# CLASS-6TO DIVIDE A QUANTITY IN A GIVEN RATIO

TO DIVIDE A QUANTITY IN A GIVEN RATIO -

To divide a quantity in a given ratio, you'll need to follow these steps:-

(1) Understand the Ratio:- First, make sure you understand the given ratio. The ratio expresses the relationship between the parts into which you want to divide the quantity. The ratio will be in the form a:b, where "a" and "b" are two numbers.

(2) Add the Ratio Parts:- Add together the two numbers in the ratio to find the total number of parts. In other words, find a + b.

(3) Determine the Total Quantity:- Identify the total quantity that you want to divide in this ratio. This could be a specific amount of money, objects, or any other measurable quantity.

(4) Calculate the Size of Each Part:- Divide the total quantity by the total number of parts (a + b) to find the size of each part. This will be the unit quantity for the ratio.

(5) Allocate the Parts:- Multiply the unit quantity by "a" to find the quantity for the first part, and multiply it by "b" to find the quantity for the second part. This allocation ensures that you've divided the quantity in the given ratio.

(6) Divide the Total Quantity into Parts:- Divide the total quantity into parts according to the ratio. To do this, you can use proportions or direct division. Here's how:

• Using Proportions:-
• Set up a proportion where one side represents the given ratio, and the other side represents the divided quantities.
• For example, if you have a total quantity of 120 units and a ratio of 2:3, you can set up the proportion: 2/3 = x/120, where x represents the unknown quantities.
• Cross-multiply and solve for x: 2 * 120 = 3x, x = (2 * 120) / 3 = 240 / 3 = 80.
• So, you would divide the quantity into 2 parts of 80 units each and 3 parts of 80 units each.

• Direct Division:-
• Add the two numbers in the ratio to find the total number of parts. In the example with a ratio of 2:3, there are 2 + 3 = 5 parts in total.
• Divide the total quantity by the total number of parts to find the quantity for each part.
• For example, if you have 120 units to divide in a 2:3 ratio, you would divide 120 by 5 to get 24 units per part.
• Then, multiply each part by the respective ratio number to find the quantities in the given ratio. In this case, you'd have 2 parts of 24 units each and 3 parts of 24 units each.

Here's a step-by-step example:-

Suppose you want to divide \$300 in the ratio 2:3.

1. Understand the Ratio:- The given ratio is 2:3, which means you want to divide the quantity into two parts and three parts.
2. Add the Ratio Parts:- 2 + 3 = 5.
3. Determine the Total Quantity:- The total quantity is \$300.
4. Calculate the Size of Each Part:- \$300 รท 5 = \$60. This is the size of each part.
5. Allocate the Parts:For the first part (2 parts):- \$60 * 2 = \$120. For the second part (3 parts): \$60 * 3 = \$180.

So, you would divide \$300 into \$120 and \$180 in the ratio 2:3.

Always double-check your calculations to ensure that the parts add up to the total quantity, confirming that you've divided it correctly according to the given ratio.