In this Grade 7 Saxon Math Course 2 lesson, students learn to reduce fractions using prime factorization and to find the greatest common factor of two numbers. The lesson also introduces canceling, a technique for reducing fractions before multiplying by pairing any numerator with any denominator across two or more fractions. These methods are applied to increasingly complex fraction multiplication problems to simplify calculations efficiently.
Section 1
📘 Reducing Fractions, Part 2
Instead of reducing a fraction after multiplying, we can reduce before we multiply. This process, also known as canceling, works by pairing any numerator with any denominator to divide out common factors.
Next, we'll walk through several examples, including how to use prime factorization to find common factors and how to cancel across multiple fractions at once.
Section 2
Using prime factorization to reduce
To reduce a fraction using prime factorization, rewrite the numerator and the denominator as products of their prime factors. Then, identify and cancel out pairs of common prime factors that form a fraction equal to 1.
Think of this as a matching game for numbers! By breaking down big numbers into their prime building blocks, you can easily spot the common parts and remove them. This method guarantees you'll find the simplest form of a fraction without any guesswork, turning a monster fraction into a mini one.
Section 3
Greatest common factor
The greatest common factor (GCF) of two numbers is the greatest whole number that divides both numbers evenly. It can be found by identifying all the common prime factors of the two numbers and multiplying them together.
Meet the GCF, the biggest boss factor two numbers have in common! Using prime factorization, just find all the prime team members shared by both numbers and multiply them. This single 'boss factor' can then simplify a fraction in one clean shot, making your life way easier.
Section 4
Reducing before multiplying
When multiplying fractions, you can simplify the problem by pairing any numerator with any denominator and dividing both by a common factor. This method is also known as canceling.
Why do the hard work after you multiply? Canceling lets you shrink the numbers before you multiply, making the whole problem simpler. It's like tidying up as you go! Find a numerator-denominator pair with a common factor, reduce them, and cruise to the right answer with smaller, friendlier numbers.
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Section 1
📘 Reducing Fractions, Part 2
Instead of reducing a fraction after multiplying, we can reduce before we multiply. This process, also known as canceling, works by pairing any numerator with any denominator to divide out common factors.
Next, we'll walk through several examples, including how to use prime factorization to find common factors and how to cancel across multiple fractions at once.
Section 2
Using prime factorization to reduce
To reduce a fraction using prime factorization, rewrite the numerator and the denominator as products of their prime factors. Then, identify and cancel out pairs of common prime factors that form a fraction equal to 1.
Think of this as a matching game for numbers! By breaking down big numbers into their prime building blocks, you can easily spot the common parts and remove them. This method guarantees you'll find the simplest form of a fraction without any guesswork, turning a monster fraction into a mini one.
Section 3
Greatest common factor
The greatest common factor (GCF) of two numbers is the greatest whole number that divides both numbers evenly. It can be found by identifying all the common prime factors of the two numbers and multiplying them together.
Meet the GCF, the biggest boss factor two numbers have in common! Using prime factorization, just find all the prime team members shared by both numbers and multiply them. This single 'boss factor' can then simplify a fraction in one clean shot, making your life way easier.
Section 4
Reducing before multiplying
When multiplying fractions, you can simplify the problem by pairing any numerator with any denominator and dividing both by a common factor. This method is also known as canceling.
Why do the hard work after you multiply? Canceling lets you shrink the numbers before you multiply, making the whole problem simpler. It's like tidying up as you go! Find a numerator-denominator pair with a common factor, reduce them, and cruise to the right answer with smaller, friendlier numbers.
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter