Dividing Decimals by Whole Numbers

Example 1: The Lachance family drove cross country on a 4,615.8 mile trip in 49 days. Find the average number of miles driven per day.

Analysis: We need to divide 4,615.8 by 49 to solve this problem.

Step 1: Estimate the quotient using compatible numbers.

Step 2: Use long division to find the quotient.

Decide where to place the first digit of the quotient.

Round to estimate the quotient digit.

Multiply, subtract and compare.

Bring down the next digit from the dividend. Continue dividing.

Bring down the 5.   4 x 49 = 196   Bring down the 8.   2 x 49 = 98

Place the decimal point in the quotient.

Check your answer: Multiply the divisor by the quotient to see if you get the dividend.

Step 3: Compare your estimate with your quotient to verify that your answer makes sense

Our quotient of 94.2 makes sense since it is close to our estimate of 90.

Answer: The average number of miles driven per day was 94.2.

Estimating the quotient lets us verify that the placement of the decimal point is correct, and that we have a reasonable answer. For example, if our estimate was 90 and our quotient was 9.42, then we would know that we made a division error. Let's look at some more examples of dividing a decimal by a whole number.

Example 2: 

Analysis: The divisor 8 is larger than the dividend 6.6. Therefore, we will need to place a zero in the quotient.

Step 1: Estimate the quotient using compatible numbers.

Step 2: Use long division to find the quotient.

Decide where to place the first digit of the quotient.

Round to estimate the next quotient digit.

Multiply, subtract and compare.

Bring down the next digit from the dividend. Continue dividing.

Place the decimal point in the quotient.

Check your answer: Multiply the divisor by the quotient to see if you get the dividend.

Step 3: Compare your estimate with your quotient to verify that your answer makes sense.

Our quotient of 0.825 makes sense since it is close to our estimate of 0.7.

Answer: The quotient of 6.6 and 8 is 0.825

Example 3: 

Analysis: The divisor 36 is larger than the dividend 18.288. Therefore, we will need to place a zero in the quotient.

Step 1: Estimate the quotient using compatible numbers.

Step 2: Use long division to find the quotient.

Decide where to place the first digit of the quotient.

Round to estimate the next quotient digit.

Multiply, subtract and compare.

Bring down the next digit from the dividend. Continue dividing.

Write 0 as our quotient digit.   Bring down the second 8.   8 x 36 = 288.

Place the decimal point in the quotient.

Check your answer: Multiply the divisor by the quotient to see if you get the dividend.

Step 3: Compare your estimate with your quotient to verify that your answer makes sense.

Our quotient of 0.508 makes sense since it is close to our estimate of 0.5.

Answer: The quotient of 18.288 and 36 is 0.508.

In Examples 1 to 3, we used long division and showed each step. When dividing a decimal by a whole number, we use the following procedure:

1. Estimate the quotient.
2. Perform the division.
   
   1. Remember to place a zero in the quotient when the divisor is larger than the dividend.
   2. Place the decimal point in your quotient.
   3. Check your answer: Multiply the divisor by the quotient to see if you get the dividend.
3. Compare your estimate with your quotient to verify that the answer makes sense.

Example 4: 

Analysis: 28 is the divisor and 355.6 is the dividend.

Step 1: Estimate the quotient using compatible numbers.

Step 2: Use long division to find the quotient.

Decide where to place the first digit of the quotient.

Round to estimate the quotient digit.

Multiply, subtract and compare.

Bring down the next digit from the dividend. Continue dividing.

Bring down the 5.   2 x 28 = 56   Bring down the 6.   7 x 28 = 196

Place the decimal point in the quotient.

Check your answer: Multiply the divisor by the quotient to see if you get the dividend.

Step 3: Compare your estimate with your quotient to verify that your answer makes sense.

Our quotient of 12.7 makes sense since it is close to our estimate of 12.

Answer: The quotient of 355.6 and 28 is 12.7.

Example 5: 

Analysis: 6 is the divisor and 6.036 is the dividend.

Step 1: Estimate the quotient using compatible numbers.

Step 2: Use long division to find the quotient.

Decide where to place the first digit of the quotient.

Multiply, subtract and compare.

Bring down the next digit from the dividend. Continue dividing.

Bring down the 0. 0 does not divide 6 Bring down the 3. 3 does not divide 6 Bring down the 6. 6 x 6 = 36

Place the decimal point in the quotient.

Check your answer: Multiply the divisor by the quotient to see if you get the dividend.

Step 3: Compare your estimate with your quotient to verify that your answer makes sense.

Our quotient of 1.006 makes sense since it is close to our estimate of 1.

Answer: The quotient of 6.036 and 6 is 1.006.

Example 6: Look for a pattern. Then find each quotient using mental arithmetic.

Answer:

Example 7: Sandy has 5.8 kg of coffee. If she puts the coffee into 8 bags, how much coffee will each bag contain?

Answer: Each bag will contain 0.725 kg of coffee.

Summary: When dividing a decimal by a whole number, we use the following procedure:

1. Estimate the quotient.
2. Perform the division.
   
   1. Remember to place a zero in the quotient when the divisor is larger than the dividend.
   2. Place the decimal point in your quotient.
   3. Check your answer: Multiply the divisor by the quotient to see if you get the dividend.
3. Compare your estimate with your quotient to verify that the answer makes sense.

Exercises

Directions: Read each question below. You may use paper and pencil to help you divide. Click once in an ANSWER BOX and type in your answer; then click ENTER. After you click ENTER, a message will appear in the RESULTS BOX to indicate whether your answer is correct or incorrect. To start over, click CLEAR.

1.	ANSWER BOX:    RESULTS BOX:

2.	ANSWER BOX:    RESULTS BOX:

3.	ANSWER BOX:    RESULTS BOX:

4.	ANSWER BOX: $   RESULTS BOX:

5.	What is the average speed in miles per hour if a plane flew 1,856.4 miles in 5 hours? ANSWER BOX:  mph    RESULTS BOX: