Name
6-1
Date
Enrichment
Greatest Possible Error
When you measure a quantity, your
measurement is more precise when you use a
smaller unit of measure. But no measurement
is ever exact—there is always some amount of
error. The greatest possible error (GPE) of a
measurement is one half the unit of measure.
INCHES
1
2
length of line segment:
1}38} inches, to the nearest }18} inch
unit of measure: }18} inch
GPE: half of }18} inch, or }116} inch
At the right, you see how the GPE for the
ruler shown is calculated as }116} inch. Since
1}38} 5 1}16}
6 , the actual measure of the line
segment may range anywhere from 1}15}
6 inches
7
to 1}1}
6 inches.
Use the GPE to give a range for the measure of each line
segment.
2.
1.
INCHES
}5}
8
1
INCHES
2
}1}
4
inch to }78} inch
3.
1
2
inch to }34} inch
4.
INCHES
1
2
CM 1
}9}
1}17}
6 inches to 1 16 inches
2
3
4
5
3.5 cm to 4.5 cm
5. Using this scale, the weight of a bag of
potatoes is measured as 3 pounds. What is
the range for the actual weight of the
potatoes?
6. Using this container, the amount of a liquid
is measured as 20 milliliters. What
is the range for the actual amount
of the liquid?
0
50 mL
40 mL
3
pounds
1
30 mL
2
17.5 milliliters to
22.5 milliliters
2}78} pounds to 3}18} pounds
© Glencoe/McGraw-Hill
42
20 mL
10 mL
Mathematics: Applications
and Connections, Course 1
Name
6-2
Date
Enrichment
Using 1 as a Benchmark
When you estimate sums of proper fractions, it often helps to use the
number 1 as a benchmark, like this.
Two halves make a whole, so }12} 1 }12} 5 1.
If two fractions are each less than }12}, their
sum is less than 1.
If two fractions are each greater than }12}, their
sum is greater than 1.
}3} 1 }4} , 1
8
9
Fill in each
1. }23} 1 }58}
with , or ..
2
1
4. }2570} 1 }170}
Fill in each
3
1
50
3. }130} 1 }151}
1
2. }5} 1 }7}
38
1
5. }9}
1 }7}
9
5
1
24
2
6. }4}
1 }36}
5
9
1
with one of the given fractions.
7. }72} }37} }47} }57}
8. }181} }171} }161} }151}
9. }15} }25} }35} }45}
10. }215} }1225} }1235} }2245}
Fill in each
with , or . .
11. 1}58} 2 1}12}
}1}
2
9
14. 1 2 }49}
9
}5} 1 }7} . 1
8
9
}1}
2
© Glencoe/McGraw-Hill
}1} 1
2
.1
}1} 1
2
,1
}1} 1
2
.1
}1} 1
2
,1
}9} 1
16
.1
}9} 1
16
,1
}6} 1
13
.1
}6} 1
13
,1
12. 1 2 }15}
1
}1}
2
0
13. 1 2 }11}
9
}1}
2
15. 4}37} 1 }13}
5
16. 3 2 }47}
2}12}
43
Mathematics: Applications
and Connections, Course 1
Name
6-3
Date
Enrichment
Mystic Hexagons
A hexagon is a six sided figure. In a mystic hexagon, the sum
of the numbers along each side is the same number. This number
is called the mystic sum. For example, the mystic sum for the
hexagon at the right is 20.
6
5
9
12
10
20
2
1
15
15
3
13
4
For each mystic hexagon, write the mystic sum in
the blank in the middle. Then find the missing
fractions along the sides.
1.
2.
Complete each mystic hexagon. Be sure to express
all your answers in simplest form.
3.
© Glencoe/McGraw-Hill
4.
44
Mathematics: Applications
and Connections, Course 1
Name
6-4
Date
Enrichment
Unit Fractions
Did you know?
A unit fraction is a fraction whose numerator is
1 and whose denominator is any counting
number greater than 1.
unit fractions
→
}1}
2
}1}
3
The Rhind Papyrus indicates
that fractions were used in
ancient Egypt nearly 4,000
years ago. If a fraction was
not a unit fraction, the
Egyptians wrote it as a sum
of unit fractions. The only
exception to this rule seems
to be the fraction }2}.
}1}
10
A curious fact about unit fractions is that each
one can be expressed as a sum of two distinct
unit fractions. (Distinct means that the two new
fractions are different from one another.)
}1} 5 }1} 1 }1}
2
3
6
}1} 5 }1} 1 }1}
3
4
12
3
}1} 5 }1} 1 }1}
10
11
110
1. The three sums shown above follow a pattern. What is it?
Let n be the denominator of the given
fraction. The denominators of the distinct
unit fractions are (n 1 1) and n(n 1 1).
2. Use the pattern you described in Exercise 1. Express each
unit fraction as a sum of two distinct unit fractions.
}1} b.
1
20
5
1
a. }14} }}
}1}
5
}1} 1 }1} c.
30
6
}1} 1 }1} d.
13
156
}1}
12
1
1 1}
}
101 10,100
}1}
100
Does it surprise you to know that other fractions, such as }56}, can be
expressed as sums of unit fractions? One way to do this is by using
equivalent fractions. Here’s how.
10}
}5} 5 }
6
12
→
10}
}
}6}
}4}
}1}
}1}
12 5 12 1 12 5 2 1 3
→
}5} 5 }1} 1 }1}
6
2
3
3. Express each fraction as a sum of two distinct unit fractions.
1
a. }23} }}
}1}
1
2
6
}1}
1
15
5
1
b. }145} }}
}1}
1
18
2
1
c. }59} }}
1
4. Express }45} as the sum of three distinct unit fractions. }}
2
}1}
1
15
3
1
d. }25} }}
1 }14} 1 }21}
0
5. CHALLENGE Show two different ways to express }12} as the
sum of three distinct unit fractions.
© Glencoe/McGraw-Hill
45
Mathematics: Applications
and Connections, Course 1
Name
6-5
Date
Enrichment
Equations with Fractions and Decimals
m 1 }13} 5 0.6
w
Sometimes an equation involves both fractions
and decimals. To solve an equation like this,
you probably want to work with numbers in the
same form. One method of doing this is to start
by expressing the decimals as fractions. The
example at the right shows how you might solve
w.
the equation m = }13} = 0.6
m 1 }13} 5 }23}
Write 0.6
w as
a fraction.
m 5 }23} 2 }13}
m 5 }13}
Name the number that is a solution of the given equation.
}1}
2
1. z 5 }18} 1 0.375;
}1}, }3}, }1}, }3}
8 8 2 4
3. c 1 0.6 5 }45};
}1}, }3}, 1}1}, 1}2}
5 5 5 5
5. }14} 1 r 5 0.75;
}1}, }1}, }3}, 1
4 2 4
}1}
2
}1}
5
2. 0.75 2 }34} 5 b;
0, }14}, 1, 1}14}
0
4. 0.6
w 5 j 2 }13};
}1}, }2}, 1, 1}1}
3 3
3
1
6. d 2 0.1 5 }17}
0;
}1}, }3}, }4}, }9}
2 5 5 10
}4}
5
Solve each equation. If the solution is a fraction or a mixed
number, be sure to express it in simplest form.
4
7. }25} 1 0.4 5 k }}
5
9. 0.6w 5 n 2 }23}
1}13}
3
5
10. t 1 0.2 5 }45} }}
1
4
11. 0.375 1 g 5 }58} }}
12. y 2 0.25 5 }34}
3
5
14. q 1 0.125 5 }58} }}
15. w 5 }18} 1 0.375 1 }58}
© Glencoe/McGraw-Hill
1
1
2
13. 0.8 2 }15} 5 x }}
17. p 1 }15} 5 0.8 2 }35}
}3}
4
8. s 5 }78} 2 0.125
0
1}18}
1
2
16. 0.7 1 }110} 2 0.3 5 a }}
18. k 2 0.875 5 0.375 1 }18}
46
1}38}
Mathematics: Applications
and Connections, Course 1
Name
6-6
Date
Enrichment
The Stock Market
When you buy stock in a company, you become a part owner in that
company. You buy stock in units called shares. The stock report that you
see in a newspaper lists high and low prices per share of stock. The prices
are given as whole dollars or as halves, fourths, or eighths of a dollar.
Find the difference between the high and low prices for each
stock listed. The difference for Avon is shown as an example.
High
Low
493/8
321/4
Avon
1. 233/4
125/8
Caldor
2. 443/8
263/4
Gn Motr
3. 451/4
361/2
Hrshey
4. 511/4
293/8
K mart
5. 67
381/4
Kellogg’s
6. 45
263/8
McDonl
7. 753/4
467/8
QuakrO
8. 431/2
251/8
Sears
9. 393/8
28
Walgrn
431/8
Xerox
10. 78
Stock
Difference
49 3/8 2 32 1/4 5 17 1/8
11. What stock listed above had the greatest difference between high and
low prices? the least difference?
12. What would be the price of a share of Quaker Oats stock if it rose 21/2
above its high?
© Glencoe/McGraw-Hill
47
Mathematics: Applications
and Connections, Course 1
Name
6-7
Date
Enrichment
Fractions of Time
breakfast
classes
lunch
classes
swimming
studying
dinner
studying
watching TV
sleeping
Denise organized information about
some of her activities into the chart you
see at the right. Then she decided to
estimate what fraction of the school day
she spends studying. This is how she
did it.
4:00 P.M.–5:15 P.M.
1 h 15 min
7:00 P.M.–8:00 P.M.
1h
Total
2 h 15 min
Then she rounded 2 h 15 min to 2 h.
2
7:15 A.M. – 7:30 A.M.
8:05 A.M. – 11:30 A.M.
11:30 A.M. – 12:20 P.M.
12:20 P.M. – 2:15 P.M.
2:25 P.M. – 3:30 P.M.
4:00 P.M. – 5:15 P.M.
5:30 P.M. – 6:30 P.M.
7:00 P.M. – 8:00 P.M.
8:00 P.M. – 9:55 P.M.
10:30 P.M. – 6:45 A.M.
1
Denise estimated that she spends about }24}, or }1}
, of her day studying.
2
Use the chart above. Estimate what fraction of a school
day Denise spends on each activity.
1. swimming
about }21}
4
3. classes
about }25}
4
5. sleeping
about }13}
2. watching TV
4. eating
about }11}
2
6. at school (classes and lunch)
about }14}
7. Denise sleeps from 11:30 P.M. until
8:30 A.M. on Saturday and Sunday.
About what fraction of the seven-day
week does she spend sleeping?
8. Denise studies about 4 hours on
Saturday and about 2 hours on
Sunday. About what fraction of the
seven-day week does she spend studying?
about }11}
0
about }38}
9. Denise goes to school 180 days of
the year. About what fraction of the
365-day year does she spend in classes?
10. Denise tries to swim every day at the
same time, Monday through Friday, all
through the year. About what fraction
of the year does she spend swimming?
about }11}
0
© Glencoe/McGraw-Hill
about }112}
about }31}
0
48
Mathematics: Applications
and Connections, Course 1