Unit 1 Preassessment: Rational Number Uses

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

2/23

3/15

1/4

2/3

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.

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.

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

15

150

1.5

0.15

"Per" usually means "divide."

Explanation

"Per" usually means "divide."

3. Write 6x6x6x6x6 using exponents.

6^6

1^6

6^5

6^4

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.

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.

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

7

3

4

6

HINT: Try simplifying the first fraction.

Explanation

HINT: Try simplifying the first fraction.

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

$0.88 per oz.

$8.00 per oz.

$0.80 per oz.

$0.08 per oz.

"Per" usually means "divide."

Explanation

"Per" usually means "divide."

6. Which number is a perfect square?

36

26

32

11

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.

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.

7. Write 5/20 in simplest form.

1/5

1/4

4/5

1/20

Divide top and bottom by a common value.

Explanation

Divide top and bottom by a common value.

8. Write 42/54 in simplest form.

8/10

7/9

8/9

21/27

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.

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.

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

2 and 6/40

2 and 6/50

2 and 3/25

2

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.

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.

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

20/45

9/4

9:4

4/9

Remember, SIMPLEST FORM means to reduce, or divide the top & bottom by a common number.

Explanation

Remember, SIMPLEST FORM means to reduce, or divide the top & bottom by a common number.

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

100

300

25

75

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.

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.

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

1024

256

64

625

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.

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.

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

3/1

1/3

10/3

3/10

Remember, SIMPLEST FORM means to reduce, or divide the top & bottom by a common number.

Explanation

Remember, SIMPLEST FORM means to reduce, or divide the top & bottom by a common number.

14. Write 7 and 4/5 as a decimal.

7.8

7.9

7.4

7.45

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.

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.

15. Express 0.6 as a fraction in simplest form.

6/100

3/5

6/10

1/2

"Simplest form" means to reduce by dividing the top & bottom by a common number.

Explanation

"Simplest form" means to reduce by dividing the top & bottom by a common number.

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

2/7, 1/3, 1/4

1/3, 1/4, 2/7

1/4, 2/7, 1/3

2/7, 1/4, 1/3

Try changing them all to decimals to compare them.

Explanation

Try changing them all to decimals to compare them.

17. Express 0.4 as a fraction in simplest form.

2/5

4/100

1/4

4/10

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

Explanation

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

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

18 and 1/5

18 and 5/100

18 and 1/50

18 and 1/20

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.

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.