## Go Math! Practice Fluency Workbook Grade 6 California 1st Edition, Chapter 7 Representing Ratios and Rates

**Question. Use Proportions to convert 4ft feet to inches.**

**Given:** 4ft

**Find:** we need to convert it to inches.

We will use proportions to convert feet to inches.

Let 4ft be equal to x inches

1ft=12in

ratio=1/12

Also,4ft=x in

ratio=4/x

Both ratios are equal, so

4/x =1/12

x=12×4

x=48in

Both ratios are equal, so 4/x = 1/12

x=12×4

x=48in

4ft is equal to 48 inches.

**Question. Use Proportions to convert 6 quarts to gallons.**

**Given:** 6 quarts

**Find:** we need to convert it to gallons.

We will use proportions to convert quarts to gallons.

Let 6 quarts be equal to x gallons

1gal=4qt

ratio=1/4

Also, xgal=6qt

ratio =x/6

Both ratios are equal, so

x/6 =1/4

x =6/4

=1.5gal

6qt is equal to 1.5gal gallons.

**Question. Use proportions to convert 5km kilometers to meters.**

**Given:** 5km

**Find:** we need to convert it to meters.

We will use proportions to convert kilometers to meters.

Let 5km be equal to x meters

1km=1000m

ratio=1/1000

Also, 5km=xm

ratio=5/x

Both ratios are equal, so

5/x =1/1000

x=1000×5

x=5000m

5km is equal to 5000m meters.

**Question. Use Proportions to convert 2000g grams to kilograms.**

**Given:** 2000g

**Find:** we need to convert it to kilograms.

We will use proportions to convert grams to kilograms.

Let 2000 be equal to x kg

1kg=1000g

ratio=1/1000

Also, xkg=2000g

ratio=x/2000

Both ratios are equal, so

x/2000 =1/1000

x=2000/1000

=2kg

2000g is equal to 2 kg kilograms.

**Question. Use the conversion factor to 5qt convert quarts to cups.**

**Given:** 5qt

**Find:** we need to convert it to cups.

We will use the conversion factor to convert quarts to cups.

It is known that1qt=4cups

conversion factor= 4/1 =4

5qt =cf×5

5qt =4×5 =20cups

5quarts is equal to 20 cups

**Question. Use the conversion factor to 600cm convert centimeters to meters.**

**Given:** 600cm

**Find:** we need to convert it to meters.

We will use the conversion factor to convert centimeters to meters.

It is known that100cm=1m

conversion factor, cf=1/100

600cm=cf×600

600cm=600×1/100

600cm=6m

600cm is equal to 6m

**Question. Use proportions to 1mile convert miles to feet.**

**Given:** 1mile

**Find:** we need to convert it to feet.

We will use proportions to convert miles to feet.

Let 1mile be equal to x ft

1mile=5280ft

ratio=1/5280

Also,1mile=xft

ratio=1/x

Both ratios are equal, so

1/5280 =1/x

x=5280ft

The altitude is 1 mile which is 5280 ft.

**Question. Use proportions to 0.7 km convert kilometers to meters.**

**Given:** 0.7km

**Find:** we need to convert it to meters.

We will use proportions to convert kilometers to meters.

Let 0.7km be equal to x meters

1km=1000m

ratio=1/1000

Also,0.7km=xm

ratio=0.7/x

Both ratios are equal, so

0.7/x =1/1000

x=0.7×1000

x=700m

The distance is 0.7km which is equal to 700m.

**Question. Read the table and find the conversion factor and multiply or divide it to get our values.**

Given a table

We need to convert values from inches to feet to yard.

We will find the conversion factor and multiply or divide it to get our values.

1ft=12in

conversion factor,cf1=12

1yd=3ft

conversion factor,cf2=3

For moving right, we will multiply and for moving left, we will divide by the conversion factor.

The table will be

The filled table will be

**Question. A sheet of paper is 81/2 x 11 inches. Find the length of the frame that is 4 papers long along the length.**

**Given:** A sheet of paper is 81/2×11 inches

**Find:** we need to find the length of the frame that is 4 papers long along the length.

We will multiply the length by 4 times along the length of the paper.

Given Length=11in

We will multiply by 4

11×4=44 in

1ft=12in

Conversion factor,cf=12

We will divide the length in inches by the conversion factor

length in feet =44/12

=3.67ft

The length of the frame is 44 in and 3.67ft

**Question. A scale from feet to yards and find the conversion factor and use it to represent a larger bar with conversion factor times smaller bars.**

**Given:** A scale from feet to yards

**Find:** we need to draw a bar model.

We will find the conversion factor and use it to represent a larger bar with conversion factor times smaller bars.

Given a scale from feet to yards 1yd=3ft

Conversion factor =3/1 =3

The bar model for feet to yards will be

**Question. A scale from cups to fluid ounces and find the conversion factor and use it to represent a larger bar with conversion factor times smaller bars.**

**Given:** A scale from cups to fluid ounces

**Find:** we need to draw a bar model.

We will find the conversion factor and use it to represent a larger bar with conversion factor times smaller bars.

Given a scale from cups to fluid ounces

1cup=8ounces

Conversion factor, cf=8

The bar model for converting cups to fluid ounces will be

Bar models are good to represent conversions with small conversion factors as it is easy to represent. But in the case of a large conversion factor, it becomes very difficult to draw so many bars and also very tough to represent them. For converting miles to feet, it has a conversion factor of 5280 which is very large. Hence, the bar model is not a good choice to represent the conversion of miles to feet.

The bar model is not a good choice to represent the conversion of miles to feet.