MATH 165
HOMEWORK DUE NOVEMBER 15
FRACTIONS
DAVID MEREDITH
(1) Calculate and simplify if possible. If you change the fractions before combining them, show the changed fractions.
2 1
23 11
31 53
5 7
+
−
+
+
8 8
3 4
6
4
12 20
(2) Calculate and return simplified mixed fractions. Show how you did the
calculations.
2
3
5
2
4
7
431 + 225
345 − 271
383 + 297
3
4
8
3
5
8
(3) Go to the class iLearn site and download Page of Pica Rulers. These rulers
measure in 1/12”.
17
5 1
.
(a) On a pica ruler, mark the points , 2 and
3 6
12
(b) It is possible to use two rulers (let’s call them “slide rulers”) to illus7 3
5
trate adding and subtracting. Here is an illustration of + = .
8 8
4
3 5
9 2
+ and − .
4 6
4 3
(4) Find a fraction between two given fractions. First locate the given fractions
on a ruler (you can download a page of ordinary rulers from iLearn), then
choose a fraction on the ruler between the two given fractions. Finally
show your answer is correct by writing the two given fractions and your
in-between fraction with the same denominator. The pairs of fractions to
use are:
1 3
11 19
17 15
,
,
,
2 4
8 16
10 8
Use two pica rulers to calculate
Date: November 5, 2010.
1
2
DAVID MEREDITH
(5) Extra Credit (and hard) There is a simple formula for finding a fractiion
a
c
a+c
between two fractions and . Just use
. Can you show by example
b
d
b+d
(more than one) that this method works? Can you prove that it always
works?
Department of Mathematics
San Francisco State University
San Francisco, CA 94132
E-mail address: [email protected]
URL: http://online.sfsu.edu/~meredith