Sunday, December 14, 2014

Comparing Fractions

We have moved into working on comparing fractions. There are numerous ways that we have learned to do this. Homework this week (due January 5th) will have students using some of these methods to compare fractions. Here are the ways that we have been working on:

Draw a picture. This strategy can work with smaller fractions, but starts to get complicated with larger fractions.

Compare with like denominators. When the denominators are the same, you are comparing the numerator. The larger numerator will be the larger fraction.

Compare with like numerators. When the numerators are the same, you are comparing the denominator. The larger the denominator, the smaller the pieces will be. Therefore, the smaller denominator will give you the larger fraction.

Compare to a benchmark fraction. Determine how the fraction relates to ½ and that can help determine the larger or smaller fractions. We have also put them on a number line to help us clearly see how they compare.

Compare missing pieces. The fraction with the smallest piece missing will be the largest fraction.

visual image of fractions

Change one denominator to make a common denominator. Sometimes you only have to change one of the denominators to make common denominators.

Change both denominators to a common denominator. This allows kiddos to then compare fractions with like denominators. These are a few strategies we have talked about relating to this:

·         Change both denominators to a common denominator.

·         Multiply the denominators by each other to find a common denominator.

·         Find the least common denominator. Finding the LCD has kiddos finding the least common multiple (the smallest positive number that is a multiple of two or more numbers).

Steps to find the LCD (Least Common Denominator)

Example: Compare 1/2, 1/3, 1/5

1. List the multiples of each denominator. Make a list of at least five multiples for each denominator in the equation. Each list should consist of the denominator numeral multiplied by 1, 2, 3, 4, and so on.

Multiples of 2: 2 x 1 = 2; 2 x 2 = 4; 2 x 3 = 6; 2 x 4 = 8; 2 x 5 = 10
Multiples of 3: 3 x 1 = 3; 3 x 2 = 6; 3 x 3 = 9; 3 x 4 = 12; 3 x 5 = 15
Multiples of 5: 5 x 1 = 5; 5 x 2 = 10; 5 x 3 = 15; 5 x 4 = 20; 5 x 5 = 25

2. Identify the lowest common multiple. Scan through each list and mark any multiples that are shared by each original denominator. After identifying the common multiples, identify the lowest denominator.

Note that if no common denominator exists at this point, you may need to continue writing out multiples until you eventually come across a shared multiple.
Example: 2 x 15 = 30; 3 x 10 = 30; 5 x 6 = 30
The LCD = 30

3. Rewrite the original equation. In order to change each fraction in the equation so that it remains true to the original equation, you will need to multiply each denominator by the same factor used to multiply the corresponding denominator when reaching the LCD. Be sure to multiply the numerator AND denominator of each fraction by the factor.

Example: 15 x (1/2); 10 x (1/3); 6 x (1/5)

New mathematical statement: 15/30 > 10/30 > 6/30

Please let me know if you have any questions. 

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