ClassX Video Lessons Youtube Channel TutoringHour Simplifying Fractions the Easy Way! | Reducing Fractions to Their Lowest Terms
Hey there! Welcome to a fun lesson on simplifying fractions. Today, we’re going to learn how to make fractions easier to understand by reducing them to their simplest form. Let’s dive in!
Imagine you have a yummy pizza sliced into six equal parts. If you eat three slices, how many slices are left? That’s right, three out of six slices are still there. But did you know you can make this fraction simpler?
When you look at the leftover pizza, you can see that half of it is still there. So, the fraction three over six is the same as one-half. Cool, right?
Let’s learn how to do this with numbers. One way is to break down the numbers into their prime factors. Prime factors are numbers that can only be divided by one and themselves.
For example, the number three is already a prime number. The number six can be broken down into two times three. When you see the same number in both the top and bottom of the fraction, you can cancel them out. This leaves you with one over two, which is the simplest form of the fraction.
A fraction is in its simplest form when the only number that can divide both the top and bottom is one.
Let’s try another one! We have the fraction twelve over fifteen. First, we break down twelve into two times two times three. Fifteen can be broken down into three times five. The number three is common in both, so we cancel it out. Now we have four over five, which is the simplest form!
Another way to simplify fractions is by using the greatest common factor, or GCF. Let’s simplify ten over thirty-five.
First, list the factors of ten: one, two, five, and ten. Now, list the factors of thirty-five: one, five, seven, and thirty-five. The number five is the biggest factor they both share, so it’s the GCF.
Divide both the top and bottom of the fraction by five. Ten divided by five is two, and thirty-five divided by five is seven. So, the simplest form is two over seven.
Let’s try one more! We have eighteen over twenty-four. The factors of eighteen are two, three, six, nine, and eighteen. The factors of twenty-four are two, three, four, six, eight, twelve, and twenty-four. The biggest common factor is six.
Divide both the top and bottom by six. Eighteen divided by six is three, and twenty-four divided by six is four. So, the simplest form is three over four.
Now that you know how to simplify fractions, it’s time to practice! Try solving some problems on your own and see how quickly you can simplify fractions. Remember, practice makes perfect!
Thanks for learning with us today! Keep practicing, and you’ll be a fraction-simplifying pro in no time!
Pizza Fraction Fun: Create your own paper pizza! Cut a circle out of paper and divide it into different numbers of equal slices, like 4, 6, or 8. Use crayons or markers to color some slices to represent fractions. For example, color 3 out of 6 slices. Now, try to simplify the fraction by finding an equivalent fraction with fewer slices. Can you see how many slices you can color to represent the same fraction in its simplest form?
Fraction Hunt: Go on a fraction hunt around your house or classroom. Look for items that can be divided into parts, like a chocolate bar, a set of crayons, or a pack of stickers. Choose one item and divide it into equal parts. Use these parts to create a fraction. Then, try to simplify the fraction by finding the greatest common factor of the numerator and denominator. Share your findings with a friend or family member!
Story Time with Fractions: Write a short story or draw a comic strip about a character who loves to simplify fractions. Maybe they are a chef who needs to simplify recipes or a builder who uses fractions to measure materials. Include at least two examples of fractions being simplified in your story. Share your story with the class and explain how the character simplified the fractions.
Sure! Here’s a sanitized version of the YouTube transcript:
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Hello and welcome to Tutoring Hour! In this video, we’ll learn how to simplify fractions.
Let’s take this pizza for instance. We’ll slice it into six equal parts. If you eat three slices, what fraction of the pizza will be left over? We’ll have three out of six slices remaining.
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Now, to make this fraction simpler, we can combine the leftover pieces. You can see that one half of the pizza is left, so three over six, when reduced or simplified, is equivalent to half of the pizza.
Now, let’s see how this can be done mathematically. One simple but effective way is to write the numerator and denominator as products of their prime factors.
So, three can be written as one times three, or just three, and six can be written as two times three. The three in the numerator and the three in the denominator cancel each other out, leaving us with one over two.
Now we cannot reduce this any further, as the only common factor between the numerator and denominator is one. From this, we can conclude that a fraction is said to be in its simplest form if one is the only common factor of its numerator and denominator.
As simple as ABC, isn’t it? Let’s go through another example by reducing or simplifying the fraction twelve over fifteen.
Now, twelve can be written as two times two times three, and fifteen can be written as three times five. The three in the numerator and the three in the denominator cancel each other out, and multiplying what’s left gives us four over five. So, twelve over fifteen is reduced to four over five. Great job!
Now, we’ll take a look at how to simplify fractions using the greatest common factor (GCF). The fraction is ten over thirty-five.
Before we proceed, let’s list out the factors of the numerator, ten, which are one, two, five, and ten. The factors of thirty-five are one, five, seven, and thirty-five. The factor five is common to both the numerator and denominator, so five is our GCF.
Now, we’ll divide the numerator and denominator by five. First, let’s divide ten by five, which gives us two, and thirty-five divided by five is seven. So, our reduced fraction is two over seven. Two and seven have no common factors except one, hence we can conclude that the fraction has been reduced to its lowest term.
Let’s simplify one more fraction using the GCF method. This time we have eighteen over twenty-four. First, we’ll list out the factors of eighteen: two, three, six, nine, and eighteen.
Now, let’s also write down the factors of twenty-four: two, three, four, six, eight, twelve, and twenty-four. The factors two, three, and six are common to both lists; however, the greatest common factor is six.
So, we will divide both the numerator and the denominator by six. Eighteen divided by six is three, and twenty-four divided by six is four. So our reduced fraction is three over four.
Now that’s what we call simplifying! It looks like we’ve totally nailed it in a jiffy. It’s time to start putting it into practice by solving some of these worksheets at TutoringHour.com.
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