Section 1.4 - Rational Numbers

1. Which statement is true?

-5 < -3

-2.3 > -2.15

-2 2/5 < -2.4

-3.21 > -3.2

The given statement "-5

Explanation

The given statement "-5

2. Rename 3/8 as a decimal

0.375

0.38

0.4125

0.425

To convert a fraction to a decimal, divide the numerator (3) by the denominator (8). In this case, 3 divided by 8 equals 0.375. Therefore, the correct answer is 0.375.

Explanation

To convert a fraction to a decimal, divide the numerator (3) by the denominator (8). In this case, 3 divided by 8 equals 0.375. Therefore, the correct answer is 0.375.

3. Of which set does 0 not belong?

Natural numbers

Whole numbers

Integers

Rational numbers

The set of natural numbers includes all positive whole numbers starting from 1. Since 0 is not a positive number, it does not belong to the set of natural numbers.

Explanation

The set of natural numbers includes all positive whole numbers starting from 1. Since 0 is not a positive number, it does not belong to the set of natural numbers.

4. To which set of numbers does -2.75 belong?

Natural numbers

Whole numbers

Integers

Rational numbers

The number -2.75 belongs to the set of rational numbers because it can be expressed as a fraction, -11/4, where the numerator and denominator are integers. Rational numbers include integers, fractions, and decimals that can be written as a fraction. Since -2.75 can be written as a fraction, it falls under the category of rational numbers.

Explanation

The number -2.75 belongs to the set of rational numbers because it can be expressed as a fraction, -11/4, where the numerator and denominator are integers. Rational numbers include integers, fractions, and decimals that can be written as a fraction. Since -2.75 can be written as a fraction, it falls under the category of rational numbers.

5. How can 0.54 be written as a fraction?

5/9

6/11

17/30

27/50

To write 0.54 as a fraction, we need to consider the decimal place value. The digit 5 is in the hundredths place, so we can write it as 5/100. Simplifying this fraction gives us 27/50, which is the equivalent fraction for 0.54.

Explanation

To write 0.54 as a fraction, we need to consider the decimal place value. The digit 5 is in the hundredths place, so we can write it as 5/100. Simplifying this fraction gives us 27/50, which is the equivalent fraction for 0.54.

6. A basketball team has won 0.625 of its games. If the team has played 24 games, how many games has the team won?

14

15

16

18

If the basketball team has won 0.625 of its games, it means they have won 62.5% of their games. To find the number of games they have won, we multiply the percentage by the total number of games played. So, 0.625 * 24 = 15. Therefore, the team has won 15 games.

Explanation

If the basketball team has won 0.625 of its games, it means they have won 62.5% of their games. To find the number of games they have won, we multiply the percentage by the total number of games played. So, 0.625 * 24 = 15. Therefore, the team has won 15 games.

7. How can -3 2/3 be written as the quotient of two integers?

-11 / 3

-3 / 11

-11 / -3

-3 / - 11

To write -3 2/3 as the quotient of two integers, we need to convert the mixed number to an improper fraction. -3 2/3 can be written as -11/3, where -11 is the numerator and 3 is the denominator. This is the correct answer.

Explanation

To write -3 2/3 as the quotient of two integers, we need to convert the mixed number to an improper fraction. -3 2/3 can be written as -11/3, where -11 is the numerator and 3 is the denominator. This is the correct answer.

8. Which fraction is greater than 3/10, but less than 1/3?

3/8

7/20

7/25

5/16

The fraction 5/16 is greater than 3/10 because when both fractions are converted to decimals, 5/16 is approximately 0.3125 while 3/10 is 0.3. On the other hand, 5/16 is less than 1/3 because when both fractions are converted to decimals, 5/16 is approximately 0.3125 while 1/3 is approximately 0.3333. Therefore, 5/16 is the fraction that is greater than 3/10 but less than 1/3.

Explanation

The fraction 5/16 is greater than 3/10 because when both fractions are converted to decimals, 5/16 is approximately 0.3125 while 3/10 is 0.3. On the other hand, 5/16 is less than 1/3 because when both fractions are converted to decimals, 5/16 is approximately 0.3125 while 1/3 is approximately 0.3333. Therefore, 5/16 is the fraction that is greater than 3/10 but less than 1/3.

9. Which sentence is true?

All whole numbers are also natural numbers

All integers are also rational numbers

All rational numbers are also integers

All integers are also whole numbers

All integers can be expressed as fractions with a denominator of 1, making them rational numbers. This is because any integer divided by 1 will result in a fraction. Therefore, the statement "All integers are also rational numbers" is true.

Explanation

All integers can be expressed as fractions with a denominator of 1, making them rational numbers. This is because any integer divided by 1 will result in a fraction. Therefore, the statement "All integers are also rational numbers" is true.