Question

1.An electrician cut 5 1/2 feet of wire into three equal sections. After cutting, how long was each piece?

2.Pete mixed 4 1/6 cups of popcorn with 3 5/6 cups of pretzels. He then divided the snack into bags with 3/4 cup in each. After dividing, how many bags of snack bags will Pete have?

Answer 1

Part 1)
`1(5)/(6)\ ft`

Part 2)
`10(2)/(3)\ bags`

Explanation:

Part 1)

step 1

Convert mixed number to an improper fraction

`5(1)/(2)\ ft=(5*2+1)/(2)=(11)/(2)\ ft`

step 2

Divided the improper fraction by 3

`((11/2))/(3)=(11)/(6)\ ft`

step 3

Convert to mixed number

`(11)/(6)=(6)/(6)+(5)/(6)=1(5)/(6)\ ft`

Part 2)

step 1

Convert mixed number to an improper fractions

`4(1)/(6)\ cups\ popcorn=(4*6+1)/(6)=(25)/(6)\ cups\ popcorn`

`3(5)/(6)\ cups\ pretzels=(3*6+5)/(6)=(23)/(6)\ cups\ pretzels`

step 2

Adds the two quantities

`(25)/(6)+(23)/(6)=(48)/(6)=8\ cups`

step 3

Divide the total cups by 3/4 to find the number of bags

so

`(8)/((3/4))=(32)/(3)\ bags`

step 4

Convert to mixed number

`(32)/(3)\ bags=(30)/(3)+(2)/(3)=10+(2)/(3)=10(2)/(3)\ bags`