John's Responses in WyzAnt Answers

This sort of question is very much in keeping with the so-called "Singapore Math" curriculum. Students are taught to understand numbers backwards and forwards, really understand place value, what it means when you "borrow" when solving a subtraction problem, how to multiply multi-digit numbers by "breaking them apart" into their component (place value) parts. 

a. For example, how many hundreds are in the number 1,234? (Hint: It's not 2)

b. How many tens are in the number 1,234? (Hint: It's not 3)

c. In the problem 374 -289, what are you borrowing from the 7 in order to subtract the numbers in the ones place (originally, the 9 from the 4, which students will initially say "you can't do") (Hint: You're not borrowing "1")

a. 12

b. 123

c. 10

The simplest way to find a common denominator is to "skip count" (count by multiples) by each of the numbers in question. For example, 9, 18, 27, 36, 45, 54, 63, 72 . . . and 12, 24, 36, 48, 60, 72, 84, . . . . Any numbers on both lists are "common denominators" (36 and 72); the first such number on both lists is the Lowest Common Denominator (LCD). 

A more complicated way involves using the prime factorizations of the numbers in question. The p. f. for 9 = 3 x 3; the p. f. for 12 = 2 x 2 x 3. Next, line the two p.f.'s up like this, showing where any factors from the p.f.'s overlap:

2 x 2 x 3

           3 x 3

Now, write the factors out in one line, using all the factors from the 2 lines, but where they overlap, write only one of the 2 overlapping factors:

2 x 2 x 3 x 3 = 36 (the LCD)

When you can't remember even a basic equation like the one listed below, make up your own much simpler problem and see if you can deduce the underlying relationship between the simpler numbers in order to apply your understanding to the actual problem.

For example, "2 is what percent of 4?" Well, 2 is half of 4 (2 out of 4 is equivalent to 1 out of 2), so 2 is 50% of 4. If you "see" that 2/4 = 1/2 = 0.50 = 50% then you understand the underlying relationship between the 2 and 4 in this particular problem and can now extrapolate to the actual problem.

Now, how must the 72 be related to the 480 in the original problem? As a fraction(72/480). Divide and conquer!

72 divided by 480 = 0.15 = 15/100 = 15%.