Download Section 3.5 Subtracting Fractions and Mixed Numbers

UNIT THREE: Prealgebra in a Technical World
3.5 Subtracting Fractions and Mixed Numbers
SWBAT
1. Estimate fraction, and mixed number, differences.
2. Add and subtract signed fractions.
3. Subtract mixed numbers.
In the USA most of the Pacific Northwest experiences a summer drought. For instance,
the average rainfall for summer months in Grants Pass is less than ½ an inch! We “see” this in
the graph below. Notice that the vertical scale is in fourths of an inch.
6
Grants Pass Average Precipitation
5
Inches
4
3
2
1
0
Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec
We can read this graph to find approximate rainfall values. For instance it rains about
1
1
4
2
5 inches in December and about of an inch in August. With about 5 fewer inches of rainfall,
August is a very dry month in Grants Pass! We do not need exact rainfall figures to get a good
feel for monthly differences. While we will need exact differences in some cases, such as
medication dosages, often we need only to estimate differences.
In this section we study methods for estimating results for
adding and subtracting fractions and mixed numbers, and then we study exact methods for
calculating sums and differences of these signed numbers.
219
Section 3.5 Subtracting Fractions and Mixed Numbers
Be
Estimating Fraction, and Mixed Numbers, Differences
Casey is fixing a cabinet shelf. She has
7
8
This is a dado
joint!
inch-long wood
screws, but she is not sure if these are long enough for the job.
1
She knows that the screws must be at least 2 inch longer than
1
4
the width of the cabinet she will drive the screw through. That
1
“
220
7
width is 4 inch. Will the 8 inch screw be long enough?
7
1
Casey estimates the answer to this question: 8 − 4 .
Because
3
4
1
1
7
3
− 4 = 2 , and 8 is greater than 4 , the screw is long
enough.
Often we only need to estimate the answer to subtraction problems, and when we do
need exact answers, as always, our estimates can serve to check our results. In addition, we
must estimate to check these results when using calculating technology to avoid the most
ridiculous errors. (Those are the errors that happen when our finger hits the wrong key.)
Here are three methods of thinking through estimates when finding differences:
METHOD 1: Use a number line. Just like adding positive fractions, we can think
or sketch a number line and the lengths for fractions to estimate differences.
You may always use your margins for such a quick sketch.
Example 1: Estimate
7
− 25
8
Think it through: We start with the
𝟕
𝟐
arrow is
𝟖
𝟓
pointed left to show the subtraction of this positive number. We know that
𝟕
𝟐
𝟏
𝟐
is close to 1 and is close to , but is just a little less.
𝟖
𝟓
𝟐
𝟓
ANSWER:
𝟕
𝟖
𝟐
𝟏
𝟓
𝟐
− ≈
arrow pointing right, but this time the
UNIT THREE: Prealgebra in a Technical World
Example 2: Estimate the difference
𝟔
𝟕
−
𝟔
𝟑
𝟒
𝟔
Think it through: Notice that is about 𝟖 .
𝟕
Because
𝟔
𝟑
= the difference
𝟖
𝟔
𝟕
𝟒
is very close to zero.
ANSWER:
𝟔
𝟕
𝟑
− ≈𝟎
𝟒
The more fraction facts we know, the more likely we are to find an exact answer when
estimating. For example, if we know that
continuing with mental math,
7−2
8
1
4
2
7
1
7
2
= , then we think 8 − 4 = 8 − 8 and
8
5
= . Do not be alarmed! If we find an exact answer while
8
estimating, this is good. If this happens, we need only write down the answer.
METHOD 2: If fractions have the same denominator, subtract numerators. For
3
2
1
example, 5 − 5 = 5. If we can use mental math to find equivalent fractions with
common denominators, we do so and then subtract numerators. For example,
3
10
1
3
2
1
− 5 = 10 − 10 = 10. In both cases our “estimate” is an exact answer.
3
1
4
8
Example 3: Estimate −
𝟑
Think it through: If we know immediately that
ANSWER:
𝟑
𝟒
𝟏
𝟓
𝟖
𝟖
𝟒
𝟔
𝟖
, we have
𝟔 − 𝟏 eighths.
− = .
Example 4: Estimate
9
10
−
2
5
Think it through: If we know immediately that
ANSWER:
=
𝟗
𝟏𝟎
𝟐
𝟓
𝟓
𝟏𝟎
− =
and simplify:
𝟐
𝟓
𝟓
𝟏𝟎
=
𝟒
𝟏𝟎
𝟏
= .
𝟐
, we have
𝟗 − 𝟒 tenths.
221
222
Section 3.5 Subtracting Fractions and Mixed Numbers
 Check Point 1
Estimate each of the following. Draw number lines or pies to “see” the estimate, or (when
possible) use mental math to calculate estimates that are exact answers.
a.
2
3
2
− ≈ ____
b.
5
2
3
1
− ≈ ____
c.
6
2
−
3
5
≈ ____
12
d.
6
7
4
− ≈ ____
7
METHOD 3: If denominators are only one digit apart, change one of the
denominators to the value of the other denominator and subtract. These
estimates will not be exact differences!
Example 5: Estimate
𝟕
Think it through:
𝟕
𝟗
𝟓
−
𝟖
𝟕
𝟕
𝟕
𝟖
𝟖
𝟖
is close to . Using we have
𝟗
(or 𝟓𝟖 is close to 𝟓𝟗.
7
ANSWER:
9
−
5
8
≈
𝟏
𝟒
or
7
9
−
𝟓
𝟕
𝟗
𝟗
Using we have
−
5
8
≈
𝟓
𝟖
−
𝟓
Think it through:
𝟔
𝟓
𝟔
𝟓
𝟔
𝟑
𝟓
𝟖
𝟒
𝟒
𝟓
𝟐
𝟐
𝟗
𝟗
= . Our estimate is .)
𝟗
𝟏
𝟒
𝟐
𝟕
𝟓
𝟗
𝟗
𝟖
≈ ≈ −
.)
𝟑
−
𝟓
𝟓
𝟓
𝟓
𝟓
is close to . Because
−
𝟏
𝟗
(or 𝟑𝟓 is close to 𝟑𝟔. Using 𝟑𝟔
ANSWER:
𝟏
𝟐
(Draw pies or number lines to “see” that
Example 6: Estimate
𝟐
= = . Our estimate is .
𝟐
𝟓
𝟓
𝟔
≈ or
−
𝟑
𝟓
≈
𝟏
𝟑
= 1 we have 1 𝟓
𝟑
𝟔
𝟔
we have −
𝟑
𝟓
𝟐
𝟐
𝟓
𝟓
= . Our estimate is .
𝟐
𝟏
𝟏
𝟔
𝟑
𝟑
= = . Our estimate Is .)
(Draw pies or number lines to “see” this result.)
 Check Point 2
Estimate using the method of your choice.
a.
5
4
3
− ≈ ____
5
b.
2
7
1
− ≈ ____
6
c.
5
11
−
3
≈____
10
d.
5
8
4
− ≈ ____
7
UNIT THREE: Prealgebra in a Technical World
Finally we use these strategies with mixed numbers. Often mixed numbers are easier to
estimate because they have a whole number component.
METHOD 4: Estimating with mixed numbers. Round both fractions to the
nearest integer, or nearest half, and subtract. (Hint: Keep it simple, student.)
4
7
9
8
Example 7: 7 − 5
Think it through: These mixed numbers round easily to integers and halves.
𝟒
𝟏
𝟕
𝟏
𝟏
Because 𝟕 𝟗 ≈ 𝟕 𝟐 and 𝟓 𝟖 ≈ 𝟔, we can use 𝟕 𝟐 − 𝟔 = 𝟏 𝟐 .
𝟒
𝟕
𝟏
ANSWER: 𝟕 𝟗 − 𝟓 𝟖 ≈ 𝟏 𝟐 (or if we had rounded to the whole number: 𝟕 − 𝟔 = 𝟏.)
Most often we will be able to find a good estimate by rounding to the nearest integer.
1
3
5
4
Example 8: 8 − 3
Think it through: These mixed numbers round to values that are easy to think about.
𝟏
𝟑
𝟓
𝟒
𝟖 ≈ 𝟖 and 𝟑 ≈ 𝟒 we use mental math: 𝟖 − 𝟒 = 𝟒 . (Or if we had
𝟏
𝟏
rounded to the half: 𝟖 − 𝟑 𝟐 = 𝟒 𝟐.)
1
3
5
4
8 − 3 ≈𝟒
ANSWER:
 Check Point 3
Estimate these differences.
2
1
3
6
a. 4 − 3  ______
b. 6
5
11
−3
3
10
 ______
5
1
8
4
c. 10 − 8  ______
223
224
Section 3.5 Subtracting Fractions and Mixed Numbers
Adding and Subtracting Signed Fractions
In algebra we use signed fractions to solve problems. For example, rates of change, like
dollars per hour, or feet per minute, are written as fractions. Some rates are positive, and
some rates are negative. Often we need to add or subtract rates.
When we add or subtract any signed fractions, use the rules for signs. For instance,
3
1
3
1
change the subtraction problem: − 4 − 2 to the addition problem: − 4 + (− 2). Then add to
3
1
3
1
5
find the difference − 4 − 2 = − 4 + (− 2) = − 4. (Did you use mental math?)
RULE: To add or subtract signed fractions:
A. Estimate an answer as soon as you can.
B. Find common denominators and rewrite the fractions.
C. When necessary, use the rules of signs to rewrite as
addition or subtraction.
D. Add or subtract the numerators as required. Keep the
denominator.
E. Simplify. (Write as a mixed number only if appropriate.)
1
2
Example 9: Simplify 4 − 3.
Think it through: A. Because
1
4
1
1
3
3
≈ and
2
1−2
3
3
− =
B. Common denominator is 12, so
3
12
C. Subtraction is adding opposites, so
D. Add the numerators
3+(−8)
12
1
𝟏
3
8
𝟑
= − , estimate −
=−
−
12
3
12
−
8
12
=
3
8
+ (− )
12
12
5
12
E. This result is already in simplest form.
Check: −
ANSWER:
𝟏
𝟒
5
12
is only
𝟐
𝟓
𝟑
𝟏𝟐
− =−
1
12
1
5
3
12
away from − , so −
is a reasonable answer.
UNIT THREE: Prealgebra in a Technical World
Example 10: −
10
21
+
13
14
10
1
Think it through: A. Because − 21 ≈ − 2 and
13
14
B. The common denominator is 42, so −
C. Adding opposites is subtracting −
D. Subtract the numerators
1
𝟏
2
𝟐
≈ 1, estimate − +1 =
39−20
21
20
42
=
42
10
+
+
39
42
13
=−
14
=
39
42
20
42
−
+
39
42
20
42
19
42
E. This result is already in simplest form.
𝟏𝟗
Check:
−
ANSWER:
𝟏𝟎
𝟐𝟏
𝟒𝟐
+
𝟏𝟑
𝟏𝟒
is only
=
11
𝟐
𝟒𝟐
𝟏
𝟏𝟗
𝟐
𝟒𝟐
away from , so
is a reasonable answer.
𝟏𝟗
𝟒𝟐
5
Example 11: Simplify 15 − (− 12)
𝟏𝟏
𝟑
𝟓
𝟑
𝟏
𝟏
𝟓
Think it through: A. Because 𝟏𝟓 ≈ 𝟒 and − (− 𝟏𝟐) ≈ + 𝟐, estimate + = .
𝟒
𝟐
𝟒
B. The common denominator is 60, so
11
15
− (−
5
)
12
C. Subtracting a negative is adding a positive, so
D. Add the numerators
𝟔𝟗
E. Simplify
Check:
𝟏𝟏
ANSWER:
𝟏𝟓
𝟐𝟑
𝟐𝟎
− (−
𝟔𝟎
𝟐𝟑
=
𝟐𝟎
is only
𝟓
𝟐
𝟐𝟎
44
60
+
25
60
=
44
60
44
25
= 60 − (− 60)
25
44
25
− (− 60) = 60 + 60
𝟔𝟗
𝟔𝟎
𝟐𝟑
𝟑
(If mixed numbers are required, 𝟐𝟎 = 𝟏 𝟐𝟎 . )
less than our estimate of
𝟓
𝟒
, so
𝟐𝟑
𝟐𝟎
is reasonable.
𝟐𝟑
) = 𝟐𝟎
𝟏𝟐
 Check Point 4
Simplify each of these.
a. −
19
5
5
1
− (− ) ___________________ b. − + (− ) ____________________
24
6
14
4
225
226
Section 3.5 Subtracting Fractions and Mixed Numbers
b.
Subtracting Mixed Numbers
Mixed numbers are used in the trades, in garages and in kitchens. In these applications,
we do not find negative numbers! We do find many word problems though. For instance if an
3
1
auto mechanic or welder needs to cut 3 4 inches from a 7 8 piece of metal, how much metal is
left? To answer this, we have a choice of algorithms to carry out the necessary subtraction.
THE THREE MOST COMMON ALGORITHMS FOR SUBTRACTING FRACTIONS
Separate Integers & Fractions:
1
Borrow to Subtract Fractions:
3
1
78 − 34
1
3
1
78 − 34
3
= 4 + (8 − 4) subtract integers
1
Use Improper Fractions:
6
= 4 + (8 − 8)like denominators
5
= 4 + (− 8) subtract fractions
3
= 3 8 add integer and fraction
1
6
= 7 8 − 3 8 like denominators
9
3
78 − 34
6
= 6 8 − 3 8 borrow
=
=
3
= 6 − 3 + 8 subtract fractions =
3
= 3 + 8 subtract integers
=
3
= 3 8 add integer and fraction
57
8
57
8
27
8
24
8
−
−
15
improper fractions
4
30
like denominators
8
subtract fractions
3
+ 8 find the integer
3
= 3 8 write as mixed numbers
In this book we will use the “Separate Integers and Fractions” algorithm. The
“Separate” algorithm allows us to estimate differences first and, once learned, is quicker to use.
In the final step of the “Separate” algorithm we add integer and fraction. When the
fraction is positive, we simply “put together,” but when it is negative, we use complements to
subtract mentally. Complements are fractions that add to one. In the example used in the
5
table above, 8 and
3
8
5
3
5
3
are complements. So 4 + (− 8) = 3 8 because 1 − 8 = 8. The 1 was taken
from 4 and then the complement of
5
8
is added to the remaining whole number.
 Check Point 5
Complete these “last steps” of the “separate” algorithm. Use “put together” or complements.
a. 5 +
7
16
= ______ b. 5 −
7
16
= _____
c. 7 −
5
6
= _____
d. 7 +
5
6
= _____
UNIT THREE: Prealgebra in a Technical World
The commutative and associative properties allow us to regroup the integer and fraction
parts of a mixed number when we add or subtract. For subtraction, we can simply change the
problem into adding the opposites.
3
1
4
4
Example 12: Subtract: 8 − 3
Think it through:
3
1
4
4
A. We can rewrite this using addition: [8 + ] + [(−3) + (− )]
B. Use the commutative and associative properties to regroup integers
𝟑
𝟏
with integers and fractions with fractions: [𝟖 + (−𝟑)] + [ + (− )]
C. Add the integer, and add the fractions: 𝟓 +
D. Add the integer sum to the fraction sum: 𝟓
𝟓
ANSWER:
𝟏
𝟏
𝟒
𝟒
𝟐
𝟐
𝟏
𝟐
RULE: To subtract mixed numbers:
A. Subtract the integers. (This gives you a ball park estimate!)
B. Subtract the fractions.
C. Add the integer difference to the fraction difference using complements
when necessary.
2
1
3
4
EXAMPLE 13: Subtract: 9 − 3
Think it through: A. Subtract the integers: 9 − 3 = 6
B. Subtract the fractions:
2
3
1
− =
4
C. Both differences are positive:
5
8
−
3
=
5
12
12
12
5
5
𝟔 + 12 = 𝟔 12
Check: 𝟔 12 is reasonably close to our estimate of 6.
ANSWER:
2
1
5
9 3 − 3 4 = 6 12
227
228
Section 3.5 Subtracting Fractions and Mixed Numbers
1
4
4
5
EXAMPLE 14: Simplify 4 − 1 . (Notice that “simplify” means we need to subtract )
Think it through: A. Subtract the integers: 4 − 1 = 3
B. Subtract the fractions:
1
4
4
5
5
20
− =
−
16
20
=−
11
20
C. The fraction is negative, so use its complement: 3 −
11
20
=2
9
20
9
Check: 𝟐 10 is reasonably close to our estimate of 3.
ANSWER:
1
4
9
2
7
3
8
4 4 − 1 5 = 2 20
EXAMPLE 15: Simplify 10 − 6 .
Think it through:
A. Subtract the integers: 10 − 6 = 4
B. Subtract the fractions:
2
3
7
16
8
24
− =
−
21
24
=−
5
24
5
19
C. The fraction is negative, so use its complement: 4 − 24 = 3 24
Check: 3
ANSWER:
2
19
24
7
is reasonably close to 𝟒.
19
10 3 − 6 8 = 3 24
UNIT THREE: Prealgebra in a Technical World
 Check Point 6
1
1
4
10
a. Estimate and simplify 11 − 2
___________________________________
___________________________________
___________________________________
1
7
6
15
b. Estimate and simplify 18 − 12
___________________________________
___________________________________
___________________________________
At the beginning of this section, we could “see” that the rainfall in Grants Pass decreases in the
summer months. Similiar decreases in summer rainfall are found throughout the Pacific Northwest.
Precipitation in Three Southern Oregon Cities and Seattle, Washington 1
Medford, OR
Jan
2 3/ 4
Feb
1 9/10
Mar
1 4/ 5
Apr
1 1/ 4
May
1
3/
June
5
1
July
/3
1/
Aug
2
9
Sept
/10
1
Oct
1 /2
Nov
3 2/5
Dec
3 1/3
Grants Pass, OR
Jan
5
Feb
4 1/ 3
Mar
3 2/ 3
Apr
2
May
1 1/ 4
1/
June
2
1
July
/3
1/
Aug
2
3
Sept
/4
Oct
2
Nov
5
Dec
5 1/ 3
1. http://www.wrcc.dri.edu/
Cave Junction, OR
Jan
11
Feb
8
Mar
7 3/4
Apr
4
May
2
3/
June
4
1
July
/4
1/
Aug
2
Sept
1
Oct
3 3/5
Nov
9 1/3
Dec
12 1/4
Seattle, WA
5
Jan
4 1/ 4
Feb
3 1/ 2
Mar
2 1/ 3
Apr
1 1/ 2
May
1 1/ 2
June
1
July
1
Aug
2
Sept
3 1/ 4
Oct
4 8/ 9
Nov
5 3/ 4
Dec
229
230
Section 3.5 Subtracting Fractions and Mixed Numbers
What is the difference in rainfall between Grants Pass and Medford for the month of March? By
reading the table, and quickly rounding to the nearest integer, we estimate “about 2 inches more rain
falls in Grants Pass than in Medford in March.” That estimate may be all that matters. If we want an
exact answer, we have at least three methods of subtracting fractions to choose from. It may be harder
to learn the easiest method once you know a harder algorithm, but it pays to switch algorithms here!
Separate
3
2
3
−1
Borrow
4
3 2/3
5
1. Subtract the integers:
3−1=2
2
2. Subtract the fractions:
2
4
10
12
2
− 5 = 15 − 15 = − 15
3
3. Use complements:
2
- 1 4/ 5
𝟏𝟑
2 − 15 = 𝟏 𝟏𝟓
𝐴nd that IS in the ball park!
3
2/
3
5/ 25/
3
15
- 1 4/5 4/5
1
12/
15
“borrow”
from the 3
and make
that 2 then
add 3/3 to
2/3 . .
13
/15
Subtract whole numbers.
Use common denominators
and subtract the fractions.
Remember to estimate to
check!
Use Improper Fractions
3 2/3 - 1 4/5
= 11/3 - 9/5
= 55/15 - 27/15
= 28/15
= 1 13/15
Rewrite as a
mixed
number.
Remember
to estimate
to check.
This
requires
using larger
numbers in
the
numerators.
Answer:
The difference in rainfall between Grants Pass and Medford for the month of March is 1 13/15
inches, no matter how you choose to subtract mixed numbers!
STUDY SKILLS: Ask any athlete who has learned a new method to improve his game. It is
easier to keep applying the old method than it is to learn the new one. But the final result,
playing the game better, is always worth the time it takes to change.
Take extra time now to learn the “Separate Integer and Fraction” algorithm. You will
subtract mixed numbers faster and you will have a better understanding of mixed numbers.
Your math game will be greatly improved.
UNIT THREE: Prealgebra in a Technical World
 Check Point 7
Use the table on page 229 to answer each of these questions.
(a) ABOUT how much more does it rain in Seattle in September than in Grants Pass?
___________________________________
(b) How much more does it rain in Seattle in September than in Grants Pass?
___________________________________
(c) ABOUT how much does it rain in the winter (December, January and February) in Medford?
___________________________________
(d) How much does it rain in the winter (December, January and February) in Medford?
___________________________________
(e) ABOUT how much more does it rain in the winter (December, January and February) in
Cave Junction than in Medford?
___________________________________
(f) How much more does it rain in the winter (December, January and February) in
Cave Junction than in Medford?
___________________________________
231
232
Section 3.5 Subtracting Fractions and Mixed Numbers
UNIT THREE: Prealgebra in a Technical World
3.5 Exercise Set
Name _______________________________
Skills
Determine the sign of each fraction difference, estimate, and then calculate using paper and
pencil. Attach your work. (Hint: You may be able to do some of these using mental math.)
9 1
−
10 4
Est. _______ Ans. ______
3. 1 9
−
8 16
Est. _______ Ans. ______
5. 5 5
−
6 9
Est. _______ Ans. ______
1.
7.
3 3
−
16 4
Est. _______ Ans. ______
2.
14 1
−
15 10
Est. _______ Ans. ______
4.
1 1
−
2 6
Est. _______ Ans. ______
6.
6 5
−
7 9
Est. _______ Ans. ______
8.
1 1
−
4 2
Est. _______ Ans. ______
Determine the sign of each mixed number difference, estimate, and then calculate using paper
and pencil. Attach your work. (Hint: You may be able to do some of these using mental math.)
9.
1
5
4 −1
4
6
Est. _______ Ans. ______
11.
5
3
8 −4
6
8
Est. _______ Ans. ______
10.
7
11
5 −2
8
12
Est. _______ Ans. ______
12.
5
5
7 −3
8
16
Est. _______ Ans. ______
233
234
Section 3.5 Subtracting Fractions and Mixed Numbers
13.
3
1
5 −2
4
8
Est. _______ Ans. ______
15.
3
1
7 −6
4
2
Est. _______ Ans. ______
14.
16.
3
11
9 −7
5
20
6
7
15
−2
12
16
Est. _______ Ans. ______
Est. _______ Ans. ______
For problems 17-32, find the sums and differences of signed fractions, integers and mixed
numbers. Estimate and determine the sign of your answer first. Then answer. Be sure to
change subtraction to addition where necessary.
1 5
17. − −
4 6
3
19. 2 − (− 8)
21.
23.
3
1
+ (5 )
4
8
2−
2
5
18.
7
−3
−( )
8
10
Est. ______ Ans. ______ 20.
5
5
7 +3
8
16
Est. ______ Ans. _____
11
20
Est. ______ Ans. ______
Est. _____ Ans. ______
Est. ______ Ans. ______
22.
1−
Est. ______ Ans. _____
24.
−
5
11
+ (− )
12
16
Est. ______ Ans. _____
Est. _______ Ans. ______
UNIT THREE: Prealgebra in a Technical World
1
1
25. 9 + 3
6
3
Est. ______ Ans. _____
26.
9
11
11
−5
16
12
Est. ______ Ans. _____
2
9
27. 6 − 4
5
20
Est. _____ Ans. ______
28.
8
11
7
−5
16
8
Est. ______ Ans. ______
Est. _____ Ans. ______ 30.
6
7
4
−2
12
9
Est. ______ Ans. ______
Est. _____ Ans. _____
−4 +
29. 10 − 7
3
8
1
9
31. 5 − 4
8
10
Applications
32.
5
7
Est. ______ Ans. _____
UPS
Show your work on your own paper. Keep your work neat so that you can check. Write a
sentence to answer each question.
33.
Susan is cutting 3 pieces of molding for her kitchen from a 16' piece. She needs pieces
1
1
1
that are 1 ft. 8 8 in, 5 ft. 7 4 in., and 7 ft. 9 16 in. Will she be able to get all of these
lengths from a 16' piece? If so, how much scrap will be left over? (FYI: Knowing the
amount of scrap gives the cutter an idea of how much room for error is allowable.)
34.
Rudy needs to cut 2 pieces of fabric from a 6-yard piece. One is 3 8 yards, and the other is
3
1
2 4 yards. How much fabric (if any) will be left over after he cuts away the material he
needs?
35.
3
Leonard needs 4 pieces of molding for his cabinets. He needs two pieces that are 8' 6 4 ",
5
7
one that is 5' 10 8 ", and one that is 4' 2 16". long. How much molding does he need?
36.
3
When Mindy competed for the first time in pole vaulting, she vaulted 7 4 ft. As a senior in
1
college her best height was 13 4 ft. How much higher did she vault in college than in her
first competition?
235
236
Section 3.5 Subtracting Fractions and Mixed Numbers
1
3
37.
The Dow reported that a stock opened at 30 8 and closed at 28 4. How much value had
the stock lost for that day?
38.
A chest and dresser are to be placed along a 14 2 ft. wall. The chest measures 3 ft. 4 8 in.
1
3
1
and the dresser measures 6 ft. 3 4 in. If they are placed on the same wall, how much wall
space will be left over? Ed wants to buy a flat screen TV and wants the biggest one that
will fit on the same wall. Will the 60" TV he wants fit in the remaining space on the wall?
39.
A student studied 2 hours, 11 minutes on Monday and 1 hour 59 minutes on Tuesday.
Express the total number of hours she studied in the two days as a mixed number.
40.
Otis is reimbursed for the miles he drives delivering pizzas. His miles for one week were:
1
7
1
1
4 10, 3 10, 1 5 and 5 2 . If he is reimbursed 50 cents per mile, how much money will he be
compensated?
41.
Rosa has two stacks of books on the floor. She measures them to see how many feet of
book shelves she needs to hold them all. One stack is 3 ft. 8 in. tall, and the other is 4 ft. 5
in. tall. Her bookcase has 6 ft. of shelves. How many feet of books will she need to get rid
of?
Review and Extend
42. You have 3 full rolls of wallpaper border at 5 yards each and you have 5 feet left over on a
third roll. You measure your bedroom and find that the length of your room is
14 feet 6 inches and the width of your room is 10 feet 4 inches.
(a) Label the diagram of a bedroom with the measurements given,
but use feet only, (no inches!)
(b) How much wallpaper border do you have?
(c) Do you need more wallpaper border to put this border around the whole room? If not,
exactly how much more wallpaper border do you need? If you do have enough wallpaper
border, how much will you have left once you finish?