Basic Knowledge for Number Manipulation

1. Basic Starting Knowledge

2. When Manipulating Numbers…. • Whenever you are working with numbers remember to always align the numbers on the decimal point.

3. Adding and Subtracting • When adding two or more numbers, it may be called the sumor total

4. Multiplication and Estimation • Multiplication is the same as adding a number that number of times IE: 3 x 5 = 5+5+5 • When multiplying two numbers, the two numbers are called factors and the answer is called a product.

5. Placing the decimal point in the product… • When there are 2 decimal places in the first factor and 1 decimal place in the second factor, for a total of 3 places. You multiply and then count left 3 places from the right-hand side of the product and place the decimal point. EX: 45.67 x 4.5 = 205.515

6. Rounding • First you MUST know where all your plave values are…. • When you round, you find the digit in the place value you are rounding to, look to the right, if the number to the right is 5 or greater, add one to the place value and backfill with 0’s. If the number to the right is less than 5, then leave the place digit alone and fill all the digits to the right with 0’s. • Ex: Round 768.95 to the nearest ten…770.00

7. Rounding • Find the number, look next door, 5 or greater, add one more, 4 or less, let it rest.

8. Multiplication by 10,100 or 1,000 • To multiply by 10, 100 or 1,000, move the decimal point in the factor that is not a multiple of 10 one place to the right for each zero in the factor that is a multiple of 10. • Ex: 876 x 10 = 8,760

9. Division and Estimation • Division is the opposite of multiplication. • 80 divided by 5 = 5 80

10. Name the parts… Quotient – the answer to a division problem. Divisor – the number of groups into which the dividend is to be split. Dividend – any number that is to be divided

11. Time Factors that you must know: • 60 seconds = • 60 minutes = • 24 hours = • 365 days = • 12 months = • 4 weeks = • 52 weeks = • 1 minute • 1 hour • 1 day • 1 year • 1 year • 1 month • 1 year

12. Dividing by 10, 100 or 1,000 • To divide by 10, 100 or 1,000, move the decimal point in the dividend to the left as many places as there are zeros in the divisor…. • Ex: 5,700 divided by 10 = 570

13. Finding an average • Average – a single number used to represent a group of numbers. • Found by adding several numbers and dividing the sum by the number of items added….also called the mean.

14. Multiplication by 1¢ and 10¢ • To multiply by 1¢, or by $0.01, move the decimal point in the other factor two places to the left and attach a dollar sign. • Ex: 78 x 1¢ ($0.01) = $.78

15. Basic Starting Knowledge

16. When Manipulating Numbers…. • Whenever you are working with numbers remember to always align the numbers on the decimal point.

17. Adding and Subtracting • When adding two or more numbers, it may be called the sumor total

18. Multiplication and Estimation • Multiplication is the same as adding a number that number of times IE: 3 x 5 = 5+5+5 • When multiplying two numbers, the two numbers are called ________ and the answer is called a ___________.

19. Placing the decimal point in the product… • When there are 2 decimal places in the first factor and 1 decimal place in the second factor, for a total of 3 places. You multiply and then count left 3 places from the right-hand side of the product and place the decimal point. EX: 45.67 x 4.5 = 205.515

20. Rounding • First you MUST know where all your plave values are…. • When you round, you find the digit in the place value you are rounding to, look to the right, if the number to the right is 5 or greater, add one to the place value and backfill with 0’s. If the number to the right is less than 5, then leave the place digit alone and fill all the digits to the right with 0’s. • Ex: Round 768.95 to the nearest ten…770.00

21. Rounding • Find the number, look next door, 5 or greater, add one more, 4 or less, let it rest.

22. Multiplication by 10,100 or 1,000 • To multiply by 10, 100 or 1,000, move the decimal point in the factor that is not a multiple of 10 one place to the right for each zero in the factor that is a multiple of 10. • Ex: 876 x 10 = 8,760

23. Division and Estimation • Division is the opposite of multiplication. • 80 divided by 5 = 5 80

24. Name the parts… _________– the answer to a division problem. _________– the number of groups into which the dividend is to be split. __________– any number that is to be divided

25. Time Factors that you must know: • 60 seconds = _____________ • 60 minutes = _____________ • 24 hours = _____________ • 365 days = _____________ • 12 months = _____________ • 4 weeks = _____________ • 52 weeks = _____________

26. Dividing by 10, 100 or 1,000 • To divide by 10, 100 or 1,000, move the decimal point in the dividend to the left as many places as there are zeros in the divisor…. • Ex: 5,700 divided by 10 = 570

27. Finding an average • Average – a single number used to represent a group of numbers. • Found by adding several numbers and dividing the sum by the number of items added….also called the mean.

28. Multiplication by 1¢ and 10¢ • To multiply by 1¢, or by $0.01, move the decimal point in the other factor two places to the left and attach a dollar sign. • Ex: 78 x 1¢ ($0.01) = $.78