Addition of Fractions with unlike Denominators. Where is the most difficulty in adding fractions?...
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- Slide 1
- Addition of Fractions with unlike Denominators
- Slide 2
- Where is the most difficulty in adding fractions? Knowing how
to find a common denominator and changing the fraction to an
equivalent fraction.
- Slide 3
- Common Mistake with Adding Fractions Many students simply add
across.
- Slide 4
- Why students make this mistake with adding fractions Students
do not understand what a fraction is. They just see the numbers and
add. They don't understand that the 3 is a third and the 5 is a
fifth or they do not understand the concept of different
units.
- Slide 5
- Example: The 2 represents a half The 8 represents an eighth You
can't add eighths and halves together so you must find a unit that
they both have in common. 8 would be the unit they have in common
which is called the common denominator. The problem would then look
like this: But how do you find the common denominator?
- Slide 6
- A common example you can show your students why you must use a
common denominator to add Can you add oranges and apples together?
Not unless you rename the oranges fruit and the apples fruit. Then
you would have 3 fruit + 4 fruit = 7 fruit. When you use common
denominators you are doing the same thing. You are renaming the
units to a number that both denominators have in common.
- Slide 7
- Fraction Strips This is a way to show students visually the
equivalence of fractions.
http://theapple.monster.com/training/articles/4324-4th-grade-adding-and-subtracting-fractions
- Slide 8
- Some other ways for students to visualize fractions Graham
crackers-they are sectioned off into pieces you can break apart.
M&M's- you can use the different colors to the total number of
m&m's to represent different fractions. Playing cards-you can
use two different cards to represent a fraction. Pizza
slices-slices to the whole. Money- dimes, nickels, quarters, to
make a dollar. You can almost use anything to represent
fractions.
- Slide 9
- http://www.inspiration.com/kidspiration-math-examples
- Slide 10
- Visuals are a good way to show younger students the concepts of
fractions. It gives them something concrete to look at instead of
just following another math rule. Once students do understand what
a fraction is, they need to learn how to find the LCD other than
drawing it or looking at manipulatives.
- Slide 11
- Different ways to find the common denominator Example: Find a
common denominator for: Simply multiply the denominators. 3 x 8 =
24 This method will not always give you the LCD(least common
denominator). You will get the correct answer, but you may have
more steps to reduce your final answer. Write down all the
multiples of each denominator until you find a common multiple. 3:
1,2,3,4,5,6,9,12,15,18,21,24 8: 1,2,3,8,16,24 You can use prime
factorization. 3: 1 * 3 8: 2 * 2 * 2 1 * 2 * 2 * 2 * 3 = 24
- Slide 12
- When you have the common denominator what do you do then?
Example: You found that 20 is the LCD(least common denominator).
You must change each fraction to the equivalent fraction with the
denominator 20: and 20/5 =4 so you multiply the numerator and
denominator of 3/5 by 4 giving you 12/20. 20/4= 5 so you would
multiply the numerator and denominator of 1/4 by 5 giving you 5/20.
You just rewrite the fraction and add across and just rewrite your
common denominator:
- Slide 13
- Theorem Addition of Fractions with Unlike Denominators Let and
be any fractions. Then =
- Slide 14
- Example using Theorem
- Slide 15
- Exercises Try these addition problems using the theorem.
- Slide 16
- Exercises Answers
- Slide 17
- Now try the same problems by finding the LCD.
- Slide 18
- Addition using LCD
- Slide 19
- Do you find using the theorem is easier than finding a common
denominator? Which method do you prefer in solving different
denominator addition problems? Do you think that the theorem should
be taught to students that have been just introduced to
fractions?
- Slide 20
- Sources Spector, Lawrence. "The Math Page." Adding and
Subracting fractions and mixed numbers. N.p., 2001-2010. Web. 10
Mar 2010.. http://www.math-drills.com/fractions.shtml Mathematics
for Elementary Teachers - Class Textbook