Transcript Reducing Numeric Fractions

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Reducing Numeric Fractions
Suggestion:
140
?
875
Work with
scratch paper
and pencil as you
go through this
presentation.
Turn Mystery into Mastery
Click to Advance
C2006 – DW Vandewater
What if we could look at a simplified
form of both numbers?
140 (2)(2)(5)(7) (2)(2) 4



875 (5)(5)(5)(7) (5)(5) 25
1.
2.
3.
4.
5.

Figure out the prime factors of both.
Do any factors cancel out? Cancel them.
Write the remaining factors.
Multiply the tops.
Multiply the bottoms.
That’s the simplest form of the fraction!
Click to Advance
What is the Key Skill?
 Prime
Factorization!

(A big name for a simple process …)

Finding out how to write a number as the product
of it’s prime factors.

Examples:
6 = 2∙3
 70 = 2∙5∙7
 24 = 2∙2∙2∙3
 13=13 because 13 is prime (no other factors)

Click to Advance
Practice:
Let’s Reduce a Fraction

Here’s the problem ->
◦
◦
◦
◦
Find the prime factors of 48
Find the prime factors of 144
Rewrite the fraction w/ primes
Cancel matching factors
◦ Rewrite the fraction
◦ Multiply top & bottom, if necessary

That is the simplest form
Click to Advance
48
144
48
/\
2 24
/ \
2 12
/\
2 6
/\
2 3
14 4
/ \
2 72
/ \
2 36
/\
6
6
/\ /\
2 3 2 3
22223

2 2 2 233
1

3
Practice:
Let’s Reduce a Bigger Fraction

Here’s the problem ->
◦
◦
◦
◦
Find the prime factors of 1848
Find the prime factors of 990
Rewrite the fraction
Cancel matching factors
◦ Rewrite the fraction
◦ Multiply top & bottom

That is the simplest form
Click to Advance
1848
990
1848
2  924
2  2  462
2  2  2  231
2  2  2  3  77
2  2  2  3  7 11
2  2  2  3  7 11
2  3  3  5 11
227
35
28
15
990
2  495
2  3 165
2  3  3  55
2  3  3  5 11
More Practice

See if you can find the simplest forms.
Do the work on paper and click to see the answer
252 2  2  3  3  7 2  3  3 18



70
257
5
5
2145 3  5 11 13 5 11


 55
39
3 13
1
91
7 13
13
13



462 2  3  7 11 2  3 11 66
59
59

both prime
101 101
Click to Advance
Thank You

For Learning about
◦ Prime Factorization
◦ Reducing Numeric fractions