minutes is $126-(68 + 17)=126 - 85 = 41$ students.

Step3: Calculate the total number of minutes fifth - graders jumped

The total minutes is $68\times50+17\times30 + 41\times40=3400+510+1640=5550$ minutes.

Step4: Calculate $648\times26$ using partial products

$648\times26=(600 + 40+8)\times(20 + 6)=600\times20+600\times6+40\times20+40\times6+8\times20+8\times6=12000+3600+800+240+160+48 = 16848$. Option A is correct.

Step5: Check the products in question 9

• For A: $296\times3=(300 - 4)\times3=900-12 = 888

eq678$.

• For B: $548\times8=(500 + 40+8)\times8=4000+320+64 = 4384$. This is correct.
• For C: $416\times7=(400 + 10+6)\times7=2800+70+42 = 2912

eq28742$.

• For D: $473\times5=(400 + 70+3)\times5=2000+350+15 = 2365$. This is correct.

Answer:

1. The area of the pasture is 19776 square - feet.
2. The fifth - graders jumped for 5550 minutes.
3. A. 12000, 800, 160, 3600, 240, + 48, 16848
4. B. 548×8 = 4384, D. 473×5 = 2365