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Warming Up to Decimals

Multiplying Decimals

Dividing Decimals

This week, your student will add and subtract numbers using what they know about the meaning of the digits. In earlier grades, your student learned that the 2 in 207.5 represents 2 hundreds, the 7 represents 7 ones, and the 5 represents 5 tenths. We add and subtract the digits that correspond to the same units like hundreds or tenths. For example, to find 10.5+84.3, we add the tens, the ones, and the tenths separately, so 10.5+84.3=90+4+0.8=94.8.

Any time we add digits and the sum is greater than 10, we can “bundle” 10 of them into the next higher unit. For example, 0.9+0.3=1.2.

To add whole numbers and decimal numbers, we can arrange 0.921+4.37vertically, aligning the decimal points, and find the sum. This is a convenient way to be sure we are adding digits that correspond to the same units. This also makes it easy to keep track when we bundle 10 units into the next higher unit (some people call this “carrying”).

Here is a task to try with your student:

Find the value of 6.54+0.768.

Solution: 7.308. Sample explanation: there are 8 thousandths from 0.768. Next, the 4 hundredths from 6.54 and 6 hundredths from 0.768 combined make 1 tenth. Together with the 5 tenths from 6.54 and the 7 tenths from 0.768 this is 13 tenths total or 1 and 3 tenths. In total, there are 7 ones, 3 tenths, no hundredths, and 8 thousandths.

This week, your student will multiply decimals. There are a few ways we can multiply two decimals such as (2.4)⋅(1.3). We can represent the product as the area of a rectangle. If 2.4 and 1.3 are the side lengths of a rectangle, the product (2.4)⋅(1.3) is its area. To find the area, it helps to decompose the rectangle into smaller rectangles by breaking the side lengths apart by place value. The sum of the areas of all of the smaller rectangles, 3.12, is the total area.

Find (2.9)⋅(1.6) using an area model and partial products.

Solution: 4.64. The area of the rectangle (or the sum of the partial products) is: 2+0.9+1.2+0.54=4.64

This week, your student will divide whole numbers and decimals. We can think about division as breaking apart a number into equal-size groups.

For example, consider 65÷4. We can image that we are sharing 65 grams of gold equally among 4 people. Here is one way to think about this:

Everyone gets 10+6+0.2+0.05=16.25 grams of gold.

The calculation on the right shows different intermediate steps, but the quotient is the same. This approach is called the partial quotients method for dividing.

Here is how Jada found 784÷7 using the partial quotient method.??

Solution

IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyright 2017-2019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). OUR's 6–8 Math Curriculum is available at https://openupresources.org/math-curriculum/.