Dividing whole numbers and decimals

What it looks like when your child can do it

• — Splitting a 38 dollar pizza bill four ways, your child gets 9 with 2 left over, then keeps going past the decimal point to 9.50 dollars each.
• — Given 12 ÷ 1.5, your child moves both decimal points one place, divides 120 by 15, and gets 8.
• — After dividing, your child multiplies back without being reminded: 8 x 1.5 = 12.

How to teach it at the kitchen table

1. 01

   Name the parts and the four moves

   The number being split is the dividend, the number you divide by is the divisor, and the answer is the quotient. Long division repeats four moves in the same order: divide, multiply, subtract, bring down.

2. 02

   Keep going past the decimal point

   When dollars or pounds are left over, write a decimal point and zeros after the dividend and put a point in the answer straight above it. For 26 ÷ 8, the 2 left over becomes 20, then 40, and the answer is 3.25.

3. 03

   Turn a decimal divisor into a whole number

   To divide by 2.5, move its point one place right to make 25, and move the point in the dividend the same one place. Moving both points multiplies both numbers by 10, which does not change the answer.

4. 04

   Say about how big the answer should be

   Before dividing 12 by 1.5, ask whether the answer should be more or less than 12. Dividing by a number bigger than 1 makes it smaller, so 80 is ruled out. Dividing by a number less than 2 leaves more than half of 12, which is 6, so 0.8 is ruled out too.

5. 05

   Always multiply back

   Multiply the answer by the divisor, then add any remainder. You should land exactly on the number you started with. This one habit catches almost every mistake.

You will need: Lined paper turned sideways · A pencil · A handful of coins

Try it together

1. Try 1

   Seven nightly low temperatures add up to 266. Find the mean by dividing the total by 7.

   Listen for  38, because 7 x 38 = 266. Watch that your child divides by the number of nights, 7, and not by some other number on the page.

2. Try 2

   Four friends split a 38 dollar pizza bill evenly. How much does each one pay?

   Listen for  9.50 dollars. If your child stops at 9 remainder 2, ask what happens to the 2 leftover dollars. Money can be cut, so the division keeps going. Check: 9.50 x 4 = 38.

3. Try 3

   A 1.5 pound bag of coffee costs 12 dollars. What is the price for one pound?

   Listen for  8 dollars per pound. Both points move one place, so 12 ÷ 1.5 becomes 120 ÷ 15. Check: 8 x 1.5 = 12.

4. Try 4

   Divide 4.8 by 0.6.

   Listen for  8. Move both points one place: 48 ÷ 6 = 8. An answer of 0.8 means only the divisor's point moved.

5. Try 5

   Divide 700 by 16 and give a whole number with a remainder.

   Listen for  43 remainder 12. Check: 43 x 16 = 688, and 688 plus 12 is 700. A remainder of 16 or more means a digit in the answer was too small.

Watch for

• — Moving the point in the divisor but not in the dividend. The answer comes out 10 times too small, and multiplying back shows it at once.
• — Skipping a zero in the middle of the answer, like 12 instead of 102 for 2448 ÷ 24. Once the division starts, every digit of the dividend gets a digit above it.

If it is not there yet

• — Back up to dividing by one digit, like 84 ÷ 4 = 21, until the four moves feel automatic. Then add a second digit to the divisor.
• — If the trouble is finding each digit, spend time on multiplication facts. Every step of long division is a fact read backwards.
• — Divide money you can hold: split 10 dollars in coins four ways on the table and write down 2.50 dollars each.

A few days of this is normal, and it is time well spent. The lesson will still be there, and it will go faster.

Where this skill comes up

• Grade 6 Math Practice Workbook · Lesson 5

  The Unit Rate: How Much for One

  Needs it because finding the rate for one is a division, and the number you divide by is often a decimal like 2.5 pounds.

• Grade 6 Math Practice Workbook · Lesson 31

  One Number for the Middle

  Needs it because the mean is a division, and the total of a week of readings divided by how many has to come out right before the idea can land.