math 7 - fractions
Pre-unit 5.2: Comparing & Ordering fractions
what do i need to know?
1. ways to represent fractions
1. Parts of a whole: see
below 2. Parts of a set: see below 3. Fraction bar: see below 4. Number line: see below |
5. Number Sentence: This, of course, is the representation of the fraction with numbers. On the chart below, the number sentence is inside the CIRCLE IN THE MIDDLE.
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6. Word Sentence: This is the representation of the fraction using words. Using the same example on the chart below, the fraction (inside the middle circle) is represented as:
Two out of six Two of six Two sixth |
2. rules of thumb when comparing fractions
Comparing means determining whether a fraction is equal (equivalent) to, greater than or less than another fraction. Comparing is what you would do if you had to place the fractions on a number line in a certain order.
Let's begin with what I call the RULES OF THUMBS OF FRACTION COMPARING: I am just going to first write them down, and then (do not worry), I will go into details.
RULES OF THUMB
2 for something same
2 for nothing ever same
1. If EQUAL DENOMINATORS, Compare the numerators.
2. If EQUAL NUMERATORS, Compare the denominators
3. All fractions ARE DIVISION. That is, you can always divide the numerator by the denominator.
Let's begin with what I call the RULES OF THUMBS OF FRACTION COMPARING: I am just going to first write them down, and then (do not worry), I will go into details.
RULES OF THUMB
2 for something same
2 for nothing ever same
1. If EQUAL DENOMINATORS, Compare the numerators.
2. If EQUAL NUMERATORS, Compare the denominators
3. All fractions ARE DIVISION. That is, you can always divide the numerator by the denominator.
4. If EVERYTHING IS DIFFERENT, You can "CROSS" and compare OR "do #3" to compare.
3. using the rules of thumb to compare fractions
1. If the fractions have THE SAME DENOMINATORS and UNLIKE NUMERATORS,
the bigger the numerator, the bigger the fraction!
the bigger the numerator, the bigger the fraction!
In this example:
- The denominators are equal (same, alike): 8
- Then, we compare the numerators:
5 and 3
and
5 > 3
Then:
- The denominators are equal (same, alike): 8
- Then, we compare the numerators:
5 and 3
and
5 > 3
Then:
2. If the fractions have EQUAL NUMERATORS and UNLIKE (DIFFERENT) DENOMINATORS,
the bigger the denominator the smaller the fraction!
the bigger the denominator the smaller the fraction!
In this example:
- The numerators are equal: 3
- The denominators are different, so
we must compare them:
8 and 4
and
8 > 4
Therefore:
- The numerators are equal: 3
- The denominators are different, so
we must compare them:
8 and 4
and
8 > 4
Therefore:
3. If numerators and denominators are different, divide the numerators by the denominators for each fraction to CONVERT THE FRACTIONS TO DECIMALS.
Now, just compare the decimals you just got!
Now, just compare the decimals you just got!
4. If the numerators and denominators are different, you can USE THE "CROSS MULTIPLICATION METHOD:"
1. Multiply the DENOMINATOR of 2nd
fraction by the NUMERATOR of 1st
fraction.
2. Make note of the result, and
write it to the side of the first fraction's
numerator.
2. Repeat: DENOMINATOR of 1st
times NUMERATOR of 2nd fraction.
Take a look at these examples:
1. Multiply the DENOMINATOR of 2nd
fraction by the NUMERATOR of 1st
fraction.
2. Make note of the result, and
write it to the side of the first fraction's
numerator.
2. Repeat: DENOMINATOR of 1st
times NUMERATOR of 2nd fraction.
Take a look at these examples:
4. using models to compare fractions
The advantage of using models to compare fractions is that it is most often evident which fractions are greater or less than others JUST BY LOOKING at the model. Models are visually appealing, easy to manipulate, and can help you decide if you got the correct answer when using any of the strategies mentioned in the previous section.
Take a look at these examples:
Take a look at these examples:
video lessons
Comparing fractions - # 1
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comparing fractions - #2
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comparing fractions using models - # 1
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comparing fractions using models - # 2
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worksheets
1. For each worksheet, you will see a "DOWNLOAD FILE" PDF file to, you guessed it, download to your computer. This will allow you to print it if you so wanted it to do in paper.
2. Right underneath each of the DOWNLOAD Files, you will find the same worksheet, but in a picture format. You may prefer to look at the picture form if printing or downloading is not your preference. Just make sure you write down your answers in a piece of paper!
3. YOU DO NOT HAVE TO USE BOTH FORMATS - THAT IS, YOU DO NOT HAVE TO DO THE SAME WORKSHEET TWICE.
4. The LESSON PLAN, which you got from your GOOGLE CLASSROOM, specifies which worksheets to do at first.
5. OF COURSE, doing them all would only benefit you (and make me very happy). BUT THIS IS NOT A REQUIREMENT.
2. Right underneath each of the DOWNLOAD Files, you will find the same worksheet, but in a picture format. You may prefer to look at the picture form if printing or downloading is not your preference. Just make sure you write down your answers in a piece of paper!
3. YOU DO NOT HAVE TO USE BOTH FORMATS - THAT IS, YOU DO NOT HAVE TO DO THE SAME WORKSHEET TWICE.
4. The LESSON PLAN, which you got from your GOOGLE CLASSROOM, specifies which worksheets to do at first.
5. OF COURSE, doing them all would only benefit you (and make me very happy). BUT THIS IS NOT A REQUIREMENT.
Comparing fractions
same denominator
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same numerator
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Different numerators and denominators
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comparing fractions using models
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Ordering Fractions
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