* A Simple Overview of the Basic ( + - x / ) Operations *

Module One

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* Operations with proper fractions N < D *

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To add fractions with the same denominator just add the numerators.

2/7 + 3/7 = ______ 2/7 + 3/7 = 5/7

To subtract fractions with the same denominator just subtract the numerators.

7/9 - 5/9 = ______ 7/9 – 5/9 = 2/9

To multiply fractions, use algorithm: (Algorithm: Multiply Numerators and Denominators)

multiply the numerators then multiply the denominators.

4/5 x 2/3 = ______ 4/5 x 2/3 = 8/15 (Result does not reduce.)

Why algorithm works! Multiply can be thought of as “of” thus

4/5 x 2/3 = 4/5 of 10/15 or 4/5 of 2/15+2/15+2/15+2/15+2/15 = 8/15

To divide fractions, use algorithm: (Algorithm: Invert 2^nd Fraction and Multiply Fractinons.)

then multiply the numerators then multiply the denominators.

2/3 / 1/6 = ______ 2/3 / 1/6 = 2/3 x 6/1 = 12/3 = 4

Why algorithm works! Just like whole numbers, How many 1/6s are in 2/3?

1 = 1/6+1/6+1/6+1/6+1/6+1/6 or 2/3 = 1/6+1/6+1/6+1/6 thus 2/3 has 4 ( 1/6s )

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* Operations with improper fractions N > D or Mixed Numbers*

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To add Mixed Numbers the two fractions have same denominator simply add the whole numbers

then add the numerators of the fractions keeping the common denominator.

2 3/8 + 3 4/8 = ______ 2 3/8 + 3 4/8 = 5 7/8

To subtract Mixed Numbers with fractions having same denominator simply subtract whole numbers

then subtract numerators of the fractions keeping the common denominator.

5 4/5 - 2 3/5 = ______ 5 4/5 - 2 3/5 = 3 1/5

To multiply Mixed Numbers use the algorithm:

Change the Mixed Numbers to Improper Fractions then Multiply as Fractions.

1 1/2 x 1 3/4 = ______ 3/2 x 7/4 = 10/8 = 1 2/8 or 1 1/4

Apply logic and reasoning as shown above in multiplying proper fractions.

To divide Mixed Numbers use the algorithm:

Change the Mixed Numbers to Improper Fractions

then Invert 2^nd fraction and Multiply as Fractions.

1 2/3 / 1 2/7 = ______ 5/3 / 9/7 = 5/4 x 7/9 = 35/36

Apply logic and reasoning as shown above in dividing proper fractions.

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