10.5: Homework
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- Aug 24, 2021
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- Submit homework separately from this workbook and staple all pages together. (One staple for the entire submission of all the unit homework)
- Start a new module on the front side of a new page and write the module number on the top center of the page.
- Answers without supporting work will receive no credit.
- Some solutions are given in the solutions manual.
- You may work with classmates but do your own work.
HW #1
Do each of the following steps using your C-strips.
- State how many C-strips (each an equal part of the whole) make up one unit.
- State which C-strip makes up one part of the whole.
- State the fraction that the C-strip in part b represents.
- State how many of the C-strips in part b you need to make into a train.
- State which C-strip is the length of the train you made in part c
a. If S represents 1 unit, then which C-strip represents 711?
b. If H represents 1 unit, then which C-strip represents 23?
c. If P represents 1 unit, then which C-strip represents 32?
d. If L represents 1 unit, then which C-strip represents 3 ?
e. If Y represents 1 unit, then which C-strip represents 65?
f. If O represents 1 unit, then which C-strip represents 12?
g. If B represents 1 unit, then which C-strip represents 43?
HW #2
Do each step using your C-strips.
- State how many C-strips will make up the named C-strip stated in the problem.
- Which C-strip makes up one equal part?
- State the fraction that the C-strip in part b represents.
- State how many of the C-strips in part b will make up one unit.
- Form the unit by making a train from the equal parts (C-strip in part b) and state which C-strip has the same length as that train.
a. If O represents 56, then which C-strip is 1 unit?
b. If W represents 17, then which C-strip is 1 unit?
c. If D represents 32, then which C-strip is 1 unit?
d. If N represents 43, then which C-strip is 1 unit?
e. If D represents 3, then which C-strip is 1 unit?
f. If K represents 79, then which C-strip is 1 unit?
HW #3
Do each step using your C-strips.
- State which C-strip is one unit.
- State which C-strip is the answer.
a. If N represents 23, then which C-strip represents 14?
b. If D represents 34, then which C-strip represents 32?
c. If B represents 32, this which C-strip represents 43?
HW #4
Use your fraction arrays to determine all fractions on the fraction array that are equivalent to 3/4. Do this by finding 3/4 on the array, and seeing what other numbers are the same length. Include a diagram.
HW #5
Use your multiple strips to write 6 fractions equivalent to 5/6. Draw the strips.
HW #6
Use your multiple strips to write 6 fractions equivalent to 3/8 Draw the strips.
HW #7
Compare 3/8 and 1/3 using models. Show all of the steps, and explain the procedure as shown in this module.
HW #8
Add 3/8 and 1/3 using models. Show all of the steps, and explain the procedure as shown in this module.
HW #9
Do the following subtraction using models: 3/5 – 1/4. Show all of the steps, and explain the procedure as shown in this module.
HW #10
Do the following multiplications using models. Show all of the steps, and explain the procedure as shown in this module.
a. 3/8 ⋅ 2/5
b. 4/7 ⋅ 2/3
HW #11
By looking at the final drawing someone made to model a multiplication of two fractions, determine which multiplication was performed, and then state the answer.
a. 5/6 ⋅ 2/3 OR 2/3 ⋅ 5/6
b. 1/2 ⋅ 7/8 OR 7/8 ⋅ 1/2
HW #12
If all of the dots shown for each problem represent 1 unit, determine the multiplication problem that someone did to get the answer, and state the answer.
a.
b.
HW #13
Fill in the chart showing how to do the following multiplications using C-strips. The multiplication is in the first column. State an appropriate choice for the unit (name a C-strip, or sum of two C-strips) in the second column. Write the C-strip obtained after the first part of the multiplication (which is the second fraction as a part of the unit) in the third column. Then, do the final multiplication, and write the C-strip obtained in the fourth column. In the fifth column, write a fraction using C-strips putting the final unit obtained in the fourth column as the numerator, and the unit in the denominator. Then, in the last column, write the answer as a fraction. Do not simplify.
a. | 13⋅23 | |||||
b. | 12⋅56 |
HW #14
Perform the following division using the box and dot methods. First define the unit. Then explain and show all of the steps. Include diagrams.
a. 5 ÷ 1/3
b. 3/4 ÷ 1/3
HW #15
Determine if the following statements are true or false by comparing cross products.
a. 19/23 = 57/69
b. 24/37 = 68/91
HW #16
Write each fraction in simplest form using each of the two methods:
(1) prime factorization and
(2) finding GCF.
a. 216420
b. 195286
HW #17
Use cross products to compare each of the following fractions. Use < or >.
a. 18/23 and 5/8
b. 11/18 and 121/250
HW #18
Find 3 rational numbers, written with a common denominator, between 3/8 and 5/8.
HW #19
Find 3 rational numbers, written with a common denominator, between 1/2 and 4/7.
HW #20
a. 21 of John's students have cats at home. This represents 7/10 of John's students. How many students are in John's class? Solve the problem using models. Explain how the model works.
b. At an elementary school, 38 teachers drive alone to work. This represents 2/3 of the teachers. How many teachers work at the school? Solve the problem using models. Explain how the model works.
HW #21
Write in words how to read each of the following decimals.
a. 0.7
b. 0.67
c. 3.28
d. 19.835
HW #22
Multiply the following decimals mentally then do it again by showing the same steps as shown in this module..
a. (0.3)(0.8)
b. (1.2)(0.4)
c. (1.22)(2.3)
d. (3.2)(2.41)
HW #23
For each fraction, determine if it can be written as an equivalent fraction with a power of ten in the denominator. If a fraction cannot be written as a terminal decimal, explain why not. Otherwise, show ALL of the steps to write it as a terminal decimal.
a. 1116
b. 3125
c. 112
d. 940
e. 2156
HW #24
Rewrite each of the following decimals as simplified fractions. For repeating decimals, use the techniques shown in this module. Then, check your answer using a calculator by dividing the numerator by the denominator to see if the result matches the original problem.
a. 0.ˉ7
b. 0.¯72
c. 0.¯235
d. 0.2ˉ5
e. 0.3¯42