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Questions and Answers
What is the absolute value of a rational number?
What is the absolute value of a rational number?
- It represents the distance from zero on the number line. (correct)
- It can never be negative.
- It can be zero, but never negative.
- It is always greater than zero.
Which of the following sets does NOT include rational numbers?
Which of the following sets does NOT include rational numbers?
- The set of natural numbers ($\mathbb{N}$)
- The set of integers ($\mathbb{Z}$)
- The set of whole numbers
- The set of real numbers ($\mathbb{R}$) (correct)
What correctly represents the relationship among the sets W, ℤ, and ℚ?
What correctly represents the relationship among the sets W, ℤ, and ℚ?
- Every rational number can be expressed as a fraction of two integers. (correct)
- Integers include both positive and negative rational numbers only.
- Natural numbers encompass all integers and rational numbers.
- All natural numbers are integers but not all integers are rational.
On a number line, which of the following statements about rational numbers is true?
On a number line, which of the following statements about rational numbers is true?
Which of the following statements best describes a rational number?
Which of the following statements best describes a rational number?
Which option correctly defines the set ℤ?
Which option correctly defines the set ℤ?
What is a necessary condition for a number to be classified as rational?
What is a necessary condition for a number to be classified as rational?
What is the definition of a rational number?
What is the definition of a rational number?
Which of the following fractions represents a rational number?
Which of the following fractions represents a rational number?
How should improper fractions be represented on a number line?
How should improper fractions be represented on a number line?
Where are negative rational numbers located on a number line?
Where are negative rational numbers located on a number line?
Which of the following is NOT a rational number?
Which of the following is NOT a rational number?
Where do positive proper fractions exist on a number line?
Where do positive proper fractions exist on a number line?
What is the representation of the rational number $\frac{2}{5}$ on the number line?
What is the representation of the rational number $\frac{2}{5}$ on the number line?
What is the set of all rational numbers denoted by?
What is the set of all rational numbers denoted by?
How would you locate the number $\frac{3}{2}$ on a number line?
How would you locate the number $\frac{3}{2}$ on a number line?
What is the result of the expression $4 - 2$?
What is the result of the expression $4 - 2$?
Calculate the difference of $−5.3 − 3.45$.
Calculate the difference of $−5.3 − 3.45$.
Determine the value of $y - ( + 5)$ when $y = 4$.
Determine the value of $y - ( + 5)$ when $y = 4$.
Find the remaining length of the rope after cutting off pieces of lengths $4$ m and $7$ m from a $23$ m rope.
Find the remaining length of the rope after cutting off pieces of lengths $4$ m and $7$ m from a $23$ m rope.
What is the weight of the bananas if the total weight is $58$ kg, $11$ kg is apples, and $18$ kg is oranges?
What is the weight of the bananas if the total weight is $58$ kg, $11$ kg is apples, and $18$ kg is oranges?
Evaluate $15 - (−y - 2)$ when $y = 7$.
Evaluate $15 - (−y - 2)$ when $y = 7$.
What is the result of multiplying $7/5$ by $11/3$?
What is the result of multiplying $7/5$ by $11/3$?
What is $−3 − 2$?
What is $−3 − 2$?
What property is illustrated when rewriting the equation by grouping terms differently?
What property is illustrated when rewriting the equation by grouping terms differently?
In the equation involving sums, if $a + b = c$, which of the following is also true?
In the equation involving sums, if $a + b = c$, which of the following is also true?
Using the properties of addition, how is $(a + b) + c$ equivalent to $a + (b + c$)?
Using the properties of addition, how is $(a + b) + c$ equivalent to $a + (b + c$)?
What does the equation $a + (-b) = 0$ represent in terms of properties?
What does the equation $a + (-b) = 0$ represent in terms of properties?
When calculating the sum of $3, 5,$ and $6$ using properties of addition, the result must always equal?
When calculating the sum of $3, 5,$ and $6$ using properties of addition, the result must always equal?
Which equation shows the application of the Communicative property?
Which equation shows the application of the Communicative property?
If $a + b = c$ and $b + a$ is calculated, which outcome is expected?
If $a + b = c$ and $b + a$ is calculated, which outcome is expected?
In the example provided, when $3 + 5 + 6$ is computed, which sequence follows the Associative property correctly?
In the example provided, when $3 + 5 + 6$ is computed, which sequence follows the Associative property correctly?
What should be done first when adding two rational numbers with different signs?
What should be done first when adding two rational numbers with different signs?
In the operation −9 + 4, which sign should be chosen for the result?
In the operation −9 + 4, which sign should be chosen for the result?
For the operation −5 + 3, what is the final result?
For the operation −5 + 3, what is the final result?
What is the absolute value of the result for the operation −6 + 4?
What is the absolute value of the result for the operation −6 + 4?
How do you determine the sign of the result when adding −5 and 4?
How do you determine the sign of the result when adding −5 and 4?
When combining −5 + 3, what is the correct calculation to find the difference of the absolute values?
When combining −5 + 3, what is the correct calculation to find the difference of the absolute values?
In the expression −5 + 3, what is the correct final result?
In the expression −5 + 3, what is the correct final result?
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Study Notes
Rational numbers
- A number that can be written in the form of a/b, where a and b are integers and b ≠0, is called a rational number.
- Rational numbers are represented by the symbol ℚ, where ℚ ⊂ ℤ ⊂ ℕ.
- Rational numbers with a positive sign are located on the right side of zero on a number line, and rational numbers with a negative sign are located on the left side of zero.
- Proper fractions are located between 0 and 1 on the number line.
- Improper fractions are located on the number line by first converting them to mixed fractions.
- Mixed fractions are located on the number line by first converting them to improper fractions.
- To find the sum of two rational numbers with different signs, follow these steps:
- Take the sign of the addend with the greater absolute value.
- Subtract the absolute value of the smaller addend from the absolute value of the larger addend.
- Put the sign of the larger addend in front of the difference.
- Rational numbers can be expressed as decimals and are either terminating or repeating.
- To multiply any two rational numbers, multiply the numerators and the denominators.
- To add or subtract rational numbers with different denominators, a common denominator must be found.
- The additive identity of rational numbers is 0.
- The multiplicative identity of rational numbers is 1.
- To find the difference between two rational numbers, the smaller rational number is subtracted from the larger rational number.
Properties of Rational Numbers
- Closure Property: For any two rational numbers a and b, a + b and a × b are also rational numbers.
- Associative Property: For any three rational numbers a, b and c, (a + b) + c = a + (b + c) and (a × b) × c = a × (b × c).
- Commutative Property: For any two rational numbers a and b, a + b = b + a and a × b = b × a.
- Distributive Property: For any three rational numbers a, b and c, a × (b + c) = a × b + a × c.
- Identity Property: 0 is the additive identity and 1 is the multiplicative identity.
- Inverse Property: Each rational number has an additive inverse and each non-zero rational number has a multiplicative inverse.
Absolute Value of Rational Numbers
- The absolute value of a rational number 'a' is denoted as '│a│' and it represents the distance of 'a' from 0 on the number line.
- The absolute value of a non-zero rational number is always positive.
- The absolute value of 0 is 0.
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