math alegbra 9th grade ny regents

Question

students were asked to write a formula for the length of a rectangle by using the formula for its perimeter, p=2l+2w.. three of their responses are shown below

1. l= 1/2(p) -w
2. 1/2(p-2w)
3. p-2w/2

which are correct?

Answer 1

We are given the formula P=2l+2w and need to isolate (solve for) l. To do so, we would start by "moving over" the 2w. The opposite of adding 2w is subtracting 2w, and so we would subtract 2w on both sides, to start our process of getting l alone, while keeping the equation balanced:

P = 2l + 2w

-2w -2w

P - 2w = 2l

The 2 next to the l indicates multiplication, so the opposite is division. We will divide by 2 on both sides of the equation in order to get l alone.

P - 2w = 2l

2 2

1/2P - w = l, which can be rewritten as:

l = 1/2P-w

This is exactly what Option 1 says, so option 1 is correct. Now let's explore the other answer choices.

For choice 2, which is 1/2(P-2w), if we distribute, we will get 1/2P-w, which is the exact same thing as Choice 1. Since Choice 1 is correct, Choice 2 must also be correct.

Another way to tell that Choice 2 is correct is to look back at the step in which we got

P - 2w

2

Multiplying by 1/2 is the same thing as dividing by 2. So since

P - 2w

2

is a correct step, 1/2(P-2w) must also be correct.

For choice 3, we would need to determine what was meant by the typed "p-2w/2"

If this was meant as P - 2w

2

then choice 3 is not correct, as it is not equivalent to our other correct answer choices.

However, if it was meant as P-2w

2

then Choice 3 is also correct, as this is one of the exact steps we saw when solving.

Issues of typing math equations as they appear on paper would not be so much of an issue once tutoring, as tutoring sessions would either be in person, or would utilize virtual tools so that the math appears exactly as it is intended.

Answer 2

1 is the correct answer because it is complete with the equal sign

Since

p = 2l + 2w

Stepwise

You can start by factoring out 2 on one side of the equation to give

p= 2(l + w)

Next divide both sides of the equation by 2 to give

p/2 = l + w

Then to solve for the length, l, subtract w from both sides of the equation to give

p/2 - w = 1/2(p) - w = l

Answer selection 1 is complete with the equal sign

Answer selection 2 is not set equal to anything, however once put in simplest terms, by distributing the 1/2 through the parentheses, is equal to selection 1.

I hope you find this useful, if you have any questions please send me a message