In this article, you will learn about the rules of dividing a quantity into two given ratios. The ratio will indicate their relative sizes and always expresses the ratio numbers in the lowest possible terms. A ratio compares two or more different quantities but they have the same units of measure. In this 6th Grade Math Concept dividing a quantity in two given ratios word problems, students can get the questions that are relevant to how to divide a quantity into two given ratios with detailed solutions.
On this page, we will discuss a definition of dividing a quantity into two given ratios, rules, and solved example problems on dividing a quantity into two given ratios. This activity page on dividing a quantity into two given Ratios is a fun-learning workbook to solve all the questions.
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What is Dividing a Quantity in Two Given Ratios?
Dividing a quantity into two given ratios is stated as taking a common multiple that is x and then finding each part in terms of x. We have to divide a number into two parts having a ratio of 3:2 then, let the common multiple be x. Thus, the two parts are 3x and 2x. You can also download the worksheet on dividing a quantity into two given ratios pdf from this page.
Rules of Dividing a Quantity in Two Given Ratios
The rules of dividing a quantity into two given ratios are explained below. If a quantity K is divided into two parts in the ratio of X: Y, then
(i) The first part is X/(X + Y) × K, and
(ii) The Second part is Y/(X + Y) × K.
Problems on Dividing a Quantity into Two Given Ratios
Problem 1:
Divide $280 in the ratio of 3: 5.
Solution :
As given in the question, the ratios are 3:5.
In the ratio of 3: 5, the first quantity is 3 parts and the second quantity is 5 parts.
The Total number of parts are 3 + 5 = 8.
So, the 8 parts are $280.
1 part is 280/8 = $35
3 parts is 3 x 35 = $105
5 parts is 5 x 35 = $175
So, after dividing $280 the values are $105 and $175 in the ratio of 3:5.
Problem 2: Two numbers are in the ratio of 5:4. If the sum of the numbers is 72, find the numbers.
Solution:
In the given question, the sum value is 72 and the ratio is 5:4.
The Sum of terms of the ratio is 5 + 4 = 9.
So, the First number is 5/9× 72= 40.
The Second number = 4/9× 72 = 32.
Thus, the numbers are 49 and 42.
Problem 3: The length and breadth of a rectangle are in the ratio of 4:7. Find the length, If the breadth is 77 cm?
Solution :
Given that,
The Breadth value is 77 cm.
The ratio of length to breadth is 4: 7.
So, the Breadth is divided into 7 parts.
7 parts are 77 cm.
The first part = 77/7 = 11 cm and the length is 4 parts.
The 4 parts are 4 x 11 cm = 44 cm.
Hence, after dividing the rectangle’s length is 44 cm.
Problem 4: In a village, there are 1,21,000 people, and the ratio of men to women is 6: 5. Find the number of men and women?
Solution :
As given in the question, the data
The Number of people in the village is 1,21,000.
The men to women ratio is 6: 5.
The total number of parts are 6 + 5 = 11.
So, the 11 parts are 1,21,000.
The first part is 121000/11 = 11000.
The Number of men in the village is 6 x 11,000 = 66,000
Next, the number of women in the village = 5 x 11,000 = 55,000
Therefore, the number of men and women is 66000 and 55000.
Problem 5: Divide 5 kg 500 gm in the ratio of 5: 6. Write the dividing quantity values.
Solution :
In the question, the given quantity is 5 kg 500 gm.
First, we have to convert the given measurement into one unit.
We know that,1 kg = 1000 gm.
So, 5 kg will be in grams is 5 x 1000 = 5000 gm.
The 5 kg 500 gm is 5000 + 500 = 5500 gm.
Now, the given ratio is 5: 6.
The total number of parts are 5 + 6 = 11.
11 parts are 5500.
1 part = 5500/11 = 500
The Quantity of 1st part is 5 x 500 = 2500 grams.
The Quantity of the 2nd part is 6 x 500 = 3000 grams
So, 2 kg 500 gm and 3 kg are the two parts.
Hence, the 2kg 500gm and 3kg are the two quantities.
Problem 6: Divide 2 m 25 cm in the ratio of 5: 4.
Solution :
The Given quantity = 2 m 25 cm
First, we have to convert the given measurement into one unit.
We know that,1m = 100 cm.
So, the 2 m is 2 x 100 = 200 cm.
Next, the 2 m 25 cm is 200 + 25 = 225 cm.
The Given ratio is 5: 4.
So, the total number of parts is 5 + 4 = 9.
9 parts are 225.
1 part is 225/9 = 25
The Quantity of 1st part is 5 x 25 = 125 cm.
The Quantity of 2nd part is 4 x 25 = 100 cm.
Thus the two dividing quantities are 125cm and 100cm.
Problem 7: Divide 5 hours in the ratio of 1: 5.
Solution :
As given in the question, the quantity is 5 hours and the ratio is 1:5.
We all know that 1 hour is 60 minutes.
So 5 hours will be 5 x 60 = 300 minutes.
The total number of parts are 1 + 5 = 6.
6 parts are 300.
The 1 part is 300/6 = 50.
The Quantity of 1st part is 1 x 50 = 50 minutes.
The Quantity of 2nd part is 5 x 50 = 250 minutes.
Hence, the two quantities are 50 minutes and 250 minutes.
Problem 8: If a: b = 3: 7, then find the ratios of the following:
(i) (2a+ 5b): (3a+ 6b)
(ii) (a+ 2b): (7a- b)
Solution:
Given ratio a: b = 3: 7
The given equation is (2a+ 5b): (3a+ 6b).
Now, we will substitute the values of a and b in the above equation. we get,
(2a+ 5b): (3a+ 6b) = ((2×3)+(5×7)): ((3×3)+(6×7)) = (6+35): (9+42) = 41: 51
Thus, the ratio of the equation (2a+ 5b): (3a+ 6b) is 41: 51.
(ii) Given equation is (a+ 2b): (7a- b)
The values of a and b were given are 3 and 7.
Now, substitute the values in the above equation.
(a+ 2b): (7a- b) = (3+(2×7)): ((7×3)-7) = (3+14): (21-7) = 15: 14
Hence, the ratio is 15: 14.
Problem 9: What number should be added to the ratio of 13: 33? So, the ratio becomes 4: 9.
Solution:
The Given ratio is 13: 33
Now, we need to add the number so that we can get the ratio of 4: 9.
First, we add the number 3 to the given ratio of 13: 33.
Then the value is 13+3: 33+3 is 16: 36.
So, the ratio becomes 16: 36 which is 4: 9.
Therefore, the number 4 should be added to the given ratio.
FAQs on Dividing a Quantity in a two given ratios
1. How do you divide the ratio?
First, create a fraction that has a numerator equal to the ratio being divided and the denominator equal to the ratio it is being divided by. For example, the value (3/5) / (1/3) is represented as 3/5 divided by 1/3. Then Invert the denominator and change the division symbol to a multiplication symbol.
2. What is dividing a quantity into two given ratios?
Dividing a quantity into two given ratios is stated as taking a common multiple that is x and then finding each part in terms of x. We have to divide a number into two parts having a ratio of 3:2 then, let the common multiple be x. Thus, the two parts are 3x and 2x.
3. What are the rules for dividing a quantity into two given ratios?
The rules of dividing a quantity into two given ratios are explained below. If a quantity K is divided into two parts in the ratio of X: Y, then
(i) The first part is X/(X + Y) × K, and
(ii) The Second part is Y/(X + Y) × K.