Question

Evaluate the following expressions.

Answer 1

`a.`
`(49)/(50)`

`b.`
`8`

Explanation:

`a.`
`(1)/(2) +(2)/(5) +(2)/(25)`

To solve this, we must first find the LEAST COMMON MULTIPLE (LCM).

To find the LCM, we must list the multiples of the denominators, then find the smallest multiple that all three numbers have in common.

2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50

5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50

25: 25, 50

The LCM is 50.

Now that we have found the LCM, we will change the fractions so that all three have a denominator of 50.

To do this, we multiply the numerator and the denominator by the same number.

`(1)/(2) *(25)/(25) =(25)/(50)`

`(2)/(5) *(10)/(10) =(20)/(50) \\`

`(2)/(25) *(2)/(2) =(4)/(50)`

Now that all fractions have the same denominator, we can add them. Remember, when adding fractions, the denominators stay the same. Only add the numerators.

`(25)/(50) +(20)/(50) +(4)/(50) \\\\=(49)/(50)`

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`b.`
`(2)/(3) *(30)/(7) *(14)/(5)`

To multiply fractions, multiply the numerators, then the denominators. Lastly, simplify the product.

`2*30*14=840\\3*7*5=105`

`(840)/(105) =(8)/(1)`