A/B + B/C + C/D

Home Adding/Subtracting Comparing Fractions A/B + B/A A x A/B Mult Mixed Numbers Mult Mixed Nums (II) 1/A + 1/AB + 1/ABB 1/A - 1/AB - 1/ABB Add 3 Fractions Calculate Frac 1 Calculate Frac 2 Repeating Decimal Repeating Decimal 2 Repeating Decimals 3 A/B + B/C + C/D

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Adding 3 Fractions In The Form: a/b + b/c + c/d:

A.  When adding 3 fractions in this form such that each letter is one number greater than the previous, use the following formula:

2 + a2d - (d + 2)

    bcd

B.  Note:  This is usually true!!  When a = 1, you get: 1/2 + 2/3 + 3/4.  When you use this formula, the answer is 2 -1/12 which is not a real answer.  When a = 1, the answer is 1 11/12.  The above formula is true for a>1.

C.  Basically the formula says the whole number is always 2.  The numerator is a2d - (d+2) and the numerator is the product of the denominators.

D.  Examples:

Ex [1]  4/5 + 5/6 + 6/7 = _______ (mixed number)

a.  The whole number is 2.

b.  The numerator is 42 x 7 - 9 = 16 x 7 - 9 = 112 - 9 = 103.

c.  The denominator is 5 x 6 x 7 = 30 x 7 = 210.

d.  The answer is 2 103/210.

Ex [2]  10/11 + 11/12 + 12/13 = ________ (mixed number)

a.  The whole number is 2.

b.  The numerator is 102 x 13 - 15 = 1300 - 15 = 1285.

c.  The denominator is 11 x 12 x 13 = 11 x 156 = 1716.

d.  The answer is 2 1285/1716.

 

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