Fractions name a part of a set or whole.
Equivalent Fractions
How to make an equivalent fraction
You can multiply or divide BOTH the numerator and the denominator by the SAME number to make an equivalent fraction.
Multiplying makes the numerator and denominator larger, but still equivalent.
Dividing makes the numerator and denominator smaller, but still equivalent. This is also referred to as reducing the fraction to simplest form.
Make an equivalent fraction for 2/5
1. Choose a number to multiply by. I will choose 4. (you can choose ANY number)
2. Multiply BOTH the numerator and the denominator by 4.
3. So 2 x 4 = 8 and 5 x 4 = 20
4. The new equivalent fraction for 2/5 is 8/20
Reduce 36/42 to make an equivalent fraction
1. Figure out which number has BOTH 36 and 42 as multiples
2. For these numbers, the answer would be 6.
3. divide 36 AND 42 by 6
4. So 36 divided by 6 = 6 and 42 divided by 6 = 7
5. The new reduced equivalent fraction is 6/7
Tips for Comparing Fractions
Tip #1
If the numerator is the SAME, compare the denominators.
The SMALLER the denominator, the BIGGER the fraction.
2/3 > 2/8 because the numerator is the same and since 3 is SMALLER than 8, 2/3 is the LARGER fraction.
Tip #2
If the denominator is the SAME, compare the numerator.
The BIGGER the numerator, the BIGGER the fraction.
4/6 > 2/6 because they both have a denominator of 6 and 4 is greater than 2.
Tip #3
If Tip #1 or #2 do not apply, you will need to draw a model/number line to compare.
1/2 > 3/8 because:
1/2 extends farther down the number line making it the LARGER fraction.
Check out this cool Blendspace to learn more!
Check out this fun interactive game you can play at home to practice!
https://play.kahoot.it/#/k/451a7fda-1d49-4ffb-b616-50803312dbd4
Ordering Fractions
Put these fractions in order least to greatest:
1/3, 4/6, 2/12
Step 1: Find a common denominator (a denominator that all fractions have in comon)
Think? What # can I divide 3,6,& 12 into evenly?
Answer? 12
The common denominator is 12
Step 2: make equivalent fractions with the new denominator
Change each fraction so the denominator is 12 for all three.
1/3 = 4/12 4/6 = 8/12 2/12 stays the same
(for help making equivalent fractions, see notes above)
Step 3: Put the fractions in order
Least to greatest order would now be:
2/12, 4/12, 8/12
Try these out! Bring in your work for a treat tomorrow!
Ordering Fractions
Put these fractions in order least to greatest:
1/3, 4/6, 2/12
Step 1: Find a common denominator (a denominator that all fractions have in comon)
Think? What # can I divide 3,6,& 12 into evenly?
Answer? 12
The common denominator is 12
Step 2: make equivalent fractions with the new denominator
Change each fraction so the denominator is 12 for all three.
1/3 = 4/12 4/6 = 8/12 2/12 stays the same
(for help making equivalent fractions, see notes above)
Step 3: Put the fractions in order
Least to greatest order would now be:
2/12, 4/12, 8/12
Try these out! Bring in your work for a treat tomorrow!
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| Making equivalent fractions with the same denominators Adding Fractions with LIKE denominators
Step 1: Add the numerators ONLY
Step 2: Reduce/Simplify if possible
2/8 + 4/8 = 6/8
2 + 4 = 6 and the denominator of 8 remains the same
6/8 has both even numbers so you can divide both by 2 to reduce it to 3/4
6/12 + 5/12 = 11/12
11 is a PRIME number so this fraction cannot be reduced, it is already in simplest form.
Divide by 3 and 6/9 in simplest form is 2/3
Divide by 3 and 3/6 in simplest form is 1/2
Half-Way
Students need to be able to quickly recognize when a fraction represents 1/2.
The following are common fractions that equal 1/2
2/4
3/6
4/8
5/10
6/12
7/14
8/16
9/18
10/20
Subtracting Fractions with Like Denominators
Step 1: Subtract the numerators ONLY
Step 2: Reduce/Simplify if possible
10/12 - 2/12 = 8/12 10-2 = 8 (numerator) and the denominator of 12 stays the same 8/12 have a common factor of 4 so divide the numerator and denominator by 4 to reduce the fraction to 2/3 Multiplying Fractions Step 1: multiply the numerators Step 2: multiply the denominators Step 3: simplify/reduce if possible Examples: 3/6 x 7/8 = numerators: 3 x 7 =21 denominators 6 x 8 = 48 answer is 21/48 This can be reduced by dividing by 3 so the reduced answer is 7/16 Multiplying a fraction by a Whole Number Option 1: multiply the whole # by the numerator, keeping the denominator the same 5 x 3/6 = (5 x 3)/6 = 15/6 reduces to 5/2 Option 2: put a 1 under the whole number then follow steps 1-3 for multiplying fractions as normal 5 x 3/6 = 5/1 x 3/6 = (5 x 3)/(1 x 6) = 15/6 reduces to 5/2   
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