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FromTheMoon [43]
2 years ago
13

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

Mathematics
2 answers:
Yanka [14]2 years ago
5 0

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}

saveliy_v [14]2 years ago
5 0

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.

     

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