true or false

1. fraction cant be written as decimal.

2. natural numbers are referred to as counting numbers.whole numbers consists of counting numbers.whole numbers consist of counting numbers as well as the number 0

3. intergers do not include negative numbers.

4. classifying numbers is another phrase used for naming numbers.

5.rational numbers include fractions,decimals,terminating decimals,repeating decimals,and negative numbers.

6. irrational numbers are the same as rational numbers

7. together,rational numbers and irrational numbers form the sets of real numbers.

8.any example that proves a statement is true is a counterexample.

9. an inequality is a mathematical sentence that compares the value of two expressions using a inequality symbol, such as <or>.

10. two numbers that are the same distance from the same distance from zero on a number line but lie in opposite directions are opposites.

11. the absolute value of a number is its distance from 1 on a number line.

It usually helps answering questions like this - which are really all about definitions - by thinking up an example or two. Usually the answer isn't far behind:

1. Here's a fraction: 1/2. Can that be written as a decimal?

2. Is -5 a whole number? Is zero a whole number?

3. Is -5 an integer?

4. I name the number 3.14159... "pi". Does that classify it?

5. Are the following rational numbers? 1/2, 0.4, 0.3333333...., -10?

6. The square root of 2 is an irrational number. If it's a rational number, you can find two integers P and Q such that P/Q = the square root of 2. Can you?

7. Can you think of a real number that isn't either a rational or an irrational?

8. Here's a statement: "Grass is green". A counterexample is something that proves that the original statement cannot be true. I've just seen some green grass. Does that prove that grass is not green?

9. My wallet contains $10, whereas my friend's wallet contains $5. That describes an inequality - but it isn't a mathematical sentence (though it could be translated into one). Or do we mean the *mathematical definition* of an inequality?

10. Is +5 the opposite of -5? If I make $5 profit, is that the opposite of saying that I make a loss of $5? (I think there's an element of semantics here, to be honest.)

11. What is the absolute value of 10? Is it 9? Because that's the distance between 10 and 1 on a number line.

Does that help?

jjlk

1. False. Fractions can be written as decimals. For example, 1/2 is equivalent to 0.5 in decimal form.

2. True. Natural numbers refer to counting numbers, and whole numbers include counting numbers and the number 0.

3. False. Integers do include negative numbers. Integers are a set of numbers that include counting numbers, their negatives, and zero.

4. False. Classifying numbers and naming numbers are not interchangeable phrases. Classifying numbers refers to categorizing numbers based on their properties, while naming numbers refers to assigning names to specific numbers (e.g., one, two, three).

5. True. Rational numbers indeed include fractions, decimals, terminating decimals, repeating decimals, and negative numbers.

6. False. Irrational numbers are not the same as rational numbers. Irrational numbers cannot be expressed as fractions or decimals, and they do not terminate or repeat.

7. True. Rational numbers and irrational numbers together form the sets of real numbers, which include all possible numbers on the number line.

8. False. A counterexample is an example that disproves a statement, not proves it to be true. To prove a statement true, one needs to provide a valid proof or logical reasoning.

9. True. An inequality is indeed a mathematical sentence that compares the value of two expressions using inequality symbols like < (less than) or > (greater than).

10. True. Two numbers that are equidistant from zero but in opposite directions on a number line are referred to as opposites.

11. False. The absolute value of a number is its distance from zero on a number line, not specifically 1. The absolute value of a number is always positive.

1. False. A fraction can be written as a decimal. To convert a fraction to a decimal, divide the numerator (the top number) by the denominator (the bottom number). For example, 1/2 can be written as 0.5 in decimal form.

2. True. Natural numbers are often referred to as counting numbers and include positive integers starting from 1. Whole numbers include counting numbers as well as the number 0.

3. False. Integers include negative numbers as well as positive numbers and zero. So, negative numbers are part of the set of integers.

4. True. Classifying numbers refers to the process of categorizing or naming different types of numbers based on their properties. It is another phrase used for naming numbers.

5. True. Rational numbers include fractions, decimals, terminating decimals (decimals that end), repeating decimals (decimals that have a repeating pattern), and negative numbers. They can be written as a ratio of two integers.

6. False. Irrational numbers are not the same as rational numbers. Irrational numbers cannot be expressed as fractions and have non-repeating, non-terminating decimal representations, such as the square root of 2 or pi.

7. True. Rational numbers and irrational numbers together form the set of real numbers. Real numbers include all rational and irrational numbers.

8. False. A counterexample is an example that disproves a statement. It shows that the statement is false. Examples that prove a statement true are simply examples or instances that support the statement.

9. True. An inequality is a mathematical sentence that compares the values of two expressions using inequality symbols, such as < (less than) or > (greater than).

10. True. Two numbers that are equidistant (the same distance) from zero on a number line but lie in opposite directions are called opposites. For example, -3 and 3 are opposites.

11. False. The absolute value of a number is the distance of that number from 0 on a number line, not 1. The absolute value is always positive or zero. For example, the absolute value of -5 is 5.