Question

Judy is playing a card game. She needs to select two cards below that have a sum greater

than 5. Which two cards should she select? Prove it.

`2 (2)/(5)`


`2 (2)/(7)`


`1 (7)/(8)`


`2 (1)/(10)`


`2 (5)/(8)`
​

Answer 1

2 2/5 = 2.4
2 2/7 = 2.28
1 7/8 = 1.875
2 1/10 = 2.1
2 5/8 = 2.625

Answer 2 2/5 (2.4) + 2 5/8 (2.625) = 5.025

Answer 2

The two cards she should select are:

a)
`2(2)/(5)`

e)
`2(5)/(8)`

Step-by-step explanation

A mixed number is an addition of its whole and fractional parts.

a)

`2+(2)/(5) \\\\2*(5)/(5) +(2)/(5) \\\\(2*5)/(5) +(2)/(5) \\\\(10+2)/(5) \\\\(12)/(5) = 2.4`

b)

`2+(2)/(7) \\\\2*(7)/(7) +(2)/(7) \\\\(2*7)/(7) +(2)/(7) \\\\(14+2)/(7) \\\\(16)/(7) = 2.28`

c)

`1+(7)/(8) \\\\1*(8)/(8) +(7)/(8) \\\\(1*8)/(8) +(7)/(8) \\\\(8+7)/(8) \\\\(15)/(8) = 1.87`

d)

`2+(1)/(10) \\\\2*(10)/(10) +(1)/(10) \\\\(2*10)/(10) +(1)/(10) \\\\(20+1)/(10) \\\\(21)/(10) = 2.1`

e)

`2+(5)/(8) \\\\2*(8)/(8) +(5)/(8) \\\\(2*8)/(8) +(5)/(8) \\\\(16+5)/(8) \\\\(21)/(8) = 2.62`

After solving each mixed number we can see that the only two values that add up to +5 are a) 2.4 and e) 2.62

2.4 + 2.62 = 5.02