Division in a given ratio means splitting a total quantity into parts that maintain a specific proportional relationship, based on the ratio provided. In a division according to a given ratio, we will have a defined quantity that we must divide according to said ratio. The process ensures that the ratio between the parts stays consistent, regardless of the total amount being divided. This concept is frequently used in various scenarios, such as dividing an inheritance, sharing resources, or solving problems in geometry.
Let's use an Example:
We want to divide 100 Dollars in a 2:3 ratio. So, the quantity is 100, and the ratio provided is 2:3.
In order to do so, let's follow there simple steps:
Add the parts of the ratio. In our case: 2+3=5. Now we know that we need to divide the quantity to 5.
Divide the total amount by 5. In our case: 100:5=20 So we get 20 Dollars per part.
Multiply each of the ratio side by the part. So: 20⋅2=40, 3⋅20=60.
And so the 100 Dollars is divided into 40 Dollars and 60 Dollars , maintaining the 2:3 ratio.
From here it follows that the number of refrigerators is 75(3X), and the number of air conditioners is X=25.
We can always go back and check our result by verifying that the total number of appliances in the store is 100, as stated in the first piece of data given.
Examples and exercises with solutions for division according to a given ratio
Exercise #1
Given the rectangle ABCD
AB=X
The ratio between AB and BC is 2x
We mark the length of the diagonal A the rectangle in m
Check the correct argument:
Video Solution
Step-by-Step Solution
Given that:
BCAB=2x
Given that AB equals X
We will substitute accordingly in the formula:
BCx=2x
x2=BCx
xx2=BC
xx×x×2=BC
x×2=BC
Now let's focus on triangle ABC and use the Pythagorean theorem:
AB2+BC2=AC2
Let's substitute the known values:
x2+(x×2)2=m2
x2+x×2=m2
We'll add 1 to both sides:
x2+2x+1=m2+1
(x+1)2=m2+1
Answer
m2+1=(x+1)2
Exercise #2
Given the rectangle ABCD
AB=X the ratio between AB and BC is equal to2x
We mark the length of the diagonal A with m
Check the correct argument:
Video Solution
Step-by-Step Solution
Let's find side BC
Based on what we're given:
BCAB=BCx=2x
BCx=2x
2x=xBC
Let's divide by square root x:
x2×x=BC
x2×x×x=BC
Let's reduce the numerator and denominator by square root x:
2x=BC
We'll use the Pythagorean theorem to calculate the area of triangle ABC:
AB2+BC2=AC2
Let's substitute what we're given:
x2+(2x)2=m2
x2+2x=m2
Answer
x2+2x=m2
Exercise #3
In a box there are 28 balls, 41 of which are orange.
How many orange balls are there in the box?
Video Solution
Answer
7
Exercise #4
There are 18 balls in a box, 32 of which are white.
How many white balls are there in the box?
Video Solution
Answer
12
Exercise #5
How many times longer is the radius of the red circle than the radius of the blue circle?
Video Solution
Answer
2
Do you know what the answer is?
Question 1
How many times longer is the radius of the red circle, which has a diameter of 24, than the radius of the blue circle, which has a diameter of 12?