Week in Review # 9
MATH 365
Marcia Drost
c
5.1 - 5.2
Drost,
2005
Created and complied by Sherry Scarborough
with thanks for additional problems from
Zach Barcevac, Lynnette Cardenas, Greg
Klein, David Manuel, Jane Schielack, and
Jenn Whitfield.
1. True or False: The set
closed under addition.
−2
2
, 0,
3
3
9
26
c.
8
25
d.
7
24
a.
000000000000
111111111111
111111111111
000000000000
000000000000
111111111111
000000000000
111111111111
000000000000
111111111111
000000000000
111111111111
000000000000
111111111111
000000000000
111111111111
000000000000
111111111111
is
2. Circle which fractions are less than onethird.
10
a.
27
b.
7. Given that the entire shape represents
one unit area, write a fraction in lowest
terms that represents the shaded portion.
b.
0000000111111
1111111
0000001111111
111111
0000000
1111111
1111111
0000000
000000
0000000
0000000
1111111
000000
111111
0000000
1111111
0000000
1111111
000000
0000000
0000000111111
1111111
0000001111111
111111
0000000
1111111
0000000111111
1111111
0000001111111
111111
0000000
1111111
1111111
0000000
000000
0000000
0000000
1111111
000000
0000000
0000000111111
1111111
0000001111111
111111
0000000
1111111
0000000
1111111
000000
111111
0000000
1111111
8. Find three rational numbers in fraction
−4
−5
and
.
form that are between
9
9
9. What is the name of the property that
guarantees that between any two distinct
rational numbers is a rational number?
5
by shading
6
a. congruent rectangles
10. Represent
3. Put the following fractions in order from
25 −9 5 4
,
, ,
smallest to largest:
16 10 11 7
b. unit segments
2
4. Find two rational numbers between
7
3
and .
7
5. Give an example of the Fundamental Law
of Fractions.
6. Circle the properties that hold for subtraction of rational numbers.
closure commutative associative
c. congruent circles
d. by shading congruent sectors (pieshaped pieces) of a circle.
11. Give an example of a rational number 20. Circle all values which are equivalent to
9
that is:
.
4
a. a proper fraction
2
a.
3
b. an improper fraction
c. a fraction that is equivalent to an
integer
b. 2
d. a fraction in simplest form or lowest terms
c.
18
8
d.
−27
12
1
4
e. a fraction not in lowest terms
12. Simplify:
28
7
5
+
−
=
a.
36 45 10
6
2
9
b. −
+
=
x 2x + 2 (x + 1)2
5
21. Find the additive inverse of 4 as an im6
proper fraction in lowest terms.
105
22. How did the early Egyptians write the
to a mixed number in lowest
13. Change
following numbers:
39
terms.
5
a.
6
2
14. Change −7
to a fraction of the form
11
a
3
where a and b are integers, such that
b.
b
4
b 6= 0. Show your work and do not just
use a rule or property.
5
c.
8
15. Using drawings and shadings of sectors of
1
2
circles, model 2 + 1 and give its sum.
2
5
23. Give an example of how the ancient
Babylonian use of fractions is still in use
t v
16. If ,
∈ Q, then by definition of subtoday.
u w
t v
traction, − = d if, and only if, what?
u w
24. True or false: Given two positive rational
17. Use the definition of less than to prove
−5
−2
<
.
7
5
numbers, the one with the largest numerator is the largest.
18. A bread recipe requires 6 23 cups of flour. 25. True or false: Given two positive rational numbers, the one with the greatest
Courtney put 3 14 cups of flour into the
denominator is the least.
bread batter. How much more flour does
she need to put into the batter? Write
an expression that describes this problem 26. True or false: Given two rational numa
c
a
c
and then simplify it to find the answer.
bers, and , then < if a · d < b · c.
b
d
b
d
1 1
19. Model + .
3 4