## Monday, May 21, 2012

### Divide Evenly: Tricks of the Trade

In math, divide evenly means when you divide two numbers, there is no remainder or there is a remainder of zero.

That leads us to the term Factors. Factors are all the integers that divide evenly into another integer (whole number). They are "what you get" when you divide. The number 1 always works as a factor.

In Excel Math, we teach students how to multiply and divide, how to find the greatest common factor between two or more numbers, and how to recognize multiples. For students who need some extra confidence building in division, here are a few ways to help them determine if a number can be divided evenly by another number.

As we said, the number 1 always works as a factor. It will divide evenly into any number.

2 will divide evenly into all even numbers. It will not divide evenly into odd numbers. Two will divide evenly into 2456, which is an even number:
2456 ÷ 2 = 1228

3 will divide evenly into all numbers whose digits add up to a number that's divisible by 3. Three will divide evenly into 2436 since its digits add up to 15 and 15 is divisible by 3:
2436 ÷ 3 = 812 5 will divide evenly into all numbers ending in 0 or 5. Five will divide evenly into 820 since it ends in 0:
820 ÷ 5 = 144

Five will also divide evenly into 375 since it ends in 5:
375 ÷ 5 = 75

9 will divide evenly into all numbers whose digits add up to a number that's divisible by 9. Nine will divide evenly into 2736 since its digits add up to 18 and 18 is divisible by 9:
2736 ÷ 9 = 304

10 will divide evenly into all numbers ending in 0. Ten will divide evenly into 820 since it ends in 0:
820 ÷ 10 = 82

Give each student 20 items that can be used for counting (buttons, tokens, paper clips, etc.). Let the students work in pairs. Write this problem on the board:
20 ÷ 10 =
Ask your students if 10 will divide evenly into 20. (yes) Ask how they can tell. (20 ends in 0 and 10 will divide evenly into numbers ending in 0)

Have the students divide their 20 counters into ten groups. Ask them how many counters are in each group? (2)
Let a child write the answer on the board:
20 ÷ 10 = 2

Now have the students divide their 20 counters into two groups. Ask them how many counters are in each group? (10)

Write this problem on the board:
20 ÷ 2 =
Ask your students if 2 will divide evenly into 20. (yes) Ask how they can tell. (20 ends in 0, which is an even number, and 2 will divide evenly into even numbers)

Let a child write the answer on the board:
20 ÷ 2 = 10
Continue in this way with multiples of 3, 5, 9, etc.