1. 5
Rational Numbers: Positive and Negative Decimals

2. R.1 Fractions
5.5 Dividing Signed Decimal Numbers
Objectives
Divide a decimal by an integer.
Divide a number by a decimal.
Estimate the answer when dividing decimals.
Use the order of operations with decimals.

3. Divide a decimal by an integer.

4. Divide a decimal by an integer.
Find the quotient ÷ (–3).
Example
First consider ÷ 3.
Step 1
Write the decimal point in the quotient directly above the decimal point in the dividend.

5. Divide a decimal by an integer.
Example
(continued)
Step 2
Divide as if the numbers were whole numbers.
Check by multiplying the quotient times the divisor.

6. Divide a decimal by an integer.
Example
(continued)
Step 3
The quotient is –7.31 because the numbers have different signs.

7. Divide a decimal by an integer.
Example
Find the quotient ÷ 9.

8. Divide a decimal by an integer.
Example
Divide 1.5 by 8. Use multiplying to check the quotient.
Keep dividing until the remainder is 0, or until the digits in the quotient begin to repeat in a pattern. If you run out of digits in the dividend, write extra zeros on the right side of the dividend so you can continue dividing.

9. Divide a decimal by an integer.
Example
(continued)

10. Divide a decimal by an integer.
Example
Divide 4.7 by 3. Round to the nearest thousandth.
Write extra zeros in the dividend so that you can continue dividing.

11. Divide a decimal by an integer.
Example
(continued)
The digit 6 in the quotient is repeating and will continue to do so. The remainder will never be 0. The quotient is a repeating decimal that goes on forever. We may write the quotient in two ways. or

12. Divide a decimal by an integer.
Example
(continued)
Check the answer by multiplying by 3.

13. Divide a number by a decimal.

14. Divide a number by a decimal.
Example
Divide

15. Divide a number by a decimal.
Example
Divide –5 by –4.2. Round to the nearest hundredth.
First consider
Move the decimal point in the divisor one place to the right so that becomes the whole number 42. The decimal point in the dividend is also moved one place to the right.

16. Divide a number by a decimal.
Example
(continued)
Rounding the quotient to the nearest hundredth gives 1.19.
The quotient is positive because both the divisor and dividend have the same sign.

17. Estimate the answer when dividing by decimals.
Example
Suppose a student was asked to estimate the quotient ÷ 2.8 using front end rounding and then find the exact answer. Find the error in the student’s solution that follows.
The exact answer should be

18. Use the order of operations with decimals.

19. Use the order of operations with decimals.
Example
Simplify using the order of operations.

20. Use the order of operations with decimals.
Example
Simplify using the order of operations.

21. Use the order of operations with decimals.
Example
Simplify using the order of operations.