Question

Express each of the following as a fraction in its simplest form

Answer 1

Answer:

see explanation

Step-by-step explanation:

(a)

Given

$\frac{y}{3}$ + $\frac{y+3}{5}$

The common denominator is 15 ( the LCM of 3 and 5 )

Multiply numerator/ denominator of first fraction by 5

Multiply the numerator/ denominator of second fraction by 3

= $\frac{5y}{15}$ + $\frac{3y+9}{15}$ ← add numerators , leaving denominator of 15

= $\frac{5y+3y+9}{15}$

= $\frac{8y+9}{15}$

(b)

Given

$\frac{3x}{8}$ - $\frac{x+5}{4}$

The common denominator is 8 ( the LCM of 8 and 4 )

Multiply numerator/ denominator of second fraction by 2

= $\frac{3x}{8}$ - $\frac{2(x+5)}{8}$ ← simplify numerators leaving denominator of 8

= $\frac{3x-2x-10}{8}$

= $\frac{x-10}{8}$

Answer 2

Answer:

a) (8y + 9)/15.

b) (5x + 10)/8.

Step-by-step explanation:

(a)  y/3 + (y + 3)/5

     The LCD of 3 and 5  is 15 so we have:

     5y/15 + 3(y + 3)/15

      = (5y + 3(y + 3)) / 15

     = (5y + 3y + 9)/15

     = (8y + 9)/15.

b)  3x/8 + (x + 5)/4

     The LCD of 4 and 8  is 8 so we have:

     3x/8 + 2(x + 5)/8

      = (3x + 2x + 10) / 8

      = (5x + 10)/8.