24 Questions
Match the following rational numbers with their equivalent forms:
- = 10/10 0 = 10/10 -2 = -20/10 -5/6 = -20/24
Match the following statements with their explanations:
Rational numbers can be found between any two given rational numbers = Countless rational numbers can be found between two rational numbers -2 can be written as -20/10 = Conversion of rational numbers to equivalent forms 0 can be written as 0/10 = Conversion of rational numbers to equivalent forms Countless rational numbers can be found between -2 and 0 = Rational numbers can be found between any two given rational numbers
Match the following with their corresponding numerators:
- = -10 0 = 0 -5/6 = -20 -2 = -20
Match the following rational numbers with their denominators:
- = 10 0 = 10 -5/6 = 24 -2 = 10
Match the following rational numbers with their equivalent forms:
-5/6 = -20/24 -2 = -20/10 0 = 0/10
- = -10/10
Match the following with their corresponding explanations:
Countless rational numbers can be found between -5/6 and 5/8 = Rational numbers can be found between any two given rational numbers -5/6 can be written as -20/24 = Conversion of rational numbers to equivalent forms 5/8 can be written as 15/24 = Conversion of rational numbers to equivalent forms -20/24 and 15/24 are equivalent forms = Conversion of rational numbers to equivalent forms
Match the following with their corresponding properties:
Rational numbers = Can be found between any two given rational numbers -5/6 = Can be written in equivalent forms 0 = Can be written in equivalent forms
- = Can be written in equivalent forms
Match the following with their corresponding characteristics:
Rational numbers = Can be written in the form a/b where a and b are integers -5/6 = Has a denominator of 6 0 = Has a numerator of 0
- = Has a numerator of -10
Match the following expressions with their simplified forms:
2 3 5 3 1 = 1/14 − 3 2 3 1 2 = 2/35
Match the following expressions with the properties used to simplify them:
2 3 5 3 1 = Commutativity − 3 2 3 1 2 = Distributivity
Match the following numbers with their additive inverses:
8 = -8 -5 = 5 2 = -2 9 = -9
Match the following values of x with the verification of the equation -(-x) = x:
11 = True -13 = True 15 = False -17 = True
Match the following numbers with their multiplicative inverses:
8 = 1/8 -5 = -1/5 2 = 1/2 19 = 1/19
Match the following expressions with their equivalent forms:
2 3 5 3 1 = 2 3/5 1 3/5
- 3 2 3 1 2 = -3 2/5 1 3/5
Match the following equations with their solutions:
- 3 2 3 1 2 = 2/35 2 3 5 3 1 = 1/14
Match the following expressions with their correct orders of operations:
2 3 5 3 1 = Multiplication first, then division
- 3 2 3 1 2 = Division first, then multiplication
Match the property with the correct operation for rational numbers:
Commutative = Multiplication Not commutative = Subtraction
Match the operation with the correct statement for rational numbers:
Addition = a + b = b + a Subtraction = a - b ≠ b - a Multiplication = a × b = b × a Division = a ÷ b ≠ b ÷ a
Match the expression with the correct calculation for rational numbers:
$\frac{-3}{8} + \frac{1}{7}$ = $\frac{1}{7} + \frac{-3}{8}$ $\frac{2}{5} - \frac{3}{4}$ = $\frac{3}{4} - \frac{2}{5}$ $\frac{-7}{6} × \frac{-4}{5}$ = $\frac{-4}{5} × \frac{-7}{6}$ $\frac{-5}{3} ÷ \frac{4}{7}$ = $\frac{4}{7} ÷ \frac{-5}{3}$
Match the operation with the correct characteristic for rational numbers:
Addition = Always commutative Subtraction = Never commutative Multiplication = Always commutative Division = Never commutative
Match the statement with the correct operation for rational numbers:
a + b = b + a = Addition a - b ≠ b - a = Subtraction a × b = b × a = Multiplication a ÷ b ≠ b ÷ a = Division
Match the operation with the correct example for rational numbers:
Addition = $\frac{-3}{8} + \frac{1}{7}$ Subtraction = $\frac{2}{5} - \frac{3}{4}$ Multiplication = $\frac{-7}{6} × \frac{-4}{5}$ Division = $\frac{-5}{3} ÷ \frac{4}{7}$
Match the operation with the correct reason for rational numbers:
Addition = Commutative property holds Subtraction = Commutative property does not hold Multiplication = Commutative property holds Division = Commutative property does not hold
Match the operation with the correct result for rational numbers:
Addition = Equal result Subtraction = Not equal result Multiplication = Equal result Division = Not equal result
Study Notes
Commutative Properties of Rational Numbers
- Addition is commutative for rational numbers, meaning that the order of numbers does not change the result: a + b = b + a.
- Subtraction is not commutative for rational numbers, meaning that the order of numbers changes the result: a - b ≠ b - a.
- Multiplication is commutative for rational numbers, meaning that the order of numbers does not change the result: a × b = b × a.
- Division is not commutative for rational numbers, meaning that the order of numbers changes the result: a ÷ b ≠ b ÷ a.
Rational Numbers Between Two Given Numbers
- There are countless rational numbers between any two given rational numbers.
- Example: Find three rational numbers between -2 and 0. Solution: Convert -2 and 0 to rational numbers with the same denominators, and then find rational numbers between them.
- Example: Find ten rational numbers between -5/6 and 5/8. Solution: Convert -5/6 and 5/8 to rational numbers with the same denominators, and then find rational numbers between them.
Multiplication of Rational Numbers
- The commutative property of multiplication can be used to simplify multiplication of rational numbers.
- Example: Find the value of (2 -3 × (-1 × 3 - 3)) × (- 3/5).
- Solution: Use the commutative property of multiplication to simplify the expression.
Exercise 1.1
- Problems involve using properties of rational numbers to simplify expressions.
- Examples: Find the value of expressions such as (-2 × 3/5 + 3/2 × -5/6) and (-3/7 × 2/5 - 1/2 × 3/7).
- Problems also involve finding additive inverses and multiplicative inverses of rational numbers.
Test your understanding of rational numbers and algebraic operations, including commutative properties and equation solving.
Make Your Own Quizzes and Flashcards
Convert your notes into interactive study material.
Get started for free
