Mat 391 Fractions and Rational No. Qz.
.
Name,
Be sure all your answers are complete giving full justification for your statements, especially on discussion problems. Answers such as "because its important" "true/yes" or "because it works" receive no credit.
1. a. Use unit square(s) to show Ethyl how to explain
to her precious little Amanda how to add 
.
Draw three unit squares. Divide the first vertically into thirds, the second horizontally into fourths and the last by thirds vertically by fourths horizontally to get the last sq divided into twelve congruent parts. Count how many of those parts fit into one vertical (1/3) column and one horizontal (1/4) row. Should get four sqs colored for the third and three squares colored for the fourth. Color any seven distinct squares on the square divided into twelfths.
b. Use unit square(s) to show
how she would multiply 
Draw one large unit square divided vertically into thirds and horizontally into fourths. Color one of the columns of thirds and one row of fourths. The product is the cross colored twelfth, 1/3 x 1/4 = the 1/12 double colored square of the square divided into twelve congruent parts.
c. Amanda is really a little bit young right now, but how will Ethyl
show her later, using unit square(s), how to divide these same rational numbers,
i.e. use unit square(s) to show your solution to 
Divide a single third column
into four parts. Division asks the question, "How much of the whole
is one fourth of a third part of the whole?" Answ: 
1/3
divided into four parts gives you a part that is 1/12 of the whole.
2. Add 
by the
method given below. Be sure to show all your work. State at least
one advantage and one disadvantage for each method given.
a. Improper Fraction
adv
disadv
b. Mixed Fraction
adv
disadv
3. Multiply 
by the
method given below. Be sure to show all your work. State at least
one advantage and one disadvantage for each method.
a. Improper Fraction
adv
disadv
b. Mixed Fraction
adv
disadv
4. Simply 
, by
any method you choose. Just, please be sure to show your work to justify
your answer.
5. Fill in the box with <, =,
> .
6. The CSME is busy making bows for the conference.
Craig is almost through. If each bow requires 5/6 ft of ribbon and there
is only 1 1/2 yards of ribbon left in one uncut
strip.
a. How many complete bows will Craig be able to make out of this last piece of ribbon?
b Use a line diagram to show how Craig could cut his ribbon to get these many bows.
c. How much of a bow is Craig lacking the material to make?
d. Will there be enough of a strip of ribbon left over for Judith to be likely to make a neckband for her cat? How much of the ribbon will be left over no matter how Craig cuts it?
e. Write an equation that reconciles the fractional part of a bow left over with the amount of material left over.
8. Show 
on the
geoboard below. Explain what your lines are intended to show.
9. Assuming all spaces are equal,
find the value of N on the number line
given below 
10. A student says that he found a quick way to divide mixed numbers. He shows you his method as follows
since
and
. Why
or why not does this work? How would you discuss this with
the student?
11. Complete the following table, finding the additive and multiplicative inverses for each entry.
|
Entry |
Additive inverse |
Multiplicative Inverse |
Entry |
Additive inverse |
Multiplicative Inverse |
|
4 |
|
||||
|
|
|
12. Estimate each of the following; indicate if the actual answer is greater than (+) or less than (–) your estimate.
a. 
b. 
c. 
Bonus: Give a detailed explanation why 
.