The Division Algorithm: Converting Decimal Division into Whole Number Division Using Fractions

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Examples, solutions, and worksheets to help Grade 6 students learn how to use estimation and place value to determine the placement of the decimal point in products and to determine that the size of the product is relative to each factor.

New York State Common Core Math Module 2, Grade 6, Lesson 14

Lesson 14 Student Outcomes • Students use the algorithm to divide multi-digit numbers with and without remainders. Students compare their answer to estimates to justify reasonable quotients.
• Students understand that when they “bring down” the next digit in the algorithm, they are distributing, recording, and shifting to the next place value.

Lesson 14 Concept Development

Example 1

Divide: 31,218 ÷ 132

First estimate the quotient. Then use the division algorithm to get an exact answer. Finally, compare the two to decide if the answer is reasonable.

Example 2

Divide: 974,835 ÷ 12.45

Example 3

A plane travels 3,625.26 miles in 6.9 hours. What is the plane’s unit rate?

Lesson 14 Exit Ticket

  1. Lisa purchased almonds for $3.50 per pound. She spent a total of $14.70. How many pounds of almonds did she purchase?
  2. Divide 125.01 ÷ 5.4. Then check your answer for reasonableness.

Problem Set
Convert decimal division expressions to fractional division expressions to create whole number divisors.

  1. 35.7 ÷ 0.07
  2. 486.12 ÷ 0.6
  3. 3.43 ÷ 0.035
  4. 5,418.54 ÷ 0.009
  5. 812.5 ÷ 1.25
  6. 17.343 ÷ 36.9

Estimate quotients. Convert decimal division expressions to fractional division expressions to create whole number divisors. Compute the quotients using the division algorithm. Check your work with a calculator and your estimates.
7. Norman purchased 3.5 lb. of his favorite mixture of dried fruits to use in a trail mix. The total cost was $16.87. How much does the fruit cost per pound?
8. Divide: 994.14 ÷ 18.9
9. Daryl spent $4.68 on each pound of trail mix. He spent a total of $14.04. How many pounds of trail mix did he purchase?
10. Mamie saved $161.25. This is 25% of the amount she needs to save. How much money does Mamie need to save?
11. Kareem purchased several packs of gum to place in gift baskets for $1.26 each. He spent a total of $8.82. How many packs of gum did he buy?
12. Jerod is making candles from beeswax. He has 132.72 ounces of beeswax. If each candle uses 8.4 ounces of beeswax, how many candles can he make? Will there be any wax left over?
13. There are 20.5 cups of batter in the bowl. This represents 0.4 of the entire amount of batter needed for a recipe. How many cups of batter are needed?
14. Divide: 159.12 ÷ 6.8
15. Divide: 167.67 ÷ 8.1

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