Dividing decimals in fifth grade involves understanding the division algorithm. By the time students are in fifth grade, they understand division means dividing into equal parts. For instance, by fifth grade students should be proficient at determining how many fives are in 15 or how many 25s are in 225. Estimation skills and number sense also play an important role in dividing decimals. These skills give students the confidence to determine a valid magnitude estimate before proceeding with the division equation.
Place the dividend, the number being divided into equal parts, inside the division bracket. Write the divisor, the number of sections into which the dividend is being divided, outside the division bracket. In the example, 225 / 25, 225 is the dividend, and 25 is the divisor.
Make a magnitude estimate. A magnitude estimate is a guess of the value of the answer to the division equation, or quotient. It is a prediction of whether the answer will have a place value in 100s, 10s, ones, tenths or hundredths, according to Everyday Math On-line. For instance, to make a magnitude estimate for the division problem 59.4 /3, round the decimal number to a whole number, 59 / 3. If you round 59 to a multiple of three, the magnitude estimate shows you the answer will be in the tens place, 60 / 3 = 20. The quotient will be close to 20, based on your magnitude estimate.
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Ignore the decimal points in both the dividend and the divisor. Divide the two numbers using partial-quotients division. Think how many of the divisors are in the dividend. For instance, 594 / 3, how many threes are in 594. There are at least 100, write 100 in a column to the side of the division bracket. Multiply 3 x 100 = 300. Subtract this number from the dividend, 594 - 300 = 294. How many threes are in 294 is the next part of the equation. There are at least 90, so place 90 in the column under the 100. Multiply 3 x 90 = 270. Subtract this number from 294, 294-270 = 24. Next, figure out how many threes are in 24, 3 x 8 = 24. Write the eight in the column with the 100 and 90. Add all of the partial-quotients, 100 + 90 + 8 = 198.
Place the decimal point in the answer to make your magnitude estimate correct. The magnitude estimate was in the tens place. The estimate was 20. Placing the decimal point between the nine and the eight makes the answer in the tens place and very close to 20. In the example, 19.8 is the quotient to the problem. Verify your answer with your magnitude estimate and your estimate.
Using the traditional long division algorithm along with the magnitude estimate will give the same answer.