Question

Can someone help me out with find the unit rate and also solve by equivalent fractions

Answer 1

Part 1)

a) The unit rate is $2.5 per pumpkin

b) The units rate is $4.5 per pound

c) The unit rate is 1 mile/hour

d) The unit rate is 2.67 mph

Part 2)

a) x=20

b) x=13

c) x=30

d) x=3

e) x=10

f) x=56

g) x=2.5

h) x=6

Explanation:

Part 1)

we know that

A unit rate is a ratio that has a denominator of 1

Part a) we know that

Andy buys 400 pumpkins for $1,000

To find out the unit rate divide the total cost by the number of pumpkin

so

1,000/400=$2.5/1 -----> the denominator is equal to 1

Part b) Sonia spend $13.50 on 3 lbs of candy What is the price of one pound?

To find the price of one lb of candy, find out the unit rate, so divide the total cost by the number of pounds

$13.50/3=$4.5 per pound

Part c) Sam walks 4 miles in 4 hours What is Sam's speed per hour?

To find the unit rate divide the total distance by the total time

so

4/4=1 mile/hour

Part d) Arnold walks 2 miles in 45 min What is his speed in mph?

To find the unit rate divide the total distance by the total time but first convert minutes to hours

45 min=45/60=0.75 h

2/0.75=2.67 mph

Part 2)

we know that

Equivalent fractions are fractions that are equal in value. To determine if two fractions are equivalent, cross-multiply the fractions--multiply the numerator of each fraction by the denominator of the other. The fractions are equivalent if the products are the same

Part a) we have

`(5)/(10)=(x)/(40)`

Multiply in cross

`5*40=10*x`

`200=10x`

Divide by 10 both sides

`x=20`

Part b) we have

`(x)/(4)=(52)/(16)`

Multiply in cross

`16*x=52*4`

`16x=208`

Divide by 16 both sides

`x=13`

Part c) we have

`(6)/(7)=(x)/(35)`

Multiply in cross

`6*35=7*x`

`210=7x`

Divide by 7 both sides

`x=30`

Part d) we have

`(10)/(x)=(80)/(24)`

Multiply in cross

`10*24=80*x`

`240=80x`

Divide by 80 both sides

`x=3`

Part e) we have

`(50)/(10)=(x)/(2)`

Multiply in cross

`50*2=10*x`

`100=10x`

Divide by 10 both sides

`x=10`

Part f) we have

`(5)/(7)=(40)/(x)`

Multiply in cross

`5*x=40*7`

`5x=280`

Divide by 5 both sides

`x=56`

Part g) we have

`(1)/(x)=(10)/(25)`

Multiply in cross

`1*25=10*x`

`25=10x`

Divide by 10 both sides

`x=2.5`

Part h) we have

`(5)/(x)=(20)/(24)`

Multiply in cross

`5*24=20*x`

`120=20x`

Divide by 20 both sides

`x=6`