Dividing Decimals by Decimals

Unit 13 > Lesson 7 of 11

Problem 1:	Do you see a pattern in each table below? Use mental arithmetic to find each quotient, then mouse over the red text.
	Table 1 Table 2 Table 3
Explanation:	The patterns in the tables above were created by multiplying the divisor and the dividend by the same power of 10. In each pattern, the quotient remains the same. Thus, multiplying both the divisor and dividend by the same power of 10 maintains the equality of the expression.

Problem 2:xxx	Continue each pattern below by multiplying the divisor and the dividend by 10 until the divisor is a whole number. Then find each quotient.
	? ? ? ? ? ?
Answer:

Let's compare Problems 1 and 2 above. In both problems, the quotients remain the same even though the divisors and dividends are multiplied by powers of 10. However, the divisors in Problem 1 are whole numbers; whereas the divisors in Problem 2 are decimals. Let's look at some examples of dividing by a decimal divisor.

Example 1:
Analysis:	The divisor is 0.8. To make it a whole number, we will multiply both the dividend and the divisor by 10.
	Multiply the divisor by a power of 10 to make it a whole number. Multiply the dividend by the same power of 10. Place the decimal point in the quotient. Divide the dividend by the whole-number divisor to find the quotient.
Answer:	The quotient of 9.6 and 0.8 is 12.

Thus, the quotient of 9.6 and 0.8 and the quotient of 96 and 8 are both 12. Let's look at another example.

Example 2:
Analysis:	The divisor is 0.35. To make it a whole number, we will multiply both the dividend and the divisor by 100.
	Multiply the divisor by a power of 10 to make it a whole number. Multiply the dividend by the same power of 10. Place the decimal point in the quotient. Divide the dividend by the whole-number divisor to find the quotient.
Answer:	The quotient of 13.93 and 0.35 is 39.8

Note that in Example 1, the quotient is a whole number (12), and in Example 2, the quotient is a decimal (39.8).

Example 3:
Analysis:	The divisor is 0.009. To make it a whole number, we will multiply both the dividend and the divisor by 1,000.
	Multiply the divisor by a power of 10 to make it a whole number. Multiply the dividend by the same power of 10. Place the decimal point in the quotient. Divide the dividend by the whole-number divisor to find the quotient.
Answer:	The quotient of 5.4 and 0.009 is 600.

Example 4:
Analysis:	The divisor is 3.06. To make it a whole number, we will multiply both the dividend and the divisor by 100. After dividing, we will round the quotient to the nearest tenth.
	Multiply the divisor by a power of 10 to make it a whole number. Multiply the dividend by the same power of 10. Place the decimal point in the quotient. Divide the dividend by the whole-number divisor to find the quotient.
Answer:	Rounded to the nearest tenth, the quotient of 201.4 and 3.06 is 65.8.

Example 5:
Analysis:	The divisor is 5.3. To make it a whole number, we will multiply both the dividend and the divisor by 10. After dividing, we will round the quotient to the nearest cent (hundredth).
	Multiply the divisor by a power of 10 to make it a whole number. Multiply the dividend by the same power of 10. Place the decimal point in the quotient. Divide the dividend by the whole-number divisor to find the quotient.
Answer:	Rounded to the nearest cent, the quotient of $9 and 5.3 is $1.70.

Example 6:	Gold costs $802.70 per ounce. How much would of an ounce cost? Round your quotient to the nearest cent.
Analysis:
Divide:
Answer:	Rounded to the nearest cent, of an ounce of gold would cost $2,140.53

Exercises

1.	ANSWER BOX: RESULTS BOX:

2.	ANSWER BOX: RESULTS BOX:

3.	ANSWER BOX: $ RESULTS BOX:

4.	ANSWER BOX: RESULTS BOX:

5.	If 5.2 pounds of nails cost $16.96, then how much would 1 pound cost? Round your answer to the nearest cent. ANSWER BOX: $ RESULTS BOX: