11 Questions
What is the reciprocal of the fraction 2/5?
5/2
The reciprocal of a fraction is always less than 1.
False
What is the result of multiplying a fraction by its reciprocal?
1
To simplify a fraction, we need to find the greatest common divisor (GCD) of the _______ and denominator.
numerator
Match the following operations with their equivalent fraction operations:
Addition = Combining like terms with the same denominator Subtraction = Combining like terms with the same denominator Multiplication = Multiplying numerator and denominator by the same number Division = Multiplying by the reciprocal of the divisor
What do you do to find the reciprocal of a fraction?
Swap the numerator and denominator
The result of multiplying a fraction by its reciprocal is always zero.
False
What is an example of an algebraic expression that can be written as a fraction?
2/x can be written as the fraction 2/1 × 1/x
To simplify a fraction, you need to divide both the numerator and denominator by their _______________________.
greatest common divisor (GCD)
Match the following with their equivalent operations:
Multiplying a fraction by its reciprocal = Resulting in 1 Simplifying a fraction = Dividing by the greatest common divisor (GCD) Finding the reciprocal of a fraction = Swapping the numerator and denominator
You can simplify a fraction by multiplying both the numerator and denominator by the same number.
False
Study Notes
Finding Reciprocals
- To find the reciprocal of a fraction, swap the numerator and denominator.
- Example: The reciprocal of 3/4 is 4/3.
Multiplying By Reciprocals
- Multiplying a fraction by its reciprocal equals 1.
- Example: (3/4) × (4/3) = 1
- This property can be used to simplify fractions and solve equations.
Fractions In Algebra
- Fractions can be used to represent algebraic expressions.
- Example: 2/x can be written as 2 × (1/x) or 2/x
- Fractions can be added, subtracted, multiplied, and divided just like numbers.
Simplifying Fractions
- To simplify a fraction, divide both numerator and denominator by their greatest common divisor (GCD).
- Example: Simplify 6/8
- Find the GCD of 6 and 8, which is 2.
- Divide both numerator and denominator by 2: 6 ÷ 2 = 3, 8 ÷ 2 = 4
- Simplified fraction: 3/4
Finding Reciprocals
- Swap the numerator and denominator to find the reciprocal of a fraction.
- For example, the reciprocal of 3/4 is 4/3.
Multiplying By Reciprocals
- Multiplying a fraction by its reciprocal results in 1.
- This property is useful for simplifying fractions and solving equations.
- Example: (3/4) × (4/3) = 1.
Fractions In Algebra
- Fractions can represent algebraic expressions.
- Example: 2/x can be written as 2 × (1/x) or 2/x.
- Fractions can be added, subtracted, multiplied, and divided just like numbers.
Simplifying Fractions
- To simplify a fraction, divide both numerator and denominator by their greatest common divisor (GCD).
- Steps to simplify a fraction:
- Find the GCD of the numerator and denominator.
- Divide both numerator and denominator by the GCD.
- Example: Simplify 6/8.
- GCD of 6 and 8 is 2.
- Divide both numerator and denominator by 2: 6 ÷ 2 = 3, 8 ÷ 2 = 4.
- Simplified fraction: 3/4.
Finding Reciprocals
- To find the reciprocal of a fraction, swap the numerator and denominator.
- The reciprocal of a whole number is 1 divided by that number.
- Example: reciprocal of 3/4 is 4/3, and reciprocal of 5 is 1/5.
Multiplying By Reciprocals
- Multiplying a fraction by its reciprocal always results in 1.
- Example: 3/4 × 4/3 = 1.
- The numerator and denominator cancel each other out when multiplying by reciprocals.
Fractions In Algebra
- Fractions can represent algebraic expressions.
- Example: 2/x can be written as 2/1 × 1/x.
- Fractions can simplify algebraic expressions and make them easier to work with.
Simplifying Fractions
- To simplify a fraction, divide both numerator and denominator by their greatest common divisor (GCD).
- Example: 6/8 can be simplified by dividing both numbers by their GCD, which is 2, resulting in 3/4.
- Simplifying fractions makes them easier to work with and compare.
Learn how to find reciprocals, multiply by reciprocals, and use fractions in algebraic expressions.
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