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.