standard_description: Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.
problem_activity: Problem 1
Josie makes 1.7 liters of lemonade. Josie’s mom tells her to split it evenly with her brother. How much lemonade, in liters, will Josie and her brother each get?
Problem 2
Here is how Mai used base-ten diagrams to calculate 0.62 ÷ 5. She started by representing 0.62.
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She then made 5 groups, each with 1 tenth. There was 1 tenth left. She unbundled it into 10 hundredths and distributed the hundredths into 5 groups. Here is her diagram for 0.62 ÷ 5.
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Mai should have a total of 12 hundredths, but her diagram shows only 10. Why?
She did not originally have thousandths, but in her diagrams each group has 4 thousandths. Why?
What value has Mai found for 0.62 ÷ 5?
Problem 3
Here is how Lin calculated 0.62 ÷ 5.
|                 Lin wrote the dividend, 0.62, and the divisor, 5.                  | She subtracted 5 groups of different amounts from 0.62, starting with 5 groups of 0.10, then 5 groups of 0.02. |                Lin wrote 0 to the right of the 2, which made 0.020.                | Lastly, she subtracted 5 times 0.004 from 0.020, which left no remainder.                          Then she added 0.100 + 0.020 + 0.004, which gave a quotient of 0.124. |
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| .. image:: https://d21royfkw9g4l6.cloudfront.net/9FyZXfKqijxVpRgv2Bc6qf_CDWBZL.png |               .. image:: https://d21royfkw9g4l6.cloudfront.net/nxKMGc5DKRKgY6x2FVmo07_YDGM41.png               | .. image:: https://d21royfkw9g4l6.cloudfront.net/O3iHOw3zlpAkiFdwXHFNPB_NVXARD.png |                                            .. image:: https://d21royfkw9g4l6.cloudfront.net/91UkRicG3K9xdXGPqEsgOT_06NZSH.png                                            |
Lin put a 0 after the remainder of 0.02. Why? Why does this 0 not change the value of the quotient?
What value did Lin find for 0.62 ÷ 5?
Problem 4
Solve. Show or explain your work.
27 ÷ 6
0.84 ÷ 8
18.03 ÷ 6
3 ÷ 4


aligns: no