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In this video, the ratios involve decimals and fractions. You will learn how to simplify such creatures.
This webinar was sponsored by the National Center on Intensive Intervention (NCII) and National Center on Systemic Improvement (NCSI) and presented by Drs. Russell Gersten, Sarah Powell, and Robin Finelli Schumacher. The webinar discusses 1) the importance of fractions instruction and typical challenges faced by students, 2) share recommendations for fractions instruction, and 3) provide considerations for supporting students within secondary or Tier 2 and intensive intervention.
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Title: Multiplying Fractions - Fast And Easy Math Learning Videos
When we multiply two fractions, we can show the multiplication using the same array we’ve used before, like this.
Since we’re dealing with fractions of numbers, we need whole units that are bigger than these that we’ve used before. We can zoom in a little like this.
Now we can see each whole unit in more detail.
We start by showing the first fraction in the problem, two-fifths, on this scale.
So, we divide each unit into five equal parts to show fifths.
We show the second fraction on this scale.
So, we divide each unit into four equal parts to show fourths.
Next, two show the first fraction, we count two-fifths here, and show the second fraction by counting three-fourths here.
The product of these fractions is shown by this array.
We’re multiplying fractions, so the first thing we need to know is how many parts are in each whole unit in the answer. A whole unit is shown here
We have five parts per unit times four parts per unit.
When we multiply these two numbers, we see that we have twenty parts in a whole unit.
This means the denominator of the answer is 20.
Next, we need to know how many of these parts we have in the array we created by multiplying the fractions. Two parts are counted on this side, and three parts are counted on this side.
Two times three is six, so when we connect the lines we see that the array has six of these parts in all.
This means the numerator of the answer is 6.
Again, there are twenty parts in each whole unit, so the denominator is 20.
We have six parts in the array, so the numerator is six.
So the product of the two fractions is six-twentieths.
Now notice that the numerator, six, is equal to the product of the two numerators in the fractions we multiplied.
Two times three equals six.
Also notice that the denominator, twenty, is equal to the product of the two denominators in the fractions we multiplied.
Five times four equals twenty.
Here’s another example.
We can show the problem in an array.
We will show two-thirds on this side.
So, we divide the whole units into thirds, and count up two-thirds.
We will show the second fraction, 5/2 on this side.
So, we divide the whole units into halves, and count up five-halves.
The array for our problem looks like this.
So now we have whole units that have three parts times two parts.
So, we have six parts in each whole unit.
This means the denominator in the answer is 6.
To find the numerator of the answer, we count two parts times five parts.
So, there are a total of 10 parts counted in the array.
This means the numerator is 10.
Again, each unit is divided into six parts, so the denominator is six.
We count ten of these parts.
So, the numerator is ten.
Again, notice that the numerator in the answer is the product of the numerators in the fractions we multiplied.
The denominator is the product of the denominators in the fractions we multiplied.
We could solve every multiplication problem with fractions using diagrams like this. But, that would take a long time. In every case, the answer would be the same as we get if we just multiplied the numerators and denominators as we did in these examples.
We saw that when we multiply the denominators, we find how many parts are in each whole unit, which tells us the size of the parts in the array that represents the answer.
When we multiply the numerators, we find how many parts we have in the array.
Now that we know what multiplying fractions means, we can use these facts to solve all multiplication problems with fractions.
Here we have four-fifths times one-half. To multiply these two fractions, first we multiply the numerators.
Four times one equals 4.
Next, we multiply the denominators.
Five times two equals ten.
So the answer is four-tenths.
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Title: Rewriting Fractions with LCM as Common Denominator - Fast And Easy Math Learning Videos
You’ve already learned how to find the least common multiple of two numbers. In this lesson, you’ll learn to use the least common multiple of two numbers to find a common denominator for two fractions.
Here’s an example, one sixth and four ninths. One way to find a common denominator for these two fractions is to use the least common multiple of the denominators. First, let’s find the least common multiple of 6 and 9.
We start with six and list some multiples, as shown here.
Then we take 9 and list some multiples.
The least common multiple is the smallest number included in both of these lists of multiples. In this case, it’s 18.
Now let’s use that as the common denominator to rewrite both fractions.
One-sixth becomes three eighteenths.
And four ninths becomes eight eighteenths.
Another example, three fourths and three tenths. We start by finding the least common multiple of the denominators, 4 and 10.
We start by listing some multiples of four, as shown here.
Then we list some multiples of 10.
The least common multiple is 20.
We now can rewrite the fractions with a common denominator of 20.
Three fourths becomes fifteen twentieths.
And three tenths becomes six twentieths.
Last example, three fourths and one sixth. To find the common denominator, we find the least common multiple.
We list some multiples of 4 as shown here, then some multiples of 6.
The least common multiple is 12.
So, the least common denominator is 12.
We now rewrite each fraction with a denominator of 12.
Three fourths becomes 9 twelfths and one sixth becomes 2 twelfths.
In the remainder of this lesson, you’ll rewrite fractions with a common denominator after using the least common multiple of the denominators to find a common denominator.
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Fractions are of the form p/q where q is not zero. If p is greater than q then the fraction is called improper fraction. Value of improper fraction is more than 1. We can divide the numerator by the denominator and then write it as a mixed number. Visual illustrations in this video help to understand the concept clearly in a very simple language. Video can help teachers and instructor to explain the concept. Thanks. Here are two Playlist: https://www.youtube.com/playli....st?list=PLJ-ma5dJyAq
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Improper Fractions Complete Concept: https://www.youtube.com/watch?v=ARZA0VPREzQ&list=PLJ-ma5dJyAqr-3tiWdwQ6eAXre-k_d1X-&index=22
Fraction more than or equal to one are improper fractions.
Fraction represents part of the whole
Proper fractions lies between zero and one.
between any two fractions we have infinite fractions
Area Model to Multiply Proper Fraction: https://www.youtube.com/watch?v=tl8aXA6ciGc&list=PLJ-ma5dJyAqp7sSkSQQAE1sE5i4bgxX-N
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Title: Comparing Fractions to 1 - Fast And Easy Math Learning Videos
In this lesson, you will learn when a fraction is less than one whole unit, equal to one whole unit, or more than one whole unit. A fraction equals one whole unit when the numerator and denominator are the same. This example shows us that two-thirds does not equal one. The numerator and denominator are not the same.
Here's another example of a fraction that does not equal one. Five-thirds does not equal one. The numerator and denominator are not the same.
Now let's look at a fraction that does equal one whole unit. Three-thirds equals one. The numerator and denominator are the same.
Here's another example of a fraction that is equal to one. Six-sixths equals one. The numerator and denominator are the same.
Now let's take look at fractions that are less than one and more than one. Four-sixths is less than one. A fraction is less than one when the numerator is less than the denominator.
Here's an example of a fraction that is more than one. Fifteen-sixths is more than one. A fraction is more than one when the numerator is more than the denominator.
Now try a few problems on your own. To solve this problem, you must click on the correct answer, like this.
The correct answer is less than. One-third is less than 1. For the problems that follow, click on the correct answer.
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Using #Mathigon Polypad to show how you might explain addition of unlike fractions. I made this quick video on my phone e while sitting at a McDonald’s.
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Title: Equivalent Fractions: Reducing Fractions to Simplest Terms
You’ve already learned how to reduce fractions by rewriting them with a smaller denominator, and you’ve learned how to find the greatest common factor of two numbers.
In this lesson, you’ll put both of these together to rewrite fractions with the smallest possible numbers. This is referred to as “reducing the fraction to simplest terms.” Before we begin, lets’ look at some new words we use when describing fractions.
The first one is term. Term is another way of saying “number”. Five is a term.
Three-fourths is a term.
And two and five-eighths is a term.
When we write a proper or improper fraction, the numerator is a term and the denominator is a term.
When dealing with fractions we also refer to simplest terms or lowest terms. These both mean the same thing. When a fraction is written in simplest terms, or lowest terms, it means the fraction is written with the smallest possible numbers for the numerator and denominator. A fraction is written in simplest terms when the greatest common factor of the numerator and denominator is one.
Here’s an example. Five-twelfths is written in simplest terms. The greatest common factor of 5 and 12 is one. This means neither the numerator nor the denominator can be written with a smaller number.
Another example. Seven-thirds is written in simplest terms. The greatest common factor of the terms is one, so seven and three are the smallest numbers that can be used to write the fraction.
Nine-fourteenths is written in simplest terms. The greatest common factor of the terms is one.
Six-eighths is not written in simplest terms. One is not the greatest common factor of the terms.
This means we can write this fraction with smaller numbers without changing its value. To find the new numerator and denominator, we need the greatest common factor of six and eight. Two is the greatest common factor. We can use two to rewrite the fraction and reduce it to its simplest terms.
We reduce the terms by dividing each term by the greatest common factor, which is 2. When we divide six by two we get three.
And when we divide eight by two we get four.
Three-fourths is the same fraction as six-eighths, but it’s now written in simplest terms.
When we reduce the terms of a fraction using the greatest common factor, we refer to this as “reducing the fraction to simplest terms”. The value of the fraction remains the same, but the numbers used to write it are smaller.
In the remainder of this lesson, you’ll be asked to determine if a fraction is written in simplest terms. If the fraction is not written in simplest terms, you will be asked to reduce the fraction.
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In this video, I teach you how to add Fractions with different denominators.
If you have any questions, please leave them in the comment section below! Also, if you find the videos helpful, please like, share, and subscribe!
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Title: Comparing Unit Fractions On A Number Line - Fast And Easy Math Learning Videos
In this lesson you’ll learn how to compare unit fractions.
A unit fraction is any fraction that has 1 as the numerator. For example, one-half, one-fourth, or one-seventh.
To compare unit fractions let’s start by using a number line.
You already know that when we divide one whole into halves we get two equal parts.
When we divide one whole into thirds we get three equal parts.
When we divide one whole into fourths we get four equal parts.
And so on. So you can see that when we split the whole into more parts,
each part gets smaller
So a unit fraction with a larger denominator is a smaller number, and a unit fraction with a smaller denominator is a larger number.
Let’s look at an example: one-fourth and one- sixth.
Let’s look at these on the number line.
We can see that one-fourth is larger than one-sixth because it’s farther to the right on the number line.
One-fourth has a smaller denominator so it’s a larger number than one-sixth.
Let’s look at another example: one-twelfth and one-half. The number with the larger denominator is the smaller number.
So one-twelfth is less the one-half. In the remainder of this lesson you’ll get practice comparing unit fractions.
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Title: What is the bottom number of a fraction - Fast And Easy Math Learning Videos
In this lesson, you will begin to learn about fractions. Fractions are used to describe the PARTS of whole units. A fraction is written like this:
In this lesson, you'll learn about the BOTTOM number of a fraction.
To create a fraction we divide a whole unit into equal parts. The BOTTOM number of a fraction tells us the number of equal parts in each whole unit. Here's an example. This box is one whole unit. We'll divide the box into four equal parts...
Since the parts are equal each part is a fraction of the whole unit. There are four equal parts in all, so the BOTTOM number of each fraction is four.
In this example there are three whole units.
One.
Two.
Three.
Each whole unit is exactly the same size. When whole units are the same size we can divide them into fractions. Each of these whole units is still divided into four equal parts.
Here’s another way of looking at the equal parts of whole units or fractions. There are six whole units and each whole unit is divided into two equal parts. We can put the whole units together like this.
Each whole unit is now a line instead of a box. The tallest line show the beginning and end of each whole unit.
We’ve just created a number line. A number line is another way to show fractions which are just equal parts of whole units.
Notice this arrow.
The arrow points to one of the fractions on the number line.
You’ll learn to write the name for fractions like this. For this lesson you will ONLY write the BOTTOM number of the fraction.
In this example there are two equal parts in each whole unit.
So the bottom number for this fraction, is two
Here’s a different fraction on the same number line.
Each whole unit is still divided into two equal parts so the bottom number for this fraction is also two.
Here’s another example. There are FOUR parts in each whole unit, so the bottom number for this fraction is four.
The bottom number for this fraction is also 4.
And the bottom number for this fraction is also 4. For any fraction on this number line the bottom number will always be four since each whole unit has four equal parts.
In the remainder of this lesson you will write the bottom number for the fraction shown by the arrow on a number line like these.
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This lesson explains how to compare fractions with the same numerator. For more videos and instructional resources, visit TenMarks.com. TenMarks is a standards-based program to complement any math curriculum with scaffolded lessons, guided practice, inquiry-based tasks, assessments and interventions.
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Title: Fractions: Numerator and Denominator - Fast And Easy Math Learning Videos
In this lesson, you will learn some fraction terminology. The top number is the numerator. For this fraction, one is the numerator.
And the bottom number is the denominator. Two is the denominator.
The bar between the numerator and denominator is called a fraction bar
Let's look at a few examples of numerators and denominators.
For this fraction, the numerator is three
And the denominator is four.
Let's extend what you've learned about the numerator and denominator. The numerator, the top number, shows how many parts are counted.
In this example, seven parts are counted, so the numerator is seven.
The denominator, the bottom number, shows the number of parts in each whole unit.
There are two parts in each whole unit, so the denominator is two.
In this example, eleven parts are counted, so the numerator is eleven, and there are five parts in each whole unit.
So, the denominator is five.
Here, the numerator is nine and the denominator is three.
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