Mark wants to round to the nearest hundred to estimate the sum of 271 and 582. He wrote 270 + 580 = 850.

Part A
What mistake did Mark make?
A.
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Mark should have rounded 271 to 250 and rounded 582 to 550: 250 + 550 = 800.
B.
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Mark should have rounded 271 to 250 and rounded 582 to 600: 250 + 600 = 850.
C.
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Mark should have rounded 271 to 300 and rounded 582 to 500: 300 + 500 = 800.
D.
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Mark should have rounded 271 to 300 and rounded 582 to 600: 300 + 600 = 900.
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Part B
What is the sum of 271 and 582 rounded to the nearest hundred?
A.300
B.850
C.900
D.1,000

Step-by-step explanation:

Part A:

Mark did not round to the nearest hundreds, he rounded to the nearest tens.

Option A (Incorrect):

271 and 582 are normally not rounded down, unless we are using limits coming from the left and a unique equation.

Option B (Incorrect):

271 as the same problem as option A, but 582 rounding to 600 is correct. It doesn't make sense to round both numbers differently, unless stated.

Option C (Incorrect):

271 rounding to 300 is correct, but 582 is not normally rounded down to 500 unless we are using limits coming from the left and a unique equation. Unless stated, don't round both numbers differently.

Option D (Correct):

271 rounded to 300 and 582 rounded to 600 looks correct for rounding to the hundreds.

Part B:

There are two ways to solve this question:

One way:

271 + 582 = 853

Round 853 to the nearest hundred for 900

(Note: Round 853 to the nearest tens for 850.)

Second way:

271 + 582

Round Numbers:

300 + 600

= 900

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explanation

the graph has a slope of 1/3 because each time you move up 1, you go to the right 3. so, slope = rise/run = 1/3. we can cross choice a off the list since we want a slope of 3, rather than 1/3.

the first table shown has a slope of -3. this is because the rise is -6 and the run is 2, so slope = rise/run = -6/2 = -3. note how x increases by 2 each time (run) and y drops by 6 each time (rise). choice b can be eliminated.

the second table has a slope of 3. each time x goes up by 1, the y values increase by 3. slope = rise/run = 3/1 = 3. alternatively you can use the slope formula to prove that the slope is 3 here. use any two rows of values to generate the two points. choice c is one of the answers

the third table also has a slope of 3. let's use the slope formula to prove as such. i'm going to use the first two rows of the table. so i'll use the two points (2,1) and (5,10)

m = slope

m = (y2-y1)/(x2-x1)

m = (10-1)/(5-2)

m = 9/3

m = 3 so we get a slope of 3

choice d is the other answer