Question

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Answer 1

4)
`(34)/(35)`

5)
`(3)/(2)`

Explanation:

Adding Fractions

To add two or more fractions, generally with different denominators, we must first find the Least Common Multiple (LCM) of them.

To find the LCM we can follow this procedure:

List the prime factors of each number.

Multiply each factor the greatest number of times it occurs in either number.

4) We have the sum:

`\displaystyle (4)/(7)+(2)/(5)`

We must find the LCM of 5 and 7.

Since both numbers are prime, the LCM is just their product 35.

Now we divide the LCM by each denominator and multiply by its corresponding numerator as follows:

`\displaystyle (4)/(7)+(2)/(5)=(4*5+2*7)/(35)=(34)/(35)`

Answer:

`\boxed{(34)/(35)}`

5) \displaystyle \frac{7}{8}+\frac{3}{4}

Find the LCM of 8 and 4:

Prime factors of 8: 2,2,2

Prime factors of 4: 2,2

LCM = 2*2*2 = 8.

`\displaystyle (7)/(8)+(3)/(4)=(7*1+3*2)/(8)=(12)/(8)`

Simplifying by 4:

`\displaystyle (7)/(8)+(3)/(4)=(3)/(2)`

Answer:

`\boxed{(3)/(2)}`