If the product of two positive fractions \( a \) and \( b \) is \(\frac{15}{56}\), find three pairs of possible values for \( a \) and \( b \).
Answer (3)
all you have to do is find pairs of factor for both 15 and 56 e.g. 1,15 3,5 1.56 2, 28 4, 14
so three possibilities could be 1/1 x 15/56 3/4 x 5/14 1/2 x 15/28
Answer
Find out the three pairs for possible values for a and b .
To prove
As given
T h e p ro d u c t o f tw o p os i t i v e f r a c t i o n s a an d b i s 56 15 .
i.e it is written in the form.
a × b = 56 15
When
a = 2 3 , b = 28 5
Than
2 × 28 3 × 5 = 56 15
When
a = 4 3 , b = 14 5
Than
4 × 14 3 × 5 = 56 15
When
a = 2 1 , b = 28 15
Than
2 × 28 1 × 15 = 56 15
Hence proved
To find pairs of fractions that multiply to 56 15 , we can consider various combinations of factors. Three valid pairs are: 4 3 and 14 5 , 8 5 and 7 3 , and 28 15 and 2 1 . Each pair, when multiplied together, gives the required product.
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