29 Questions
If the sum of two rational numbers is -4 and one of them is 6, what is the other number?
-10
If the sum of two rational numbers is -5 and one of them is -3, what is the other number?
-2
What should be added to -5 to get -2?
-3
What should be added to 2 to get -1?
-3
If we subtract 5 from -3, what is the result?
-8
What does it mean when two rational numbers are considered equivalent?
Their values are equal.
What is the product of -18 and 4 in the context of rational numbers?
-72
Which of the following sets of rational numbers are equivalent to each other?
{-15, -30, -45, -60}
In the context of rational numbers, what is the result when dividing -5 by -48?
30
If two rational numbers have different numerators but the same denominator, are they considered equivalent?
No
What is a rational number that is neither positive nor negative?
0
What is the result of adding 5/4 and 11/(-8)?
-3/4
What is the additive inverse of -11/8?
-8/11
What is the result of multiplying -15 and its additive inverse?
30
What is the sum of -3/5 and 7/8?
-13/40
What is the result of -(5/2) + 3?
-5/2
What is the difference between 21/8 and -11/4?
-9/4
What do the points A', B', and C' on the number line represent?
Integers
Why is a rational number expressible as a terminating decimal?
If its denominator has only prime factors 2 and 5
How is the rational number -2 represented on the number line?
-11/4
What does it mean for a rational number to be expressible as a repeating decimal?
Its denominator has prime factors other than 2 and 5
What type of decimal does every rational number end up being?
Repeating decimal
How can you determine if a rational number will be a terminating decimal?
By checking if its denominator has no prime factors other than 2 and 5
What is the additive inverse of 9?
-5
Express $-32$ in standard form.
-40
What should be added to $-3$ to get $5$?
8
What is the multiplicative inverse of $7$?
1/7
What is the sum of $-2$ and its multiplicative inverse?
0
Which rational number is equivalent to $-14$?
-21
Study Notes
Equivalent Rational Numbers
- Two rational numbers are equivalent if they have the same value.
- Example: –3/4 and –18/24 are equivalent rational numbers.
- To find equivalent rational numbers, multiply the numerator and denominator by the same non-zero integer.
Finding Rational Numbers Equivalent to a Given Ratio
- Multiply the numerator and denominator of the given ratio by different integers to find equivalent rational numbers.
- Example: Find four rational numbers equivalent to 5/9.
- 5 × 2 = 10, 9 × 2 = 18 => 10/18
- 5 × 3 = 15, 9 × 3 = 27 => 15/27
- 5 × 4 = 20, 9 × 4 = 36 => 20/36
- 5 × 5 = 25, 9 × 5 = 45 => 25/45
Additive Inverse of a Rational Number
- The additive inverse of a rational number a/b is –a/b.
- Example: The additive inverse of 6/11 is –6/11.
- The additive inverse of a rational number can be found by changing the sign of the numerator.
Difference of Two Rational Numbers
- The difference of two rational numbers a/b and c/d is a/b – c/d = (ad – bc)/bd.
- Example: Find the difference of 5/6 and 3/4.
- 5/6 – 3/4 = (5 × 4 – 3 × 6)/(6 × 4) = (20 – 18)/24 = 2/24
Multiplication of Rational Numbers
- The product of two rational numbers a/b and c/d is (a × c)/(b × d).
- Example: Find the product of 3/5 and 4/7.
- (3 × 4)/(5 × 7) = 12/35
Representation of Rational Numbers on the Number Line
- Rational numbers can be represented on the number line by dividing the line into equal parts and marking the points.
- Example: Represent 3/11 on the number line.
Rational Numbers as Decimals
- A rational number can be expressed as a terminating decimal or a repeating decimal.
- A rational number is expressible as a terminating decimal if its denominator has no prime factor other than 2 and 5.
- A rational number is expressible as a repeating decimal if its denominator has at least one prime factor other than 2 and 5.
Standard Form of a Rational Number
- A rational number is in standard form if the denominator is positive and the numerator and denominator have no common divisor other than 1.
- Example: 12/16 is not in standard form, but it can be simplified to 3/4, which is in standard form.
Multiplicative Inverse of a Rational Number
- The multiplicative inverse of a rational number a/b is b/a.
- Example: The multiplicative inverse of 7/3 is 3/7.
Properties of Rational Numbers
- The sum of a rational number and its additive inverse is 0.
- The product of a rational number and its multiplicative inverse is 1.
Test your understanding of adding and subtracting rational numbers with these practice questions. Solve for the missing rational numbers in equations involving addition and subtraction. Also, practice adding or subtracting a number to reach a specific sum or difference.
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