# Unit 1 Preassessment: Rational Number Uses

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This quiz will not serve as a grade, but as a means to determine areas of strength and weakness. Please take your time and answer each question to the best of your ability.

• 1.

### Which ratio describes 20 basset hounds out of 45 dogs as a fraction in simplest form?

• A.

20/45

• B.

9/4

• C.

9:4

• D.

4/9

D. 4/9
Explanation
Remember, SIMPLEST FORM means to reduce, or divide the top & bottom by a common number.

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• 2.

### Bonnie purchased a 30-ounce package of Chocolate Chunk Cookies for \$2.40.  What is the cost per ounce?

• A.

\$0.88 per oz.

• B.

\$8.00 per oz.

• C.

\$0.80 per oz.

• D.

\$0.08 per oz.

D. \$0.08 per oz.
Explanation
"Per" usually means "divide."

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• 3.

### Bus Number 712 traveled 150 miles on 10 gallons of gas.  How many miles per gallon does the bus get?

• A.

15

• B.

150

• C.

1.5

• D.

0.15

A. 15
Explanation
"Per" usually means "divide."

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• 4.

### Approximately 105 out of 350 teens have their own savings account.  Express the ratio 105:350 as a fraction in simplest form.

• A.

3/1

• B.

1/3

• C.

10/3

• D.

3/10

D. 3/10
Explanation
Remember, SIMPLEST FORM means to reduce, or divide the top & bottom by a common number.

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• 5.

### Express the ratio that compares the number of purple Skittles to the total number of Skittles.

• A.

2/23

• B.

3/15

• C.

1/4

• D.

2/3

A. 2/23
Explanation
Remember, a ratio is a comparison. The first item they ask for (purple) should be written first, then the second item (the total number of Skittles) should be written second.

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• 6.

### Express 0.4 as a fraction in simplest form.

• A.

2/5

• B.

4/100

• C.

1/4

• D.

4/10

A. 2/5
Explanation
Say 0.4 in your head, "four tenths" and then write the words as fraction 4/10. Now, simplify to lowest terms.

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• 7.

### The White House is approximately 18.05 acres.  Express this decimal as a mixed number in simplest form.

• A.

18 and 1/5

• B.

18 and 5/100

• C.

18 and 1/50

• D.

18 and 1/20

D. 18 and 1/20
Explanation
Remember, a mixed number consists of a whole number and a fraction. "Simplest form" means to reduce by dividing the top & bottom by a common number.

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• 8.

### Express 0.6 as a fraction in simplest form.

• A.

6/100

• B.

3/5

• C.

6/10

• D.

1/2

B. 3/5
Explanation
"Simplest form" means to reduce by dividing the top & bottom by a common number.

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• 9.

### Write two and twelve hundredths as a mixed number in simplest form.

• A.

2 and 6/40

• B.

2 and 6/50

• C.

2 and 3/25

• D.

2

C. 2 and 3/25
Explanation
Remember, a mixed number consists of a whole number and a fraction. "Simplest form" means to reduce by dividing the top & bottom by a common number.

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• 10.

### Write 7 and  4/5 as a decimal.

• A.

7.8

• B.

7.9

• C.

7.4

• D.

7.45

A. 7.8
Explanation
To convert a mixed number to a decimal, we first convert the fraction part to a decimal. In this case, 4/5 can be written as 0.8. Then, we add the whole number part to the decimal. Thus, 7 and 4/5 can be written as 7.8.

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• 11.

### Replace the # with a number so that the fractions are equivalent:  18/21 = 6/#

• A.

7

• B.

3

• C.

4

• D.

6

A. 7
Explanation
HINT: Try simplifying the first fraction.

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• 12.

### Write 5/20 in simplest form.

• A.

1/5

• B.

1/4

• C.

4/5

• D.

1/20

B. 1/4
Explanation
Divide top and bottom by a common value.

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• 13.

### Write 42/54 in simplest form.

• A.

8/10

• B.

7/9

• C.

8/9

• D.

21/27

B. 7/9
Explanation
To simplify the fraction 42/54, we can divide both the numerator and denominator by their greatest common divisor, which is 6. When we divide 42 by 6, we get 7, and when we divide 54 by 6, we get 9. Therefore, the simplest form of 42/54 is 7/9.

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• 14.

### State the least common denominator of 8/15 and 13/25.

• A.

100

• B.

300

• C.

25

• D.

75

D. 75
Explanation
The least common denominator is the smallest multiple that both denominators, 15 and 25, can divide into evenly. The prime factors of 15 are 3 and 5, while the prime factors of 25 are 5 and 5. To find the least common denominator, we need to consider the highest power of each prime factor. In this case, the highest power of 3 is 1, and the highest power of 5 is 2. Multiplying these together gives us 3 * 5 * 5 = 75, which is the least common denominator.

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• 15.

### Write 1/4, 1/3, and 2/7 in order from least to greatest.

• A.

2/7, 1/3, 1/4

• B.

1/3, 1/4, 2/7

• C.

1/4, 2/7, 1/3

• D.

2/7, 1/4, 1/3

C. 1/4, 2/7, 1/3
Explanation
Try changing them all to decimals to compare them.

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• 16.

### Write 6x6x6x6x6 using exponents.

• A.

6^6

• B.

1^6

• C.

6^5

• D.

6^4

C. 6^5
Explanation
The given expression is 6^5. This means that the number 6 is raised to the power of 5. In other words, we multiply 6 by itself 5 times.

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• 17.

### Evaluate 4^5  ("Four to the fifth power").

• A.

1024

• B.

256

• C.

64

• D.

625

A. 1024
Explanation
When we raise a number to a power, it means that we multiply the number by itself the number of times indicated by the power. In this case, we need to multiply 4 by itself 5 times. So, 4^5 can be calculated as 4 x 4 x 4 x 4 x 4, which equals 1024.

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• 18.

### Which number is a perfect square?

• A.

36

• B.

26

• C.

32

• D.

11

A. 36
Explanation
36 is a perfect square because it can be expressed as the square of a whole number, which is 6. When 6 is multiplied by itself, the result is 36.

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