Question

Please help meHow much of a circle is shaded write in simplest form as a fraction in simplest form

Answer 1

`(4)/(15)`

Step-by-step explanation

Step 1

the shaded area is equal to

shaded area = total circle -not shaded area

a) the full circle equals 1 ( one unit)

b) let x represents the shaded area

c) the not shaded area is the sum of 2/5 and 1/3

Now , rewrite the expression

`\begin{gathered} shadedarea=totalcircle-notshadedarea \\ \text{ shaded area=1-}((2)/(5)+(1)/(3)) \\ so \\ x=1-((2)/(5)+(1)/(3)) \end{gathered}`

Step 2

Now, let's calculate

`\begin{gathered} x=1-((2)/(5)+(1)/(3)) \\ x=1-((2\cdot3+5\cdot1)/(5\cdot3)) \\ x=1-((6+5)/(15)) \\ x=1-((11)/(15)) \end{gathered}`

now, the subtraction

`\begin{gathered} x=1-((11)/(15)) \\ \text{tip: } \\ 1=(15)/(15),\text{ so} \\ x=(15)/(15)-((11)/(15)) \\ x=(15-11)/(15) \\ x=(4)/(15) \end{gathered}`

therefore, the answer is

`(4)/(15)`

I hope this helps you