Unit 3, Lesson 19
Dividing Numbers that Result in a Decimal
Accelerated 6
19.2
Activity
Here is how Lin calculated .
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Discuss with your partner:
- In the third step, Lin drew a vertical dashed line to the right of the 2 in 62. What do you think that line is for?
- She also wrote a point and a 0 to the right of 62. Then she put a 0 after the remainder of 2. What do you think the zeros are for?
- Lin subtracted 5 groups of 4 from 20. What value does the 4 in the quotient represent?
- What value did Lin find for ?
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Use long division to find the value of each expression. Then pause so your teacher can review your work.
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Use long division to show that:
, or , is 1.25.
, or , is 0.8.
, or , is 0.125.
Student Lesson Summary
We can use long division to find quotients even when the numbers involved are not whole numbers. Here is the long-division calculation of , which results in a decimal quotient.
Long division calculation of 86 divided by 4. 8 rows. First row: 21 point 5, Second row: 4, long division symbol with 86 inside. Third row: minus 8. Horizontal line. Fourth row: 6. Fifth row: minus 4. Horizontal line. Sixth row: 2 point 0. Seventh row: minus 2 point 0. Horizontal line. Eighth row: 0.
The calculation shows that, after removing 4 groups of 21, there are 2 ones remaining. We can continue dividing by writing a 0 to the right of the 2 and thinking of that remainder as 20 tenths, which can then be divided into 4 groups.
To show that the quotient we are working with now is in the tenths place, we put a decimal point to the right of the 1 (which is in the ones place) at the top. It may also be helpful to draw a vertical line to separate the ones and the tenths.
There are 4 groups of 5 tenths in 20 tenths, so we write 5 in the tenths place at the top. The calculation likewise shows .
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