Lesson 3: Division Review

Day 2

Activity 3: Long Division with Decimal Numbers

Materials: 3-hole drilled card stock (kit), colored pencils, construction paper (kit), glue or glue stick, Interactive Notebook, marker, scissors
In the last activity, all the problems involved whole numbers, but what if you need to divide numbers that have decimals? You can probably guess that the standard algorithm for dividing whole numbers works just as well for decimal numbers, with a few extra steps. Watch the following video to see how to divide with decimal numbers.
Web Link
In the video, you learned that before you can use the division algorithm, a decimal in the divisor needs to be moved to make a whole number. While it is possible to divide with a decimal divisor, it's pretty tricky, so a better option is to create an equivalent problem in which the divisor is a whole number.

Remember that in math, equivalent means equal, and problems are equivalent if the same changes are applied to every part of the problem. Let's see how this works with the following example:
What is 1.75 divided by 0.25?
The dividend is 1.75 and the divisor is 0.25. To make 0.25 a whole number, you move the decimal two places, and when you move a decimal point, you are really multiplying by a power of ten. Moving the decimal two times to make 0.25 a whole number represents multiplying by two powers of ten, (10 × 10), or 100. To keep the problem equivalent, you must multiply the dividend by this same powers of ten factor. When 1.75 is multiplied by 100, the result is 175, which is the same as moving the decimal two times to the right.
By keeping the new problem equivalent to the original problem, you ensure that the final quotient will be correct.

Next you'll create a foldable to help you remember the division algorithm. You may refer to the illustrations in Lesson 1 if you need a reminder about how to set up the construction paper. Follow these steps:
  1. Cut out the boxes from the "Steps for Division Algorithm" sheet.
  2. Put the steps in the correct order, and match the correct example problem image with each one.
  3. Once you've put the steps and matching examples in order, show them to a parent, and explain each step in your own words.
  4. Shade each step and its corresponding example in the same color, using a different colored pencil for each step.
  5. Cut about 2 inches off of the long end of a piece of construction paper so the page is about 9" × 10".
  6. Fold the sheet of construction paper in half longways. (Refer to the image guide in Lesson 1 as needed.)
  7. Cut the top half into 4 equal sections to create the flaps.
  8. Use a marker to write "Step 1", "Step 2", "Step 3", and "Step 4" onto the front of the flaps.
  9. Lift the flaps and glue the steps and the examples in the correct order. The step should go on the back of the flap and the example should go below the step.
When you are finished, glue the back of the foldable to a piece of card stock paper, and store it in your Interactive Notebook for future reference.
Student Activity Page
Your child will learn how the standard algorithm can be applied to decimal division with a few extra steps added. After watching a learning video, he will create a decimal division foldable for his Interactive Notebook that is similar to the foldables made for the other operations. The steps and matching images should be in the following order:
  1. Draw the long division symbol. Put the dividend under the symbol, and put the divisor outside the symbol. (Pairs with the image of the division sentence being converted into long-division format.)
  2. Move the decimal in the divisor to make it a whole number (if necessary). Move the decimal in the dividend the same number of places. (Pairs with the image of the arrows showing the movement of the two decimal points.)
  3. Perform the long division as usual. (Pairs with the image showing the long division problem being solved.)
  4. Move the decimal point straight up from the dividend to the quotient. (Pairs with the image of the upward arrow.)
If your child gets confused about why it's okay to move a decimal in the divisor as long as he also moves the decimal in the dividend, you can prove to him that it works using a calculator. Enter the original division problem (such as 16.8 ÷ 1.2) and write down the answer shown on the calculator. Then ask your child to move the decimal points in the original problem to create an equivalent problem. Enter this new problem into the calculator (such as 168 ÷ 12). Show that the answer to the equivalent problem is the same as the answer to the original problem.

Activity 4: Practicing Decimal Division

The algorithm for long division works for decimal numbers quite well, doesn't it? You just have to take care to make sure you are placing decimal points correctly as you work. There are many examples of real-world problems that require this type of math. Consider this problem:
Ian purchased a crate of watermelons. The crate of watermelons weighed 54 pounds in all, and each watermelon weighed 4.5 pounds. How many watermelons came in the crate?

To solve, use the steps for long division.
Did you notice that you had to add a zero to the dividend when you moved the decimal? Any time moving a decimal creates an "empty" spot, be sure to place a zero as a place value holder. Then solve as normal.

Complete the "Long Division with Decimals" activity pages. You can refer to your foldable as you work to ensure you are following the correct steps to solve each problem.
Your child will practice the steps of long division for decimal problems. Encourage him to use the foldable he created as a reminder of the correct steps to use for the division algorithm.

Answer Key:

  1. 81.27 ÷ 9 = 9.03
  2. 6288.8 ÷ 2.8 = 2,246
  3. 842.1 ÷ 2.1 = 401
  4. 59.94 ÷ 0.74 = 81
  5. 256 ÷ 0.8 = 320
  6. 42.8 ÷ 0.04 = 1,070
  7. Kelli bought 12 bags of cat food for $77.40. How much did each bag cost? ($6.45) $77.40 ÷ 12 = $6.45
  8. A box of screws weighs 55.5 ounces. If each screw weighs 0.3 ounces, how many screws are in the box? (185 screws) 55.5 ÷ 0.3 = 555 ÷ 3 = 185