How To Simplify Fractions Using Prime Factorization

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What you need to know to understand this lesson:
1--- How to do Prime Factorization
2--- How to find HCF of 2 numbers
Check Out My Previoius Videos that go into more detail on these subjects:

Hi Guys, back with another video. In this lesson you’ll learn how to use PRIME FACTORIZATION to find the Highest Common Factor (or Greatest Common Divisor) of the Numerator and Denominator of a fraction so you can simplify the fraction (also called reducing the fraction).
Knowing the HCF of two numbers is very useful when you are asked to simplify fractions. If you can find the HCF of the numerator and denominator of a fraction, you can divide both by the HCF and that will give you the fraction reduced to its simplest form.

The most common way of doing this is by listing the common factors of the numerator and denominator of the fraction and then looking for the Highest Common Factor (HCF), that is, the largest of the common factors. Then one can divide the top and bottom of the fraction using the HCF to simplify the fraction.

But this becomes difficult if your fraction Numerator and denominator are large numbers. That’s where it is better to simplify the fractions using prime factorization.

Today You’ll learn how to simplify Fractions using Prime Factorization to find the HCF. We’ll simplify the fraction 25/48 the common way, and then we will simplify the same fraction using Prime Factorization. We will also simplify a harder fraction, 1120/1750, using prime factorization. You will see that the prime factorization method is much faster and less confusing for these harder fractions, and, overall, it is a better method for simplifying even simpler fractions.

Today’s lesson is the final part of the series dealing with Prime Numbers and the benefits of knowing how to use them. I’ve linked all of the other lessons below.

Contents:
0:00 - Lesson objective/ simplifying fractions overview
0:42 - simplifying without Prime Factorization
1:59 - The problem with Large Numbers
2:58 - Using Prime Factorization To simplify 25/48
4:48 - Simplifying Bigger Numbers 1120/1750
8:10 - Other useful Videos

This lesson is part of a series covering Prime Numbers and their uses.

Check out other lessons in this series:

Music:
Intro:
deep space - ambient lofi hip hop beat (FREE FOR PROFIT USE)

Music Credit:
Prod Riddman

For more great music by Prod Riddman link to Channel below:

Outro
((FREE)) Lofi/Chill hop Type Beat - "Two Lips"

Music from the Zeeky Beats Channel:

Tags:
Prime Factorization, Prime Numbers, Prime Factors, Simplify fractions using prime factorization, How to reduce fractions, highest common factor, HCF, Greatest Common Divisor, GCD
Simplify fractions using HCF, simplify fractions using GCD, common factors,

[scmtuk]

There is a quicker way of doing this.
When you have the prime factorization of the numerator and denominator, instead of looking at the common factors, then multiplying those to find the HCF, then dividing both numbers by that HCF, all you really need to do is just cancel out the common prime factors.

For example, with 1120/1750 when writing the prime factorization, there's 2, 5 and a 7 in common.
Therefore, if you cancel these out, you're left with 2 x 2 x 2 x 2 / 5 x 5 = 16 / 25

No need to divide by 70, at all.

[TinyMaths]

Contents:
0:00​ - Lesson objective/ simplifying fractions overview
0:42​ - simplifying without Prime Factorization
1:59​ - The problem with Large Numbers
2:58​ - Using Prime Factorization To simplify 25/48
4:48​ - Simplifying Bigger Numbers 1120/1750
8:10​ - Other useful Videos