For each division, write an equation that describes the number as a multiple plus a remainder.
For example: Divide 37 by 8. 4×8 = 32 is the nearest multiple of 8 less than 37, and the remainder is 5. Therefore the answer is:
37 = 4×8 + 5.
1. Divide 12 by 5.
2. Divide 20 by 7.
3. Divide 46 by 4.
4. Divide 28 by 13.
5. Divide 59 by 11.
Find the quotient and the remainder.
1. Divide 37 by 35.
2. Divide 89 by 22.
3. Divide 427 by 10.
4. Divide 427 by 100.
5. Divide 427 by 1000.
When you divide a number, the number of whole multiples is the quotient, and the number left over is the remainder. When nine is divided by two, there are four twos and one left over: the quotient is 4 and the remainder is 1.
For each problem, list the quotient and the remainder.
1. Divide 6 by 4.
2. Divide 11 by 2.
3. Divide 10 by 5.
4. Divide 11 by 10.
5. Divide 23 by 3.
Mixing and Rearranging Factors
What is the missing number?
1. 42 = 6 x 7 = ? x 14
2. 52 = 2 x 26 = 4 x ?
3. 84 = 7 x 12 = 21 x ?
4. 48 = 8 x 6 = 16 x ?
5. 72 = 8 x 9 = ? x 18
Multiplication Patterns
1. How can you tell if a number is a multiple of ten?
2. How can you tell if a number is a multiple of five?
3. Write down the multiples of 11 from 1 x 11 to 9 x 11.
4. The ones-digits for multiples of nine follow a pattern. What is the pattern?
5. A power of nine is a multiple of nine by itself. The first power of nine is 9. The second power of 9 is 9×9. The third power of nine is 9x9x9. The ones-digits of powers of nine form a pattern. What is the pattern?
Factors
Because 2 x 3 = 6, the number 6 is called a product. 6 is the product of 2 and 3. The numbers 2 and 3 are factors of 6.
1. What are the factors of 9?
2. Is 3 a factor of 21?
3. Is 6 a factor of 33?
4. What are all of the factors of 42?
5. Every counting number has at least two factors. What are these two factors?
(A counting number is a positive whole number, such as 1, 2, 3, 4, 5, 6, and so on.) For example, what are the two factors of 7?
Try to do the multiplication by using patterns.
1. 22 x 10 = ________
2. 3 x 22 = ________
3. 3 x 220 = _______
4. 10 x 14 = ________
5. 9 x 14 = _________
What number added to this number adds up to 100?
1. 49 + ______
2. 56 + ______
3. 41 + ______
4. 61 + ______
5. 88 + ______
What number added to this number adds up to 100?
1. 13 + ______
2. 77 + ______
3. 67 + ______
4. 43 + ______
5. 83 + ______