Question

Maria played a game with her little sister for 2/5 hour and read her little sister a book for 5/8 hour. What is the best estimate for the total time maria spent With her little sister? Drag an drop an answer into each box to correctly complete the sentences. 2/5 hour is closest to [ ]. 5/8 hour is closest to [ ]. Therefore, the best estimate for the total time Maria was with her sister is close to [ ] (0 hours) ( 1/2 hour) ( 1 hour) ( 1 1/2 hour) (2 hours)

Answer 1

Answer: It was exactly 61 minutes and 50 seconds

Explanation:

Answer 2

`\text{$(2)/(5)$ hour $\approx (1)/(2)$ hour}`

`\text{$(5)/(8)$ hour $\approx (1)/(2)$ hour}`

`\text{Total $\approx$ 1 hour}`

Explanation:

Time they played a game

`(2)/(5)=(2 * 2)/(5 * 2)=(4)/(10)`

`\text{As $(5)/(10)=(1)/(2) \implies (4)/(10)\approx (1)/(2) \implies (2)/(5)\approx (1)/(2)$ hour}`

Time they read a book

`\text{As $(4)/(8)=(1)/(2) \implies (5)/(8)\approx (1)/(2)$ hour}`

Total time

Therefore, the best estimate for the total time is:

`\implies (2)/(5)+(5)/(8) \approx (1)/(2)+(1)/(2)=1\; \text{hour}`

Exact solution

`\begin{aligned}\implies (2)/(5)+(5)/(8) & = (2 * 8)/(5* 8)+(5* 5)/(8* 5) \\\\& = (16)/(40)+(25)/(40) \\\\& = (16+25)/(40) \\\\& = (41)/(40)\\\\ & = (40+1)/(40)\\\\ & = (40)/(40)+(1)/(40)\\\\ & = 1+(1)/(40)\\\\ & = 1(1)/(40)\; \text{hour} \end{aligned}`