Identify all names that apply to the number 42/7%0D%0A42%0D%0A7%0D%0A .

Question

whole number%0D%0Awhole number%0D%0A%0D%0Ainteger%0D%0Ainteger%0D%0A%0D%0Arational number%0D%0Arational number%0D%0A%0D%0Areal number

Answer 1

The number \( \frac{42}{7} \) simplifies to 6. Thus, the names that apply to the number 6 are as follows:

• Whole number: Yes, since 6 is a non-negative integer.
• Integer: Yes, as 6 is a whole number (which is a subset of integers).
• Rational number: Yes, since 6 can be expressed as \( \frac{6}{1} \), which is a ratio of two integers.
• Real number: Yes, as all rational numbers are also real numbers.

So, the complete list of names that apply to the number is:

• Whole number
• Integer
• Rational number
• Real number

Answer 2

only Rational number and Real number

The set of real numbers is a subset of the set of rational numbers.%0D%0AResponses%0D%0A%0D%0Atrue%0D%0Atrue%0D%0A%0D%0Afalse

Answer 3

The statement "The set of real numbers is a subset of the set of rational numbers" is false.

Here's the reasoning:

• The set of rational numbers consists of all numbers that can be expressed as the quotient of two integers (where the denominator is not zero). This includes integers, fractions, and whole numbers.
• The set of real numbers includes all rational numbers as well as all irrational numbers (numbers that cannot be expressed as a simple fraction, such as \(\sqrt{2}\) or \(\pi\)).

Since the real numbers encompass both rational and irrational numbers, the real numbers cannot be a subset of the rational numbers. Thus, the correct response is false.

Answer 4

Match the real-world situation with the type of numbers that would be used in that situation.

The measurements in a cookie recipe.%0D%0AThe temperature shown on a digital thermometer that does not use decimals.%0D%0AThe number of fingers in a room of five people.%0D%0AThe number of people shopping at a grocery store.
options are whole numbers. The tepmtature shown on a digital thermometer that does not use decimals. the number of 5 fingers in a room of 5 people. the number of people shopping at a grocery store.

Answer 5

Here's how to match the real-world situations with the appropriate type of numbers:

1. The measurements in a cookie recipe:

   • Option: can be fractions or whole numbers. (This would typically use rational numbers, but if we consider only whole numbers, this could apply to specific cases, like cups of flour.)

2. The temperature shown on a digital thermometer that does not use decimals:

   • Option: whole numbers. (Since there are no decimals, the temperature would be represented as whole numbers only.)

3. The number of fingers in a room of five people:

   • Option: whole numbers. (Since each person has a specific whole number of fingers, typically 10, the total number of fingers would also be a whole number.)

4. The number of people shopping at a grocery store:

   • Option: whole numbers. (The count of people is always a whole number.)

So the matches would be:

• The measurements in a cookie recipe: (Rational numbers or whole numbers, depending on the recipe)
• The temperature shown on a digital thermometer that does not use decimals: Whole numbers.
• The number of fingers in a room of five people: Whole numbers.
• The number of people shopping at a grocery store: Whole numbers.

Answer 6

The measurements in a cookie recipe. = ratinal numbers.
The temperature shown on a digital thermometer that does not use decimals. = integers
The number of fingers in a room of five people. = natural numbers
The number of people shopping at a grocery store. = whole numbers

Answer 7

Thank you for providing your associations. Here's how they match:

1. The measurements in a cookie recipe:

   • Your match: Rational numbers.
   • Explanation: This is correct, as measurements in recipes can include fractions and whole numbers (like 1/2 cup or 2 cups).

2. The temperature shown on a digital thermometer that does not use decimals:

   • Your match: Integers.
   • Explanation: This is also correct because temperatures are often displayed as whole numbers without decimal points.

3. The number of fingers in a room of five people:

   • Your match: Natural numbers.
   • Explanation: This is accurate, as the number of fingers (10 fingers per person) is a positive whole number starting from 1.

4. The number of people shopping at a grocery store:

   • Your match: Whole numbers.
   • Explanation: This is correct as well, since the number of people cannot be negative and includes zero.

Your classifications are perfectly reasonable and accurate based on the definitions of these sets of numbers. Thank you for clarifying your matches!