Math Review Fractions, Ratio and Percent (Units 6 & 7)

1. What percentage of the hundredths grids below are shaded in?

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2. Write one part-to-whole and one part-to-part ratio for the following picture. Tell what

your ratio represents and what type of ratio it is.

3. Write an equivalent ratio for the two ratios in number 2. Answers can vary. Some possibilities include: (Main idea here is that whatever you do to one side you must also do to the other side of the ratio. Such as multiply by 2…)

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4. Fill in the table below:

Decimal Fraction P-t-W Ratio Percent

0.02 2/100 2:100 2%

0.34 34/100 34:100 34%

0.78 78/100 78:100 78%

0.09 9/100 9:100 9%

0.45 45/100 45:100 45%

45% 5% 75%

Part-to-part: : 4:5 : 5:4

4:5 8:10 12:15 16:20

5:4 10:8 15:12 20:16

5:9 10:18 15:27 20:36

4:9 8:18 12:27 16:36

Part-to-whole: : whole 5:9 : whole 4:9

5. Which is greater? Explain why using pictures, numbers and words.

75% or 18 = 90% 20

75% 18/20 = 90% 18/20 is greater than 75%. To demonstrate this first I changed 18/20 into a percent so that it would be easier to compare the numbers. To change 18/20 into a percent I will make an equivalent fraction that has a denominator of 100. The denominator has to be 100 because that is what percent means; out of 100. There are 5 twenties in 100 so by multiplying the fractions numerator and denominator by 5 I can create an equivalent fraction. When I multiply the numerator by 5 the answer is 90. My equivalent fraction is 90/100, which is the same as 90%. On my hundreds grids you can see that when I shade in 90 squares on one and I shade 75 squares in the other, more of the grid is shaded when I shade 90, simply because 90 is greater than 75. On the number line, 90 is closer to 100% than 75.

Picture: Option 1 - Hundreds Grid

Picture: Option 2 - Number Line

Numbers:

75% = 75/100

=

=

(If I multiply 20 by 5 it will equal 100,

so I can multiply the numerator by 5

and create an equivalent fraction

which is out of 100. This will make

the number easier to compare.)

90/100 is 90%

18 x 5 = 90

20 x 5 = 100

0% 90% 100% 10% 20% 30% 40% 50% 60% 70% 80%

6. Place the following numbers on a number line.

35% 0.60 = 60% 5% 7 = 70% 10 Explain how you placed one of the numbers. (Be sure to use your math language…benchmarks, half, tenths, less than, greater than…)

My number line starts at 0 and stops at 100. I chose these numbers because percent is out of 100. Percent can go beyond but all of my numbers will fit in the range of 1-100. Multiples of 10 are used as my benchmarks to help me space my numbers accurately and evenly.

0.60 is sixty hundredths. This means out of 100 I have 60. Since it is already out of 100 I can change it to percent easily. 0.60 is the same as 60% because they both mean 60 out of 100. On my number line I find the 60 position which I already labeled as a benchmark.

If explaining 35% answer should include: 35 is greater than 30 but is less than 40 so it will be in between the 30 and 40 benchmarks. Each benchmark is a multiple of ten so I will need to put a mark halfway between these to show 35. It needs to go halfway because 5 is half of ten.

7. Our class made $300 at the bake sale. 20% of the money will go toward decorations for the class, 40% of the money will go towards a new DVD player and the rest will go towards a pizza party. How much money will be spent on each item? Show your work!

To find 10% (which is one jump on my number line), I divide 300 by 10. I am dividing it by 10 because 10% is one tenth of 100.

0% 90% 100% 10% 20% 30% 40% 50% 60% 70% 80%

0% 90% 100% 10% 20% 30% 40% 50% 60% 70% 80%

60 270 90 240 180 210 120 150 $0 $300 30

add 30 add 30…. and so

on

300 10 = 30……….so 1 jump on my number line will be worth 30. Once I label my number line I can see how much 20% and 40% of 300 are. 20% of $300 equals $60 because….. 10% of 300 is 30. To reach 20% on my number line, I need to make 2 jumps. This means I have 2 jumps of 30. 2 x 30 = 60. 40% of $300 equals $120 because….. 10% of 300 is 30. To reach 40% on my number line, I need to make 4 jumps. This means I have 4 jumps of 30. 4 x 30 = 120. Therefore, our class spent $60 on decorations and $120 for a new DVD player. Altogether we have spent 60 + 120 = $180. To find out what is left over for a pizza party, I will subtract it from the total I started with – 300. 300 – 180 = $120. There is $120 left over for a pizza party.

8. Sarah was baking cupcakes for her class. The recipe called for 3 cups of flour, 2 eggs, and

1 cups of sugar. In order for her to have enough cupcakes for all her classmates, she had to use 12 cups of flour. How much sugar and how many eggs will Sarah need now? Show all your work!

flour:eggs flour:sugar 3: 2 3:1 12: ? 12: ?

Ans: 12: 8 Ans: 12: 4

The ratio of flour to eggs is 3 to 2. This means that for every 3 cups of flour, Sarah will need to add 2 eggs. If she uses 12 cups of flour that means she has repeated the ratio 4 times. My picture shows that if I wanted to have 12 cups of flour, I had to repeat this recipe 4 times. There are 3 cups each time so 3 cups x 4 = 12. When I repeat the recipe that means the egg portion of the recipe is being repeated also because every time she adds 3 cups of flour, she has to add 2 eggs. So if the recipe is repeated 4 times then there would be 2 x 4 = 8 eggs in it.

3 x 4 = 12 3 x 4 = 12 2 x 4 = 8 1 x 4 = 4

Original Recipe

Original Recipe

I need to repeat

the recipe 4 times

to get 12 cups of

flour. To maintain

the ratio (and the

proper recipe)

each time I add 3

cups of flour I

must also add 2

eggs.

I need to repeat

the recipe 4 times

to get 12 cups of

flour. To maintain

the ratio (and the

proper recipe)

each time I add 3

cups of flour I

must also add 1

cup of sugar.

The ratio of flour to sugar is 3 to 1. This means that for every 3 cups of flour,

Sarah will need to add 1 cup of sugar. If she uses 12 cups of flour that means she has repeated the ratio 4 times. My picture shows that if I wanted to have 12 cups of flour, I had to repeat this recipe 4 times. There are 3 cups each time so 3 cups x 4 = 12. When I repeat the recipe that means the egg portion of the recipe is being repeated also because every time she adds 3 cups of flour, she has to add 1 cup of flour. So if the recipe is repeated 4 times then there would be 4 x 1 = 4 cups of sugar in it.

9. David got $60 for his birthday. He wants to put 40% of it in the bank. How much money will he put in the bank? Show your work!

First, I need to find 10% by dividing the total (60) by 10. Once I do that, I know

what one jump on my number line will be. 60 10 = 6 (so one jump on the number line = 6)

To find 40%, I need to make 4 jumps on my number line. (each worth 6 because 10%, or one tenth, of 60 is 6). 4 jumps x 6 per jump = 24. So, 40% of 60 is 24. So David will put $24 in the bank.

10. Sonya has 20 colored pencils. She uses 5 of the pencils to draw a picture. What percentage of the pencils did she use? Show your work

=

0% 90% 100% 10% 20% 30% 40% 50% 60% 70% 80%

6

60%

60%

60%

$0 48 54 $60 30 36 42 12 18 24

add 6 for

each

jump

20 x 5 = 100

5 x 5 = 25

To find out what percentage this was, I need to create an equivalent fraction out of 100. I need to make my equivalent fraction out of 100 because that is what percent means… out of 100. If I multiply 20 by 5, I can get 100. I must also multiply the numerator by 5 because I must do the same to each part of my fraction. This is necessary because my fraction 5/20 means that out of every 20, 5 are used. If I count 5 out of every 20, I would be repeating this 5 times to get to 100 total pencils. (See picture)

You can also create an equivalent part-to-whole ratio to find the same answer because a fraction and part-to-whole ratio are the same thing just recorded a different way.

11. 30% of the school council are boys. There are 50 students in the school council. How many students are boys?

0% 90% 100% 10% 20% 30% 40% 50% 60% 70% 80%

20 15 10 5 0 50 40 35 30 25 45

add 5 for

each

jump

5 out of 20 used

Repeating the group 5 times shows what

100 pencils would look like. I have to also

repeat the same portion that is used each

time.

5 groups = 100 pencils because 20 x 5

gives me 100 pencils in total

25 out 0f the 100 are used (5 from

each group of 20) because 5 x 5 = 25

5 out of 20 used

5 out of 20 used

5 out of 20 used

5 out of 20 used

First, I need to find 10% by dividing the total (50) by 10. Once I do that, I know what one

jump on my number line will be. 50 10 = 5

To reach 30% I need to make 3 jumps on my number line (each worth 5 because 10%, or one tenth, of 50 is 5). 3 jumps x 5 per jump = 15. So, 30% of 50 is 15. On the school council of 30 people, 15 are boys.

12. Picture Improper Fraction Mixed Number

A

2

B

2

C

1

13. Place the following numbers on the number line below. Be as accurate as possible and

remember to use benchmarks.

2

= 1

3

1

= 4

Explain how you split your line with benchmarks and how you knew where to place each

number.

I started my number line at 1 because there are no numbers that are less than 1. I

ended my line at 5 because there are no numbers greater than 5. I used the whole

5 3 2 1 4

1

2

3

numbers 2, 3 and 4 as my benchmarks between 1 and 5. These benchmarks will help

me evenly and accurately space the numbers that I have to place on the number line.

To place 13/3 on my number line I changed it to a mixed number first. The

denominator is 3 so that tells me that there are 3 pieces in a whole. The numerator is

13 so that means I have 13 pieces that I must put into groups of 3. I can make 4 wholes

and will have 1 piece left over. There are 4 wholes because 13 3 = 4 with a remainder

of 1 (13 pieces split into groups of 3, because there are 3 pieces in a whole, equal 4

wholes and 1 piece left over.)

4

is greater than 4 and less than 5 so will be in between the 4 and 5

benchmarks on my number line. The denominator 3 tells me that there are 3 parts in a

whole so I will split this section of the number line into 3 equal pieces. I need to show

one third more than 4 so I will place my dot on the first line after the 4. Math words highlighted

14. You have 14 quarter pieces of pizza left over from a party. How many full pizzas are left?

Model the amount as an improper fraction and a mixed number and explain your

answer using pictures, numbers and words.

The denominator of a fraction tells you how many pieces are in a whole. If the pizza is cut into

quarters this means that the denominator of my fraction will be 4 and that there are 4 pieces in

a whole. The numerator of a fraction tells you how many pieces you have. Since there are 14

pieces, this means the numerator of my improper fraction will be 14. That means that my

improper fraction will be 14/4.

If I group the 14 pieces of pizza into groups of four to make full pizzas, I can make 3 full pizzas

and there will be 2 more pieces in the next pizza. My mixed number will be 3

(or 3

) because

the whole number tells how many full pizzas I have and the fraction portion of my mixed

number tells me how many pieces out of the next pizza I have.

4 pieces 2 pieces 4 pieces 4 pieces

4 + 4 + 4 + 2 = 14 pieces

Rating Scale Information: 1 – Answer is incorrect. 2- Answer is incorrect but shows evidence of some understanding. (Ex: may be partially right, maybe the first steps are correct…) 3- Answer is correct. Student has an understanding of the concept but might not have the more difficult questions correct. Explanations may be present but are not as detailed, or may lack use of math terminology. 4- Answer is correct and demonstrates higher level thinking (high quality) but may not be as detailed in the explanation as a 5 answer would be, or the student may need some assistance from the teacher. (ex, asked questions to clarify instructions, needed reminder to finish an answer….) 5 – Answer is correct and explanation demonstrates higher level thinking. Explanations which include pictures, numbers and words are clear, detailed and use math language. Student work was completed independently. There will be no errors on this test. **If you are striving for a 5 on your test, be sure to support your calculations in longer answer questions with a diagram and an explanation that uses math language when it asks you to show your work and explain your answer. A 5 answer will be detailed and very clearly demonstrate a deep understanding of the concept. These students will also get the more difficult (higher level) questions completely right.