# CAHSEE Math 2.5 Number Sense

Number Sense: Drill Set 2, Problem 5. By what percent did his percentage grade increase from one test to the other?

 Algebra Percents CAHSEE Math Number Sense Language English Language Number Sense Percentages Ratios, Percentages, and Proportions Percent ChangePercents

### Transcript

00:24

By what percent did his percentage grade increase from one test to the other?

00:30

And will it be enough to get him into a shiny new tank that will be the envy of all his friends?

00:34

00:44

First of all... decreased? After taking Shmoop?

00:47

Get real. Just cross out answer D angrily and let's get serious.

00:51

OK, this question is really a 2-parter.

00:53

First, we have to convert his second score to a percentage...

00:57

...and then we have to figure out the % INCREASE from the first test to the second.

01:02

In the first test, Kyle got an 80%.

01:04

The question gives us the percentage, more or less, because it's just out of 100.

01:09

So now we have to convert the second test to a percentage score...

01:13

and we get that a familiar-looking percentage equation.

01:17

That is, 45 is to 50 as whatever-percent is to 100.

01:22

And a quick way to solve this one is to just multiply top and bottom by 2...

01:26

...50 times 2 is 100 and 45 times 2 is 90

01:30

so the answer is 90 percent. But now comes the tricky part.

01:33

It's asking for the percent IMPROVEMENT.

01:36

And there's a total curveball here that they give us in answer A, which is totally wrong.

01:43

Yes, Kyle improved from 80 to 90 percent on the 2 exams.

01:47

But his PERCENTAGE improvement was meaningfully bigger.

01:51

If he'd gone from 100 to 110 percent ...if that were even possible...

01:55

then he'd have improved 10 percent.

01:57

But here he is growing from a smaller base in 80 percent.

02:00

So hopefully it makes sense that if his percentage goes up the same amount -- 10 percent here...

02:06

...then the RATE of growth will be higher.

02:08

And here is one of the golden formulas of our math we should tattoo onto our leg:

02:15

NEW MINUS OLD OVER OLD. Or NMOOO, if we ever get stuck.

02:20

The formula gives us the RATE OF GROWTH for these kinds of problems and here the "new"

02:25

score is 90; the old score is 80. So new minus old is 90 minus 80... or 10 in

02:31

the numerator... and we put it over old, or 80, which goes in the denominator.

02:35

So we have 10 over 80, or 1 over 8 or, converting to a percentage...

02:40

...we divide 8 into 1... ...and we get 12.5%.

02:44