How to divide with decimal quotient

Multiplying the dividend and the divisor by the same power of ten does not change the quotient, the way 6 ÷ 3 and 60 ÷ 30 both equal 2. That is the whole trick here: turn 0.8 into 8 and 250 into 2500, then use the long division your child already knows.

The worked example shows each step in color, down to 312.5. The multiple-choice part then mixes in rounding a decimal quotient to a named place: 225 ÷ 15.2 to the nearest thousandth gives 14.803.

The standard is 6.NS.B.3, fluent division of multi-digit decimals with the standard algorithm.

Before question c, make it a bet. "938 divided by 0.05, more than 938 or less?" Most kids say less. Then ask, "How many nickels are in a dollar?" Twenty, so the answer is about 20 times 938, and 18,760 stops looking strange.

The likely slip is in the scaling step. Kids multiply 0.05 by 10, get 0.5, and start dividing. Ask, "Is the divisor a whole number yet?"

A note for parents on question b: it asks for 157 ÷ 0.8 to the nearest tenth, which is 196.3, but no choice shows 196.3 and the answer page ticks the exact quotient 196.25. Accept 196.25 as the exact answer, then have your child round it.

With a jar of coins, ask how many dimes make $4.50, then check it as 4.50 ÷ 0.10 by counting real dimes. In the kitchen, ask how many quarter-cup scoops fill 3 cups: 3 ÷ 0.25 = 12, and a measuring cup will confirm it.

The Grapes of Math by Greg Tang is built on the same habit as this page: change a problem into an easier one without changing its answer. Pick one riddle and solve it together.

Praise the move, not the answer: "You made the divisor whole before starting." The next sheet compares decimal products with greater than, less than, or equal.