Part of a quantity

🏆Practice part of the amount

To find the partial amount

We will divide the total amount by the denominator of the part, multiply the result obtained by the numerator of the part and obtain the partial amount.

To find the total amount

We will divide the given number (part of a quantity) by the numerator of the part.
We will multiply the result by the denominator of the part and obtain the whole quantity.

To find the part of the quantity

In the numerator - we will note the partial amount
In the denominator - we will note the total amount
We will reduce the fraction we receive and reach the desired part.

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Test yourself on part of the amount!

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What is the marked part?

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Part of a quantity

The topic of a part of a quantity in fractions is pleasant and easy if you understand the principle and logic.
Therefore, focus and see how you learn to solve questions about a part of a quantity without any problem.
In everyday life, a whole quantity can be the number of children in a class for example, and a part of a quantity is the number of children studying in a specific class.

We divide the topic into 3 situations.


The first situation: finding the amount of a part

The total amount is known
and we want to know something specific about a part of the amount.
Procedure:
We will divide the total amount by the denominator of the part.
We will multiply the result obtained by the numerator of the part and we will get the final answer.

Let's see this while asking a question:
In the music class there are 3030 students - this is the total amount.
131 \over 3 Of the class plays the guitar - that is the specific part.

How many children in the music class play the guitar? – the part of the total amount.

Solution:
to know how much is 131 \over 3
We will divide the total amount -> 3030 by the number 33 (The number that appears in the denominator of the part.
We will get:
30:3=1030:3=10
If we multiply 1010 by the numerator of the part -> 11 we still get, 1010.

That is 131 \over 3 of 3030 is 1010 children.
We can also see this in the illustration:

1.a  We will divide the total amount by the denominator of the part.

When we divide 3030 by 33 into equal parts, we get that each part is equal to 1010.
This means that-> 1010 children in the class play the guitar.

Bonus section:  
232 \over 3 of the music class play the drums.
How many children play the drums?

Solution:
Now we want to know how much is 232 \over 3 of 3030
We found out that 131 \over 3 of 3030 is 1010 children and therefore 232 \over 3 of 3030 is 2020 children. That is 2020 children play the drums.
The main way without depending on the first section:
We will divide the total amount - 3030 By the denominator of the part -> 33
We get
30:3=1030:3=10
The result 1010 we got, we multiply by the numerator of the part -> 22
We get
10×2=2010 \times 2=20

Answer:
That is 2020 children play the drums.


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Now we will move on to the second situation: finding the total amount.

The total amount is unknown
A part of an amount is known and given in a number (it is called partial amount).

The procedure is:
we will divide the given number (partial amount) by the numerator of the part.
We will multiply the result by the denominator of the part and obtain the total amount.

Let's look at this while we ask a question

66 students in the class wear a red shirt and make up 252 \over 5 of the class.
How many children are in the class?

Solution:
here we need to find the total amount, so we will solve it according to the previous steps.
We will divide the given number (the partial amount) –> 66 by the numerator of the fraction 22 and we get:
6:2=36:2=3
The result we obtained 33 we multiply by the denominator of the fraction - 55 and we will get the total amount.
We get:
3×5=153 \times 5=15

Answer:
There are 1515 students in total in the class.


Do you know what the answer is?

Now we will move on to the third (and easiest) situation: finding the part of the quantity

The total amount is known
The partial amount (the given number) is known
The part in the fraction is unknown

The procedure is:

We will divide the partial amount by the total amount - using a fraction.

That is:

In the numerator - we will note the partial amount
In the denominator - we will note the total amount
The fraction we obtained, we will reduce and obtain the desired part.


Let's exercise

77 children in the class can speak English.
There are a total of 4242 children in the class.
What part of the class can speak English?

Solution:
We will write the partial amount in the numerator 77
and in the denominator we will write the total amount 4242
We obtain:
7427 \over 42
We reduce and obtain:
161 \over 6
Answer:
161 \over 6 of the students in the class can speak English.


Examples and exercises with solutions of part of a quantity

Exercise #1

What is the marked part?

Video Solution

Answer

12 \frac{1}{2}

Exercise #2

What is the marked part?

Video Solution

Answer

410 \frac{4}{10}

Exercise #3

What is the marked part?

Video Solution

Answer

46 \frac{4}{6}

Exercise #4

What is the marked part?

Video Solution

Answer

56 \frac{5}{6}

Exercise #5

What is the marked part?

Video Solution

Answer

16 \frac{1}{6}

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