Question:Convert the following into vulgar fractions: `i) 0.75` `ii) 3.004` `iii) .0056`
i) `.075`
`= 75/100`
` = 3/4`
ii) `3.004`
`= 3004/1000`
` = 751/250`
iii) `.0056/10000`
`= 7/1250`Question:Simplify the following fractions: i) `1.84/2.99` ii) `.365/.584`
i) `1.84/2.99` = `184/299` = `8/13` ii) `.365/.584` = `365/584` = `5/8`
Question:The H.C.F of two numbers is 11 and their L.C.M is 693. If one of the numbers is 77, find the other.
The other number = `((11xx693)/77) = 99`
Question:Find the largest number that can exactly divide `513, 713` and `1107`.
Required number = H.C.F. of `513, 783` and `1107`. Now, `513 = 3^3 xx 19,` ` 783 = 3^3 xx 29,` and `1107 = 3^3 xx 41` `:.` H.C.F. = `3^3 = 27` Hence, the required number is `27`
Question:Find the greatest number which can divide 284, 698 and 1618 leaving the same remainder 8 in each case.
Required number = H.C.F. of `(284 - 8), (698 - 8)` & `(1618 - 8)` = H.C.F. of `276, 690` and `1610.` Now, `276 = 2^2 xx 3 xx 23,` `690 = 2 xx 3 xx 5 xx 23,` `1610 = 2 xx 5 xx 7 xx 23` `:.` H.C.F. of `276, 690` & `1610` is `23`. Hence, the required number is `23`.