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10.5: Homework

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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.

    1. State how many C-strips (each an equal part of the whole) make up one unit.
    2. State which C-strip makes up one part of the whole.
    3. State the fraction that the C-strip in part b represents.
    4. State how many of the C-strips in part b you need to make into a train.
    5. 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 \(\frac{7}{11}\)?

    b. If H represents 1 unit, then which C-strip represents \(\frac{2}{3}\)?

    c. If P represents 1 unit, then which C-strip represents \(\frac{3}{2}\)?

    d. If L represents 1 unit, then which C-strip represents 3 ?

    e. If Y represents 1 unit, then which C-strip represents \(\frac{6}{5}\)?

    f. If O represents 1 unit, then which C-strip represents \(\frac{1}{2}\)?

    g. If B represents 1 unit, then which C-strip represents \(\frac{4}{3}\)?

    HW #2

    Do each step using your C-strips.

    1. State how many C-strips will make up the named C-strip stated in the problem.
    2. Which C-strip makes up one equal part?
    3. State the fraction that the C-strip in part b represents.
    4. State how many of the C-strips in part b will make up one unit.
    5. 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 \(\frac{5}{6}\), then which C-strip is 1 unit?

    b. If W represents \(\frac{1}{7}\), then which C-strip is 1 unit?

    c. If D represents \(\frac{3}{2}\), then which C-strip is 1 unit?

    d. If N represents \(\frac{4}{3}\), then which C-strip is 1 unit?

    e. If D represents 3, then which C-strip is 1 unit?

    f. If K represents \(\frac{7}{9}\), then which C-strip is 1 unit?

    HW #3

    Do each step using your C-strips.

    1. State which C-strip is one unit.
    2. State which C-strip is the answer.

    a. If N represents \(\frac{2}{3}\), then which C-strip represents \(\frac{1}{4}\)?

    b. If D represents \(\frac{3}{4}\), then which C-strip represents \(\frac{3}{2}\)?

    c. If B represents \(\frac{3}{2}\), this which C-strip represents \(\frac{4}{3}\)?

    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 \(\cdot\) 2/5

    b. 4/7 \(\cdot\) 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 \(\cdot\) 2/3 OR 2/3 \(\cdot\) 5/6

    11a.PNG

    b. 1/2 \(\cdot\) 7/8 OR 7/8 \(\cdot\) 1/2

    11b.PNG

    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. 12a.PNG

    b. 12b.PNG

    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. \(\frac{1}{3} \cdot \frac{2}{3}\)
    b. \(\frac{1}{2} \cdot \frac{5}{6}\)

    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 \(\div\) 1/3

    b. 3/4 \(\div\) 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. \(\frac{216}{420}\)

    b. \(\frac{195}{286}\)

    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. \(\frac{11}{16}\)

    b. \(\frac{3}{125}\)

    c. \(\frac{1}{12}\)

    d. \(\frac{9}{40}\)

    e. \(\frac{21}{56}\)

    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. \(0.\bar{7}\)

    b. \(0.\overline{72}\)

    c. \(0.\overline{235}\)

    d. \(0.2\bar{5}\)

    e. \(0.3\overline{42}\)

    This page titled 10.5: Homework is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Julie Harland via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.