Identifying Ratios in Mathematics 5 and Visualizing Rstios

Review:
Directions: Look at the picture. Write the corresponding ratio of the
phrases based on the picture.

In the previous lesson, you were taught how to
visualize ratios of two quantities. In this lesson, we
will deal with identifying and writing equivalent
ratios.
Two ratios that have the same value are
called equivalent ratios. To find an
equivalent ratio, multiply or divide both
quantities by the same number.

In identifying and writing equivalent
ratios, you need to bear in mind
that ratios are used to compare
numbers. When you’re working with
ratios, it is sometimes easier to work
with an equivalent ratio. Equivalent
ratios have different numbers but
represent the same relationship.

Let’s try to process and answer the above
given situation.
David and Diana need to make 5 cups of
juice punch which consists of 3 cups of
pineapple juice and 2 cups of apple juice,
but it should be four times its original
recipe.

How can we know that the two ratios are equivalent?
Remember that two ratios a:b and c:d are equivalent if a
x d = b x c.
Or the product of the means equals the product of the
extremes.

In 3:2 = 12:8, the extremes are 3 and 8,
and the means are 2, 12.
Finding the product, we have:
3x 8 = 24 and 2 x 12 = 24
Since 3 x 8 = 2 x 12, then 3:2 = 12:8.
We can say that 3:2 and 12:8 are
equivalent ratios.

Let us take another example:
Example #1:
Compare the ratios 2:3 and 10:15.
Let 𝒂 = 𝟐, 𝒃 = 𝟑, 𝒄 = 𝟏𝟎 and 𝒅 = 𝟏𝟓 . If 𝒂 × 𝒅 = 𝒃 × 𝒄 ,
then the ratios 𝒂: 𝒃 and 𝒄: 𝒅 are equivalent.
2 × 15 = 30 3 × 10 = 30
Since 2 × 15 = 3 × 10 , then 2: 3 = 10: 15. We say that 2:3 and
10:15 are equivalent ratios.

What is the equivalent ratio of 3:8?
A. 15:40 B. 9:16
C. 30:40 D. 6:24

How will you find the equivalent ratios?
Multiply or divide a counting
both terms of the given ratio

Directions: Identify the equivalent and not equivalent ratios by
using the symbols “=” or "≠”. Write your answer on your
answer sheet.

Review
Directions: Identify the equivalent and not equivalent ratios by
using the symbols “=” or "≠”. Write your answer on your
answer sheet.

Now, what is the relation between the two ratios in the
previous part? Let us reduce the ratios to lowest terms by
dividing the both terms of each ratio by their GCFs.

To get a ratio equivalent to a given ratio, multiply or divide
the two numbers of the ratio by the same number.
Example:

Since 4 × 12 = 6 × 8, then 4: 6 = 8: 12. We can say that 4:6 and 8:12
are equivalent ratios. Likewise, 4:6 and 2:3 are equivalent ratios.
lesson.

Directions: Choose the letter of the correct answer.
Show your solutions on an extra sheet of paper.

There are 7 children for every 2 adults
in a plaza. How many adults are there, if
there are 21 children?
Answer: 6

Review:
Write = in the circle if the given pair of ratios are
equal and ≠ if not.

In the previous lessons, you were
able to learn the concept of ratio. A
ratio is a comparison of the
number of elements in two sets. A
ratio can be written as a fraction
(a/b) and in ratio notation (a:b).

Also, you learned how to identify
and write equivalent ratios. Note
that, two ratios a:b and c: d are
equivalent if a x d = b x c. To
generate equivalent ratios, multiply
or divide a counting number to
both terms of a given ratio.

Think and understand.
Dana has a bar of chocolate. It was divided
equally into 30 smaller pieces. When her
friends came, 15 smaller pieces were eaten.
What is the ratio of the remaining smaller
pieces to the total pieces of the whole bar?
Express the ratio in its simplest form.

The ratio of the shaded
smaller pieces to the whole
figure is 15 to 30, that is;

If you will look at the figure, you will
notice that the number of shaded parts
to the whole figure is one-half. So, we
could say that the ratio of 15 to 30 is
equal to the ratio 1 to 2, that is in fraction
form, we have;

Recall that we used 3, 5, and 15 as
our divisors of the given numbers
to get ½ and 15 is the largest
among them and is the greatest
common factor (GCF) of 15 and 30.

To get the GCF, we may follow the methods given below.
These methods were discussed in the previous lessons.

So, in order to reduce a ratio to its
simplest form, it is necessary to find the
greatest common factor (GCF) for both
terms in the ratio or fraction.
This is the shortcut to finding the
simplest form of a ratio.

Let us have an example.
Example 1: The ratio of boys to girls is 6 to 24. Express the given ratio
in its lowest term.
To do this, we will first find the GCF of 6 and 24, as shown below:

Clearly the GCF is 6. So, the largest number that can divide
both the terms of the given ratio is 6. Thus, we have:

Example 2: Express 18:12 in its simplest form.
Take note of the steps carefully.
Step 1: Find the GCF of the two numbers.

We find the greatest common factor between 18
and 12 which is 6.
Step 2: Divide the given numbers by the GCF.

Step 3: Rewrite the ratio in colon form.

Directions: Express the following ratio in its simplest form.
Follow the steps given above. The first item is done for you
as your guide.
1) 50 : 60
2) 10 : 8
3) 18 : 40
4) 64 : 72
5) 25 : 35
6) 24 : 36

To express ratio to its simplest form,
we (4) ___________ both the terms by
their GCF.
What are the steps in expressing
the given ratio in its simplest
form?

Identifying Ratios in Mathematics 5 and Visualizing Rstios

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