1 Ratios & Proportions
1 Ratios & Proportions
Explanation:
Step 2) Now read the question and understand you are being asked about a
ratio.
Step 3) We have to write the ratio of the number of students who are
staying at home to the number of students who are going on a picnic.
Or
We can simplify the ration further if we divide both with the common
number of 3. The answer will be 1:10.
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2) There are 42 people sitting in chairs on the beach. There are 16 people
sitting on the ground at the beach. What is the ratio of the number of people
sitting in chairs to the number of people sitting on the ground at the beach?
a) 42:16
b) 30:16
c) 15:42
d) 42:8
3) 9 children want chocolate cake and 6 children want truffle cake. What is
the ratio of the number of children that want chocolate cake to the number
of children that want truffle cake? Check [ ] the correct answer.
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2. There are 17 occupied seats on the bus, 11 seats are empty. What is the
ratio of number of occupied seats to empty seats?
3. 15 boys and 16 girls took part in the basketball competition. What is the
ratio of the number of girls to the number of boys who participate in the
competition?
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6. There are 8 male teachers and 5 female teachers who teach English in the
school. What is the ratio of the number of male teachers to the number of
female teachers?
7. In the swimming pool, 26 people can swim and 20 people do not know
how to swim. What is the ratio of the number of people who can swim to
those who do not know how to swim?
8. During the rainy season 45 people are wearing raincoats and 35 people
are using umbrellas at the picnic spot. What is the ratio of the number of
people in raincoats to the number of people using umbrellas at the picnic
spot?
10. Elis’s family ordered 4 veggie crunch pizzas and 2 double cheese crust
pizzas. What is the ratio of the number of veggie crunch pizzas to the
number of double cheese crust pizzas?
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           1                 6       10                                      18
  1                                                 2
           5       20                                       9     18     27       36
           5                15                              1      3         5    7
  3                                                 4
           6       12                24                     3
           1        2       3        4                      3                9    12
  5                                                6
                                     12                     7     14
          10                30       40                     6                18
  7                                                 8
           5       10                                       7     14              28
           6       12        18      24                     1      4         5    9
  9                                                 10
           4                                                2
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           2                 6       10                                      3
  1                                                 2
           4        8                                       7     14         21   28
           8                40       48                     2      6         8    10
  3                                                 4
           5       10       25       30                     5
           3        9       21       27                     4                12   16
  5                                                6
                                     36                     6     12
           11               33       44                     5                15
  7                                                 8
          15       30                                      12     24              48
           1        2        3        4                    2      4          8    10
  9                                                 10
           2                                               3
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4. 75 people like tea and 25 people like coffee. What is the ratio
of the number of people that like tea to the number of people
that like coffee?
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b. David can write 600 words in an hour. How many words can he write each
minute?
Explanation:
Step 2) Read the question again to make sure you understand what
information is wanted.
b. In 1 hr = 600 words
1 min = 60 seconds
1 min = 600/ 60
1 min = 10 words
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3) Barbara spent $144 on her birthday party for 18 guests. If the cost is at
the same rate, how many guests will there if she spends $176?
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1. Susan tips at the rate of $75 to 5 waiters. How many waiters will she be
tipping, if she can afford a $90 tip?
4. A water cooler fills 150 glasses in 30 minutes. How many glasses of water
can the cooler fill per minute?
5. A car can travel 120 km in 2 hours. How long will it take the car to travel
300 km?
6. Amilio’s designs call for 7 rectangles in every 140 cm. How many
rectangles will be present in 220 cm?
7. 2 balls can complete a full rotation in 120 minutes. How many balls can
complete a full rotation in 180 min?
8. Jeff’s trip will cost $9 if he has 2 attendees at the conference. If there are
36 attendees, how much will the trip cost Jeff?
10. Maria has 64 flowers. She makes 8 bouquets with the flowers. How
many bouquets of flowers will she have if she has 80 flowers?
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Match the word problems to their answers. Write the letter of the answer
that matches the problem.
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If you had 8 of those parts end to end how long would it be?
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            a.                       b.
       4         12              5        15
8 24
12 36 15 45
16 20 60
20 60 25 75
a. 4 to 20
b. 6 to 36
c. 13 to 72
d. 5 to 25
            Yes
            no
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1. 11 16
22 32
48
44 64
55 80
      2.
               9        7
18 14
27 21
36 28
      3.
               4        6
8 12
16 24
20 30
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1. In Lisa’s class, 24 of the students are tall and 12 are short. In Paul’s class
15 students are tall and 20 students are short. Which class has a higher
ratio of tall to short students?
2. At Janine’s party, the orchestra has 10 guitar players and 8 flute players.
At Brown’s party, the orchestra has 12 guitar players and 7 flute players.
Which party has a higher ratio of guitar to flute players?
3. Robert’s recipe has 5 onions and 9 tomatoes for the pizza. Jeff’s recipe
has 8 onions and 10 tomatoes for the pizza. Whose recipe has a lower ratio
of onions to tomatoes?
4. Lee bought 7 Zara jeans and 9 shirts from the Wall Street. Nancy bought
6 Zara jeans and 8 shirts from the Wall Street. Who has the lower ratio of
jeans to shirts?
4 bags to 8 purses
5 bags to 10 purses
Yes No
12 birds to 60 animals
17 birds to 85 animals
Yes No
9 pencils to 50 erasers
7 pencils to 49 erasers
Yes No
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2.   Paul can walk 15 steps in 5 minutes. How long does it take Paul
     to walk 75 steps at the same speed?
9.   The sum of two numbers is 150. The ratio of the same two
     numbers is 3:2. Find the bigger number.
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9.   The sum of two numbers is 200 and the two numbers are in a
     ratio of 4:6. Find the larger number.
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8.   Mazy is looking for his bow and discovers that he has 20 shirts
     for every 2 pair of bows. If he has 50 shirts, how many pairs of
     bows does he have?
9.   Two numbers are in a ratio of 7:4. Their sum is 220. Find the
     bigger number.
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3.   Jixi is at the shop and sees that 7 antiques cost $14. He needs
     56 antiques to create a small museum. How much will 56
     antiques cost?
8.   Mickey is looking for his ties and discovers that he has 20 shirts
     for every 4 ties. If he has 30 shirts, how many ties does he
     have?
9.   Two numbers are in a ratio of 5:4. Their sum is 720. Find the
     bigger number.
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4 dogs to 12 cats
5 dogs to 15 cats
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Answer:
a) Start with what you know.
3 boys =
2 girls =
3. Combine the information to show the composition of the group. If the total number of students is
equal to 250 and is composed of 5 groups, each group has 50 (250/5) students. The diagram will look
like the following:
4. To find the total number of girls, add the segments 50 + 50 = 100 girls.
5. To find the total number of boys, add the segments 50 + 50 + 50 = 150 boys.
Answer: There are 150 boys and 100 girls in the school.
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2. The tape diagram below displays the homeruns scored by three players
during a baseball game. How many homeruns did Rich score?
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1. During a clearance sale, a toy shop offers a 20% discount on all toys. You purchased
a Barbie doll and received a $10 discount. What was the total amount paid for the doll?
Use a tape diagram to solve the problem.
3. David had $80. He spent 4/5 of his money on books. How much money did he have
left? Use a tape diagram to solve the problem.
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1. The price of a small used car is three times greater than the price of a
used motorcycle. If the price of the motorcycle is $950, find the price of
the car. Use a tape diagram to solve the problem.
2. In a bag there are red and blue balls in the ratio of 2:7. If there are 14 red balls, find the number
of blue balls in the bag. Use a tape diagram to solve the problem.
3. Look at the tape diagram below for the number of boys and the number of girls in a school. Find the
total number of students in the school.
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2. Rich has a 32 centimeter long board. Hema has a 23 centimeter long board. What is
the length of their boards together? Draw a tape diagram to represent the answer.
3. Maria’s pay last week was $300. She spent $225 for
groceries. What percent of her pay was spent on groceries?
Use a tape diagram to justify your answer.
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1. Mr. John’s class took a vote for the food at their class party. Pizza
received 15 votes, but hamburgers only received 5. How many votes
did pizza receive for each hamburger vote? Use a tape diagram to
justify your answer.
2. In 2012, Katrina raised $14 for the school library. In 2013 she raised five times as much money.
How much money did she raise in 2013? Draw a tape diagram to solve the problem.
3. The ratio of boys to girls in the class is 6:8. There are 56 children in the class. How many more girls
than boys are there in the class? Use the tape diagram below to help you.
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Sally is making pies. Sally took 2 hours to knead the dough. The dough
contained 6 kilograms of flour. How long do you think it will take Sally to
knead 36 kilograms of flour? Solve using unit rates.
Explanation:
36 =3xn
12 =n
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2) Maria threw a party for the promotion she received. The party costs $20
for two people. If she invited 20 guests, what would the cost be? Solve using
unit rates.
3) Troy rides his bike 75 kilometers in 1 hour. He rides for another 5 hours.
How many kilometers can Troy ride in that time is he maintains his pace?
Solve using unit rates.
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4. Veronica loves to create creative things. She can make 5 craft pieces in 5
days. On the basis of a contract she has to make 20 pieces of crafts. How
many days will she take?
5. Brown has his own bakery. He baked 5 cakes per day. Due to the
occasion of Christmas, he started to bake 12 cakes per day. In the whole
Christmas week how many cakes will he bake?
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6. Mr. White can travel for 6 hours while taking 3 breaks of 10 minutes each.
Once, he had to travel for 36 hours. How many minutes in breaks did he
take?
7. Sofia learned 10 recipes to create party dishes. She learned these recipes
in two weeks. How many recipes can Sofia learn in 5 weeks?
9. Miss Bird is going to launch an exhibition. Miss Bird can make 8 sculptures
in 6 months. If she prepared 12 sculptures, how much time would she take?
10. Charles is going to buy 3 computer tables for $390. If he pays the same
rate, how much would it cost for 8 computer tables?
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Explanation:
Step 1) The unit price is the price per item or per unit of measure.
$40 ÷ 5 = $8.00
$70 ÷ 8 = $8.75
$50 ÷ 4 = $12.50
The unit price for the 5 rose soaps for $40.00 is the lowest. Rose soaps are
the best buy.
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1) Jolly went to the book shop. There she bought four books for $350. She
sold a book to her friend and got back 30% of her money. How much money
did she charge her friend for the book?
2) Kip has a handbag shop. Each bag costs $200. Kip is having a 20% off
sale on each bag. What is the cost of a bag now?
3) Troy bought 4 dozen bananas. 40% of the bananas were used to make
custard and 10% of the bananas were given to his son. Write the number of
bananas Troy had left?
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1. In a department store the owner paid $15 for 1 kg of sugar. The owner
marked the price up by 10% for the customers. How much does he charge
for 1kg of sugar?
2. Tom and Jerry went out for dinner. They ordered a nice meal and their bill
was $300. They also paid 15% tax on their bill. What was the amount of the
tax they paid?
4. Hall adds 50% of the entire 3-liter oil bottle to a bowl. How much oil did
he use?
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8. In our hall, there are 10 fans, but only 60% of the fans are working. Write
the number of fans that are out of order.
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  Match the following questions to their answers. Write the letter of the
  answer that matches the question.
_______ 1. 60 % of 90 a. $32
_______ 2. 80 % of 70 b. $27
_______ 3. 30 % of 10 c. $54
_______ 4. 50 % of 32 d. $9
_______ 5. 90 % of 30 e. $56
_______ 6. 40 % of 80 f. $1
_______ 7. 90 % of 100 g. $3
_______ 8. 20 % of 5 h. $24
_______ 9. 75 % of 32 i. $16
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4. William went to the toy shop. There he bought two toys at the
cost of $550. A few years later, he sold one of the toys to his
friend and got 5% of his money back. How much money did the
friend pay for the toy?
5. Heidi went to the TV shop. There she bought five TVs at the
cost of $1,025. She sold a single TV to her friend and got 30% of
her money back. How much money did she charge her friend for
the TV?
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5. Samsung has a storage area that has 3,210 items. All the
items are laptops or cell phones. 35% of the items are cell
phones. How many laptops are in the storage locker?
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Explanation:
                            ଷ
30 to 100 : 30 :100     :         = 0.3
                            ଵ
x = 0.3 (120)
x = 36
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6. What is 6% of 90?
7. What is 18% of 5?
9. What is 7% of 10?
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          1.
_______             What is 25% of 100?                   a.   11.5%
          2.
_______             What is 41% of 60?                    b.   105.6%
          3.
_______             What is 23% of 50?                    c.   24.6%
          4.
_______             What is 35% of 75?                    d.   77%
          5.
_______              What is 97% of 155?                  e.   0.4%
          6.
_______              What is 120% of 88?                  f.   25%
          7.
_______              What is 10% of 4?                    g.   150.35%
          8.
_______              What is 18% of 31?                   h.   1.6%
          9.
_______              What is 55% of 140?                  i.   26.25%
          10.
_______              What is 8% of 20?                    j.   5.58%
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1. 90% of 550 =
2. 50% of 200 =
3. 25% of 800 =
4. 35% of 650 =
5. 70% of 650 =
6. 65% of 780 =
7. 80% of 420 =
8. 45% of 650 =
9. 75% of 750 =
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12. 5% of 800 =
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Step 3: 0.4 x 50 = 20
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  3. What is 5% of 60?
                                               8. What is 25% of 75?
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Explanation:
1:3.3
2: x
    x
.
1x = 6.6
x = 6.6
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7 centimeters
60 millimeters
3) Divide.
40 yards 2 feet ÷ 2
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2) 8 m 12 cm = ____ cm
6) Multiply.
7) Divide.
8) Multiply.
9) Divide.
10) Multiply.
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  Match the word problems to their answers. Write the letter of the answer
  that matches the problem.
_______ 1. 7 qt – 4 qt 1 pt a. =
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1. Multiply.
2. Multiply.
3. Multiply.
4. Multiply.
5. Multiply.
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Explanation:
The problem is basically looking for us to find: 19% of 846
We are asked to use the decimal method. This tells us to convert the
percentage to a simple decimal and multiply it by the integer in
question.
If we consider that 1 = 100%, this would mean that 0.19 = 19%
To complete the problem: 0.19 x 846 = 160.74
160.74 would be rounded up to 161.
161 asteroids could severely damage the spaceship.
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3. A Tricky One for You: Sheila collects bottle caps. 23% of the bottle
caps in her collection are not perfectly round. Sheila has 412 bottle
caps in her collection. How many bottle caps in her collection are
perfectly round?
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                Problems                                 Workspace
Example: 15% of 40                           15%    40
                                               0.15 40
Answer: 6                                      6
18% of 50
Answer:
20% of 55
Answer:
6% of 100
Answer:
8% of 150
Answer:
25% of 80
Answer:
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                Problems                              Workspace
Example: 35% of 180                          35%    180
                                               0.35 180
Answer: 63                                     63
32% of 200
Answer:
30% of 30
Answer:
19% of 300
Answer:
8% of 150
Answer:
20% of 95
Answer:
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                Problems                              Workspace
Example: 31% of 200                          31%    200
                                               0.31 200
Answer: 62                                     62
36% of 275
Answer:
42% of 500
Answer:
45% of 320
Answer:
55% of 80
Answer:
75% of 16
Answer:
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                Problems                              Workspace
Example: 26% of 300                          26%    300
                                               0.26 300
Answer: 78                                     78
15% of 360
Answer:
30% of 220
Answer:
25% of 280
Answer:
60% of 230
Answer:
45% of 60
Answer:
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Explanation:
The fraction method tells us to put the percentage value over 100
and multiply the numerator by the given integer.
Step 1) We are looking for 26% of 364.
                        ,
Step 2)     x 364 =         = 94.64 or 95 (rounded)
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3. Lilo is allergic to mushrooms. His brother Mason has to make all of the
mushrooms pizzas that are ordered. 15% of all of the pizzas ordered have
mushrooms on them. This month there were 9,456 pizza orders. How many
mushroom pizzas did Mason make this month?
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                Problems                                 Workspace
Example: 25% of 36                           25%    36
                                                    36
Answer: 9
16% of 150
Answer:
22% of 650
Answer:
8% of 75
Answer:
11% of 400
Answer:
34% of 250
Answer:
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                Problems                                  Workspace
Example: 18% of 200                          18%    200
                                                    200
Answer: 36
36
19% of 100
Answer:
23% of 500
Answer:
9% of 400
Answer:
14% of 350
Answer:
41% of 800
Answer:
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                Problems                                   Workspace
Example: 40% of 815                          40%     815
                                                     815
Answer: 326
326
25% of 464
Answer:
20% of 185
Answer:
10% of 210
Answer:
28% of 225
Answer:
5% of 580
Answer:
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                Problems                                   Workspace
Example: 20% of 780                          20%     780
                                                     780
Answer: 156
156
15% of 480
Answer:
12% of 275
Answer:
11% of 900
Answer:
44% of 75
Answer:
48% of 275
Answer:
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Explanation:
We are told to use the ratio/proportion method. To use this method we convert the
percentage to a fraction and then place our integer under an unknown variable (x).
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              Problems                                       Workspace
Example: 22% of 200                        22%         200
20% of 225
Answer:
18% of 800
Answer:
63% of 400
Answer:
17% of 300
Answer:
25% of 440
Answer:
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Name ______________________________                      Date __________________________
                Problems                                      Workspace
Example: 75% of 20                           75%         20
23% of 1100
Answer:
28% of 100
Answer:
33% of 400
Answer:
35% of 240
Answer:
10% of 80
Answer:
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                Problems                                      Workspace
Example: 6% of 50                            6%         50
8% of 125
Answer:
70% of 10
Answer:
25% of 48
Answer:
60% of 315
Answer:
45% of 280
Answer:
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               Problems                                       Workspace
Example: 9% of 700                          9%          700
5% of 80
Answer:
13% of 1200
Answer:
4% of 75
Answer:
70% of 650
Answer:
25% of 112
Answer:
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Finding the Percentage of a Decimal Value Lesson
Explanation: The easiest method for finding the percentage of any value is to:
Step 1) convert a percentage to a decimal.
                                            18% of 58.34
Step 1) Convert percentage to a
                       decimal.
                                            18% = 0.18
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Finding the Percentage of a Decimal Value Guided Lesson
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Percentages of Decimals
Homework 1
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Comparing Percentages of Values Lesson
Explanation:
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Comparing Percentages of Values Guided Lesson
1) 43% of 68 or 34% of 86
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Student name_______________________________ Score ______________
  A. 28% OF 300
  B. 35% OF 250
ANSWER:
  A. 16% OF 500
  B. 25% OF 450
ANSWER:
  A. 15% OF 600
  B. 30% OF 450
ANSWER:
  A. 56% OF 250
  B. 65% OF 110
ANSWER:
  A. 36% OF 510
  B. 90% OF 450
ANSWER:
  A. 15% OF 500
  B. 25% OF 300
ANSWER:
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Student name_______________________________ Score ______________
  A. 23% OF 200
  B. 25% OF 150
ANSWER:
  A. 19% OF 4200
  B. 25% OF 3800
ANSWER:
  A. 45% OF 650
  B. 30% OF 485
ANSWER:
  A. 36% OF 250
  B. 65% OF 110
ANSWER:
  A. 36% OF 510
  B. 28% OF 450
ANSWER:
  A. 75% OF 550
  B. 65% OF 333
ANSWER:
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Student name_______________________________ Score ______________
  A. 63% OF 521
  B. 36% OF 251
ANSWER:
  A. 51% OF 420
  B. 28% OF 290
ANSWER:
  A. 26% OF 750
  B. 45% OF 950
ANSWER:
  A. 63% OF 520
  B. 56% OF 480
ANSWER:
  A. 39% OF 710
  B. 41% OF 550
ANSWER:
  A. 95% OF 420
  B. 85% OF 520
ANSWER:
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Student name_______________________________ Score ______________
  A. 11% OF 251
  B. 22% OF 151
ANSWER:
  A. 49% OF 241
  B. 75% OF 362
ANSWER:
  A. 62% OF 570
  B. 54% OF 625
ANSWER:
  A. 36% OF 250
  B. 25% OF 125
ANSWER:
  A. 93% OF 520
  B. 52% OF 950
ANSWER:
  A. 58% OF 333
  B. 85% OF 200
ANSWER:
92Page : © www.mathworksheetsland.com