Can you remember your 5th grade math? Let's try a couple of simple problems.
1, You left the store with 10 cookies. By the time you got home you had eaten 5 cookies so you had 5 left. What is another way to say that?
a. You have half as many cookies.
b. You have 50% fewer cookies.
c. Neither is correct
d. Both are correct.
2. Your sister Suzy left the store with 10 cookies also. She only ate 1 of her cookies on the way home so she had 9 left. Which of the following is true?
a. Suzy are 1/5 as many cookies.
b. Suzy ate 20% as many cookies.
c. Suzy ate 5 times less cookies.
d. Suzy ate 5 time fewer cookies.
e. a and b are correct
f. All are correct
g. None are correct
3. Yesterday the temperature was 100 degrees Fahrenheit (37.8 Celsius). Today the temperature is 50 degrees Fahrenheit (10.0 Celsius). Which is correct?
a. It is half as warm today.
b. It is twice as cold today.
c. It is 26% (=10/37.8) as warm today
d. None of these.
4. You eat 5 popsicles. Suzy eats 1. Which is correct?
a. You ate 5 times as many as Suzy.
b. Suzy ate 5 times less than you.
c. Suzy ate 1/5 times as many as you.
d. You ate 1/5 times more than Suzy.
e. All are correct
f. a and c are correct
g. None are correct.
5. It was 100 degrees Fahrenheit yesterday. It is 110 degrees Fahrenheit today. Which of the following is correct:
a. It is 10'% hotter today.
b. It was 91% cooler yesterday
c. It is 14.1% (=43.4/37.8) warmer today
d. It was 87.1% (=37.8/43.4) cooler yesterday
e. All are correct
f. None are correct
The answers are:
1. a, b, d
2. a, b, e
4. a, c, f
Problems 3 & 5 are easy as neither Fahrenheit nor Celsius are absolute scales so comparing one temperature to another by percentages or multiplies just doesn't make sense whichever scale you use.
Problem 1 is a warm-up for 2 and 4. With both 2 and 4 the problem is with the comparison less. If I eat 1 and you eat 3, can you really say I've eaten 3 times less? The correct grammar is 1/3 as much. This is now a common grammatical/mathematical error In fact I received this just the other day from Sam's Club.