When students are first introduced to the division of decimals numbers they can think of partitioning into equal groups in a similar way to how they have done when dividing whole numbers. In doing this they will apply their understanding of decimal place value and the important role of the decimal point as an extension of whole number place value.
Before moving on to algorithmic methods of division, students should model division into equal groups in a “hands-on” manner. Base-10 blocks can be used to do this – use a cube or a flat to represent one whole unit and the rods and units to represent the smaller units. Cuisenaire rods can be similarly re-purposed with an orange (ten) representing one whole unit and a white (one) representing one tenth.
The division examples below use a place value chart with counters to illustrate the process.
Students will already have experienced division with whole number dividends and divisors, and this will most likely have included examples, like the one above, where the quotient would have a remainder. Using decimals instead of a whole number remainder is an important progression. Highlight this difference to your children.
Regrouping different place value units is often a key step in performing multi-digit arithmetic operations although its importance can sometimes lead students to forget that it is not always required as the example above shows.
Encourage your children to estimate the answer when dividing with decimals as a check for the reasonableness of their calculation. Rounding the decimal and doing a quick mental check is one way of doing this.
Discuss with your children any patterns in the location of the decimal point and the number of zeros. Do not encourage the thought that the decimal point is moving. Instead stress that the values of the digits are decreasing by the power of 10 and, it is the digits, if anything that are moving. There is more on multiplying and dividing decimals by powers off 10 here.
|345 ÷ 101 = 34.5||13,300 ÷ 104 = 1.33|
|345 ÷ 102 = 3.45||13,300 ÷ 105 = 0.133|
|345 ÷ 103 = 0.345||20,000 ÷ 104 = 2|
|13,300 ÷ 103 = 13.3||20,000 ÷ 106 = 0.02|
As with multiplying decimals, division of decimals requires care in the placement of the decimal point.
If there is a remainder, keep adding zeros to the right of the dividend and continue to divide.