Working with decimals

Hope your Halloween weekend was great! Yesterday in class, we summed up 6.1 (introduction to decimals) to review for this section first.

As a continuation of 6.1, we covered that a decimal, such as 4 tenths (.4), can be converted from tenths to hundredths by just adding a zero after the 4. So, 4 tenths is the same as 40 hundredths because .4=.40. Then, another zero can be added to convert the decimal to thousandths, and so on.

Here is a visual of this information:


As you can see in the above picture, 6 tenths has the same amount of the unit shaded as 60 hundredths.

After this quick lesson on 6.1, we moved onto 6.2, which involved operations with decimals. For this, we used only one method to visually see how decimals can be added, subtracted, multiplied, and divided. It was really easy to understand. Each person took a scrap piece of paper and split it into 3 sections: tenths, hundredths, and thousandths. We then were given beans. For this, we had to create the problem gived by placing beans in each section to represent the number of tenths, hundredths, and thousandths. For addition, we just had to combine the beans under each section.

So, if the problem were 0.123 + 0.456, we would combine the beans in the thousandths place (9 total), then the hundredths place (7 total), and finally the tenths place (5 total).  The answer would then be 0.579.

If the sum of one section is 10 or more, however, then we would have to carry over into the next highest section. So, if the problem were .123 + .457, the thousandths section would add up to be 10. This would carry 1 bean to the hundredths place. Then there would be 5 beans in the tenths place and 8 beans in the hundredths place. The answer is then 0.58.

The same method would be used for subtraction, except we would take the second amount of beans away from the first instead of combining the two. So, if the problem were 0.782 – 0.213, you would originally put 7 beans in the tenths place, 8 beans in the hundredths place, and then 2 in the thousandths place. Next, you would take away 3 beans from the thousandths place, 1 from the hundredths place, and lastly 2 from the tenths place. If you cannot subtract one place, like the thousandths place, then you will have to borrow from the next place up, hundredths. So, 2 thousandths would become 12 thousandths after 1 hundreth is borrowed, and the problem can be completed. The answer would be 0.569.

This method only works when a decimal is being multiplied by a whole number. For example, .326 x 2. You would just have to set up the decimal twice to get the final answer. So, there would be 6 beans in the tenths place, 4 beans in the hundredths place, and 12 beans in the thousandths place. The same rule with addition applies to multiplication: if there are more than 10 beans in one place, then carry over to the next highest place. So, there would be 2 thousandths and then 5 hundredths. The final answer would be 0.652.
Division also works best when dividing by whole numbers. For this, you would have set up the first number, the decimal, and then split it into the number of groups indicated. For example, if the problem were 0.46 ÷ 2, then you would place 4 beans in the tenths column and 6 in the thousandths column. Then, split those beans into two equal groups. The answer is the total in one of these groups, 0.23.
We also had two IBL presentations in class today. The first, which was done by Ashley, involved addition and subtraction with decimals. She came up with a neat activity that involved finding prices for multiple items. Prices are great for applying decimals to real-life scenarios. Cory presented next. He did a bingo game, but we had to convert fractions to decimals and vice versa to find the corresponding square. This would be a fun game to do with kids to practice fractions and decimals.
For practice with decimals, try the games on this site.
Next post will be Wednesday!
Hope your November is off to a great start!

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