CBSE Class 8 > Class 8 Videos > Comparing with Ratios - Comparing Quantities
Comparing with Ratios - Comparing Quantities Video Lecture - Class 8
FAQs on Comparing with Ratios - Comparing Quantities
| 1. What is a ratio and how is it used in comparing quantities? |  |
Ans. A ratio is a comparison of two or more quantities. It is used to understand the relationship or proportion between the quantities being compared. Ratios are often expressed in the form of fractions, decimals, or as a colon (e.g., 2:3 or 2/3). By comparing ratios, we can determine how one quantity is related to another and make meaningful comparisons between them.
| 2. How can ratios be helpful in solving real-life problems involving quantities? | |
Ans. Ratios are extremely helpful in solving real-life problems involving quantities. They allow us to analyze and understand the relationships between different quantities, helping us make informed decisions. For example, ratios can be used to compare the price of different products, determine the mixing ratios of ingredients in recipes, or calculate distances based on a map's scale. By using ratios, we can solve problems efficiently and accurately in various everyday situations.
| 3. What are some common examples of ratios used in everyday life? | |
Ans. Ratios are commonly used in various aspects of everyday life. Some examples include: - Price comparison: Comparing the prices of different products to determine which one offers better value for money. - Recipe measurements: Determining the correct ratios of ingredients while cooking or baking. - Speed and distance: Comparing the speed and distance ratios to calculate travel time or estimate fuel consumption. - Financial planning: Analyzing the ratio of income to expenses to manage personal finances effectively. - Sports statistics: Comparing the ratios of goals scored, assists made, or points earned to evaluate the performance of athletes or teams.
| 4. How can ratios help in understanding and interpreting data? | |
Ans. Ratios play a crucial role in understanding and interpreting data. They provide a meaningful way to compare different sets of data and identify patterns or trends. By calculating ratios, we can determine the relative proportions of different variables, which helps in drawing conclusions and making predictions. Ratios also enable us to communicate data in a more concise and understandable manner, allowing for easier interpretation and analysis.
| 5. Can ratios be used to solve problems involving more than two quantities? | |
Ans. Yes, ratios can be used to solve problems involving more than two quantities. In such cases, multiple ratios can be compared simultaneously to understand the relationships between the quantities involved. By setting up proportional equations or using cross-multiplication, we can solve complex problems involving multiple ratios. This allows us to analyze the interplay between various quantities and make accurate calculations or predictions based on their relationships.
Text Transcript from Video
all right in this video I'm gonna show
you three different ways to compare
ratios and we've got person a and person
B for this problem and they're both
typists and person a can type in 50
words in 75 seconds while person B can
type 120 words in hundred 44 seconds and
for the sake of this video let's say we
want to figure out who's faster so one
way to do it I'm going to show you three
ways but one way to do it is to take
both of their ratios and write them as a
fraction so we've got 120 over 44 down
here we've got 70 50 over 75 here now
it's important to remember in ratios
what these numbers mean so 50 stands for
50 words and 75 stands for seconds 120
words and this is 144 seconds that's
really important when understanding how
to compare ratios and let's do the first
one as come getting a common numerator
so we are going to multiply this ratio
by 12 and that gives us a numerator of
650 times 12 to 675 times 12 I'm not
sure what it is
1014 1505 7 add these together I get 900
all right so this is nine 600 words in
900 seconds and then down here I can
take 120 and multiply by 5 over 5 so 120
times 5 is equal to 600 and there's our
common numerator and then 144 times 5 I
have no clue what it is
20 28:22 fourth so we've got 720 so this
is 600 words over 720 seconds so it's
really easy to see that person B is
faster because they both type 600 words
but person a needs 900 seconds to do it
while person B only needs 720 seconds so
person B is faster we know because we've
got common numerators
all right a second method to compare
these two ratios is to get a common
denominator and so we're gonna begin by
writing the ratios again set 50 over 75
and 120 over 144 and remember this is 50
words over 75 seconds 120 words over 144
seconds okay and we want to get a common
denominator and rather than just
starting with 75 and 144 and building up
to get a really massive common
denominator I'm going to show you a
little trick let's do some reducing
first and I can see that both 50 and 75
are divisible by 25 so I'm going to
divide by 1 which is 25 over 25 and that
gives us 2 over 3 and then down here
let's see I could see that 12 goes into
both of these so I'm going to divide
them both by 12 12 over 12 means I'm
dividing by 1 and 120 divided by 12 is
10 and 144 divided by 12 is 12 and now
it's really easy to see how to get a
common denominator I'm going to leave
this one alone I'm going to multiply
this guy by 4 over 4 so 2 times 4 is 8
3 times 4 is 12 so now we've got our
common denominators now we have to make
our decision who's faster well you have
to remember what these ratios mean 50
words you travel over here so this is 8
words and this is 12 seconds and over
here this is 10 words and this is 12
seconds so now we can see in 12 seconds
if both typists type for 12 seconds be
person B can do 10 words while person a
can only do 8 words so we can see that
person B is faster
our our last method for comparing these
two typists is to get a unit rate and so
you remember that a unit rate is a ratio
that has a 1 as the denominator and so
down here we want we're gonna rename
both of these ratios so that they have a
1 as a denominator so in this ratio to
turn the denominator into a 1 we need to
divide by 75 so we're going to divide by
the fraction 75 over 75 so we're
dividing by 1 to get a denominator of 1
and similarly down here we're gonna
divide by 1 but we want this denominator
to become a 1 so we're gonna divide by a
hundred and forty-four over a hundred
and forty four so really we're dividing
by one but it's a carefully chosen one
so that we get a denominator of one so
now I'm gonna bust out my calculator
truly I am because I totally forgot to
pull it out when I make this video so
I'm gonna get my little calculator
loulou calculator and I'm going to type
in 50 divided by 75 so I'm gonna do 50
divided by 75 and I get oh my goodness I
get zero point six six six six six
distances so the sixes keep going with a
bar right
so really I could just change this to
zero point six with a bar and then I'm
gonna do the same thing down here I'm
going to take 120 and I'm going to
divide by 144 and I get zero point eight
three three and the 3s keep going
forever so I'll just erase that and put
a three a bar on top of the three so now
we've got these two ratios now how does
this help us decide who's faster well if
you think about the labels this one
stands for one second and this one
stands for one second because the labels
come across now this zero point six with
a bar stands for words and this stands
for words
and so we can see that each of these
people in one second this is how many
words they can type this person can type
in point six with a bar words which is
really two thirds and then this person
can type in point eight three bar with
words in a second and we can see that
the point eight is larger than the point
six and so point B is faster
you three different ways to compare
ratios and we've got person a and person
B for this problem and they're both
typists and person a can type in 50
words in 75 seconds while person B can
type 120 words in hundred 44 seconds and
for the sake of this video let's say we
want to figure out who's faster so one
way to do it I'm going to show you three
ways but one way to do it is to take
both of their ratios and write them as a
fraction so we've got 120 over 44 down
here we've got 70 50 over 75 here now
it's important to remember in ratios
what these numbers mean so 50 stands for
50 words and 75 stands for seconds 120
words and this is 144 seconds that's
really important when understanding how
to compare ratios and let's do the first
one as come getting a common numerator
so we are going to multiply this ratio
by 12 and that gives us a numerator of
650 times 12 to 675 times 12 I'm not
sure what it is
1014 1505 7 add these together I get 900
all right so this is nine 600 words in
900 seconds and then down here I can
take 120 and multiply by 5 over 5 so 120
times 5 is equal to 600 and there's our
common numerator and then 144 times 5 I
have no clue what it is
20 28:22 fourth so we've got 720 so this
is 600 words over 720 seconds so it's
really easy to see that person B is
faster because they both type 600 words
but person a needs 900 seconds to do it
while person B only needs 720 seconds so
person B is faster we know because we've
got common numerators
all right a second method to compare
these two ratios is to get a common
denominator and so we're gonna begin by
writing the ratios again set 50 over 75
and 120 over 144 and remember this is 50
words over 75 seconds 120 words over 144
seconds okay and we want to get a common
denominator and rather than just
starting with 75 and 144 and building up
to get a really massive common
denominator I'm going to show you a
little trick let's do some reducing
first and I can see that both 50 and 75
are divisible by 25 so I'm going to
divide by 1 which is 25 over 25 and that
gives us 2 over 3 and then down here
let's see I could see that 12 goes into
both of these so I'm going to divide
them both by 12 12 over 12 means I'm
dividing by 1 and 120 divided by 12 is
10 and 144 divided by 12 is 12 and now
it's really easy to see how to get a
common denominator I'm going to leave
this one alone I'm going to multiply
this guy by 4 over 4 so 2 times 4 is 8
3 times 4 is 12 so now we've got our
common denominators now we have to make
our decision who's faster well you have
to remember what these ratios mean 50
words you travel over here so this is 8
words and this is 12 seconds and over
here this is 10 words and this is 12
seconds so now we can see in 12 seconds
if both typists type for 12 seconds be
person B can do 10 words while person a
can only do 8 words so we can see that
person B is faster
our our last method for comparing these
two typists is to get a unit rate and so
you remember that a unit rate is a ratio
that has a 1 as the denominator and so
down here we want we're gonna rename
both of these ratios so that they have a
1 as a denominator so in this ratio to
turn the denominator into a 1 we need to
divide by 75 so we're going to divide by
the fraction 75 over 75 so we're
dividing by 1 to get a denominator of 1
and similarly down here we're gonna
divide by 1 but we want this denominator
to become a 1 so we're gonna divide by a
hundred and forty-four over a hundred
and forty four so really we're dividing
by one but it's a carefully chosen one
so that we get a denominator of one so
now I'm gonna bust out my calculator
truly I am because I totally forgot to
pull it out when I make this video so
I'm gonna get my little calculator
loulou calculator and I'm going to type
in 50 divided by 75 so I'm gonna do 50
divided by 75 and I get oh my goodness I
get zero point six six six six six
distances so the sixes keep going with a
bar right
so really I could just change this to
zero point six with a bar and then I'm
gonna do the same thing down here I'm
going to take 120 and I'm going to
divide by 144 and I get zero point eight
three three and the 3s keep going
forever so I'll just erase that and put
a three a bar on top of the three so now
we've got these two ratios now how does
this help us decide who's faster well if
you think about the labels this one
stands for one second and this one
stands for one second because the labels
come across now this zero point six with
a bar stands for words and this stands
for words
and so we can see that each of these
people in one second this is how many
words they can type this person can type
in point six with a bar words which is
really two thirds and then this person
can type in point eight three bar with
words in a second and we can see that
the point eight is larger than the point
six and so point B is faster
About this Video
4.7/5 Rating
Apr 18, 2026 Last updated
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