AStart by rounding the percent and number of passes attempted by Tom Brady. Then, write the rounded percent as a fraction.
BCompare the percent and the actual number of passes completed by Tom Brady with the rounded values from Part A.
CCompare the number of passes attempted by Tony Romo with the number of passes attempted by David Garrard.
Aabout 420
BGreater, see solution.
CTony Romo, see solution.
Practice makes perfect
We want to estimate the number of passes that Tom Brady completed. Let's start by taking a look at the given table.
NFL Quarterbacks
Player
Passes Attempted
Percent Completed
T. Brady
578
69
P. Manning
515
65
T. Romo
520
64
D. Garrard
325
64
According to the table, Tom Brady completed 69 % of 578 passes. To estimate the number of passes that he completed, we will start by rounding the percent and the number of passes he attempted.
69 %of 578 ≈ 70 %of 600We can find 70 % of 600 by multiplying 70 % by 600.
70 %of 600 = 70 %* 600
Before we perform the multiplication, we will write the rounded percent as a fraction and reduce it to its simplest form. We can write a percent as a fraction by writing the number part as a numerator over 100.
According to the given table, Tom Brady completed 69 % of the 578 passes. Let's write an expression for the actual number of passes he completed.
69 % * 578In Part A, we estimated the number of passes that Tom Brady completed by rounding both the percent and the number of passes attempted.
69 % ≈ 70 %
578 ≈ 600
Notice that both the number of passes attempted and the percent were rounded up. This means that our estimate is greater than the actual number of passes he completed.
69 % < 70 % and 578 < 600
⇓
69 % * 578 < 70 % * 600
We are asked to determine whether Tony Romo or David Garrard completed more passes. Let's start by taking a closer look at the given table.
NFL Quarterbacks
Player
Passes Attempted
Percent Completed
T. Brady
578
69
P. Manning
515
65
T. Romo
520
64
D. Garrard
325
64
We can see that Tony Romo completed 64 % of 520 attempted passes and that David Garrard completed 64 % of 325 attempted passes. Since 520 > 325, 64 % of 520 must be greater than 64 % of 325. This means that Tony Romo completed more passes.
