Review & Practice Worksheets
Review Adding and Subtracting Fractions
To add or subtract fractions, you need a common denominator. To make the addition or subtraction easier, find the smallest common denominator that will work. This is called the least
common denominator or LCD.
Factor the Denominators
To find the LCD, factor the denominators. In other words, find the numbers that multiply
evenly into the denominators. If any factors in the second denominator are duplicates,
remove them. Multiply the factors you have left to get the LCD.
7
11
Factor the denominators and find the LCD: 18 + 30
?1.
Find the numbers that multiply together to equal the denominators.  18 = 2 ◊ 3 ◊ 3
30 = 2 ◊ 3 ◊ 5
Multiply, but only include the common factors once.  2 ◊ 3 ◊ 3 ◊ 5
The LCD is 90.  90
Change the Denominators to the LCD
The next question is: What do I need to multiply each denominator by to get the LCD? This
is called “building” the fraction to have a different denominator. You can’t just change the
denominator itself, because that would change the value of the fraction.
What number is the “identity” for multiplication? In other words, what number can you
?2.
multiply with any value without changing that value?
The answer is one, and all fractions with equal numerator and denominator have the value
a
one. So, you will multiply each fraction by a fraction in the form a , where a is the number
you need to multiply by in order to build the denominator into the LCD.
7
11
Change the denominators to 90: 18 + 30
?3.
309
Essential Math Skills
You need to multiply 18 by something, and 30 by something else, so they both equal 90. The
factored forms of 18 and 30 give you a clue. You need to multiply each number by the factors
of 90 that were not already in the number. This is five for 18, and three for 30.
7 a 3 k 11
35 33
a 55 k 18
+ 3 30 =
+
= 90 + 90
5 (18) 3 (30)
5 (7)
3 (11)
Add or Subtract the Numerators
Once you have a common denominator, add or subtract the numerators and write the result
over the common denominator. Then reduce the fraction by dividing out common factors
from the numerator and denominator.
35
33
Add: 30 + 90
?4.
Add the numerators.  35 33 35 + 33 68 34
+
= 90 = 90 = 45
Keep the denominator.  90 90
Add or Subtract Integers with Fractions
If you are adding or subtracting an integer and a fraction, recall that an integer can be
written as a fraction with a denominator of one.
4
Subtract: 6 - 3
?5.
4 6 4
Convert the whole number to a fraction.  6 - 3 = 1 - 3
6 3
4 18 4
Convert to the least common denominator.  1 a 3 k - 3 = 3 - 3
18 4 14
Subtract the numerators.  3 - 3 = 3
Add or Subtract Mixed Numbers
To add or subtract mixed numbers, you can convert them to improper fractions. Converting
a mixed number to an improper fraction is the same as adding an integer with a fraction.
?
1
4
6.
Subtract: 3 2 - 4 7
310
1
4 7 32
Convert to improper fractions.  3 2 - 4 7 = 2 - 7
7 7
32 2 49 64
15
1
Convert to the LCD and subtract.  a 2 ka 7 k - a 7 k 2 = 14 - 14 = - 14 = - 1 14
Review & Practice Worksheets
Adding and Subtracting Fractions
Examples:
1 1 2
3+3 =3
3 1 2 1
4-4 =4 =2
1
3 2
9
15 25
8 + 3 = 24 + 24 = 24 = 1 24
1 1
1.4 + 4 = x 3 3
2.8 + 8 = x
3
1
3.8 - x = 4 5
1
4.24 - 24 = x
1 4
5.7 + 3 = x 1
20
6.4 + x = 3
4 1
7.5 + 2 = x 1 3
8.3 2 - 4 = x
9.Marta drove ¾ mile to the grocery store and then another ½ mile to her friend’s house.
If the trip home is ¾ the length of the total trip to her friend’s house, how far did Marta
drive on the round trip?
10. Daniel is cutting down a wooden fence from 51/4 feet to a new height of 31/2 feet. How
much will he need to cut from each piece of wood?
11.Summer activities at Park Community Center include a craft class for children.
a.
Tonio was given 13/4 yard of fabric to cover a photo album. He needed an additional
3/8 yard to complete the project. How much fabric should he have received to make
the cover?
b.
Andrea was given three yards of wire to make two twisted wire necklaces, one for
herself and one for her friend. When she read the instructions, she realized she
only needed 11/3 yards for each necklace. How much wire did she need to cut off the
original piece of wire in order to make both necklaces?
311
Essential Math Skills
12.Paulette is training for a marathon.
a.
Paulette ran 23/4 miles on Saturday and ran 31/2 miles on Monday. Her goal is to run
at least 10 miles each week. How many more miles does she need to run this week
to reach her goal?
b.
Paulette likes to train four days each week and run approximately the same
distance each day. What would you suggest for her schedule for the remaining
days of this week? Explain your thinking.
13.Juan went hiking on a trail that is 11/2 miles long.
a.
Juan walked ¾ of a mile and stopped to rest. How much further does he need to
walk to hike to the end of the trail and back to the trailhead? Explain your thinking.
b.
The next day Juan took the same trail. After ½ hour he arrived at the same rest
stop. He rested for 1/4 hour and then walked to the end of the trail. That took him
another 1/2 hour. He had a total of 21/2 hours to do the hike. Did he have enough time
to stop to explore at the end of the trail for 45 minutes? Explain your thinking.
14. Jorge was planning to stop for breakfast on the way to work this morning. When he
went to start his car at 6:45 a.m., it would not start. Now, he needs to take the bus. He
starts work at 9:00 a.m. and does not want to be late. He spent 1/4 of an hour checking
the bus schedule. The bus will take 11/2 hours to get to the bus stop near work. Then
he needs to walk another ¼ hour to get to work. Will he have enough time to stop for
breakfast? Describe what you think Jorge should do to get to work on time.
15.The baseball team runs around the field three times to warm up at each practice. The
dimensions of the rectangular field are 1141/2 yards by 733/4 yards. How many total yards
does each player run for practice? Explain your thinking.
312
Answers and Explanations
Adding and Subtracting
Fractions
1
1.
x= 2
3
2.
x= 4
1
3.
x= 8
1
4.
x= 6
If Jorge starts at 6:45 a.m. then it will be 8:45 a.m.
when he arrives at work. This only leaves 15 minutes
to have breakfast. Students may present varying
scenarios regarding breakfast. However, there is only
1/4 of an hour left, and that fact needs to be taken
into consideration.
15. The distance once around the field is 3761/2 yards,
twice the length plus twice the width. Since the players are running around three times, multiply by three.
Each soccer player runs 11291/2 yards at each practice.
31
10
5.
x = 21 = 1 21
77
5
6.
x = 12 = 6 12
13
3
7.
x = 10 = 1 10
3
8.
x= 24
35
3
9.
16 = 2 16 miles
3
10.1 4 feet
1
11a.2 8 yards
1
11b. 3 yard
3
12a. 3 4 miles
12b.Responses will vary. You might suggest she run 13/4
miles one day and the remaining two miles on the
fourth day. Or, you might suggest she run 17/8 miles
each day.
13a. Juan needs to walk another 3/4 of a mile to get to
the end of the trail. He then needs to walk another
11/2 miles to return back to his starting point.
Therefore, he still needs to walk a total of 21/4 miles to
complete the round trip back to his starting point.
13b.It took Juan 11/4 hours to get to the end of the trail
including the time he rested.
It would take one hour to walk the return trail
without stopping, for a total of 21/4 hours.
Juan has 1/4 hour left to explore. This means he cannot
stay there for 45 minutes, because that would require
3/4 of an hour.
14.It would take two hours to take the bus.
i