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

Step-by-step explanation:

Answer 2

Answer:

$\text{ \dfrac{2}{5} hour \approx \dfrac{1}{2} hour}$

$\text{ \dfrac{5}{8} hour \approx \dfrac{1}{2} hour}$

$\text{Total \approx 1 hour}$

Step-by-step explanation:

Time they played a game

$\dfrac{2}{5}=\dfrac{2 \times 2}{5 \times 2}=\dfrac{4}{10}$

$\text{As \dfrac{5}{10}=\dfrac{1}{2} \implies \dfrac{4}{10}\approx \dfrac{1}{2} \implies \dfrac{2}{5}\approx \dfrac{1}{2} hour}$

Time they read a book

$\text{As \dfrac{4}{8}=\dfrac{1}{2} \implies \dfrac{5}{8}\approx \dfrac{1}{2} hour}$

Total time

Therefore, the best estimate for the total time is:

$\implies \dfrac{2}{5}+\dfrac{5}{8} \approx \dfrac{1}{2}+\dfrac{1}{2}=1\; \text{hour}$

Exact solution

$\begin{aligned}\implies \dfrac{2}{5}+\dfrac{5}{8} & = \dfrac{2 \times 8}{5\times 8}+\dfrac{5\times 5}{8\times 5} \\\\& = \dfrac{16}{40}+\dfrac{25}{40} \\\\& = \dfrac{16+25}{40} \\\\& = \dfrac{41}{40}\\\\ & = \dfrac{40+1}{40}\\\\ & = \dfrac{40}{40}+\dfrac{1}{40}\\\\ & = 1+\dfrac{1}{40}\\\\ & = 1\frac{1}{40}\; \text{hour} \end{aligned}$