In this Dividing a Quantity in a Given Ratio Concept we have included numerous problems on quantities into two or three parts of a given ratio. We will discuss the quantities of a given ratio in various aspects to get a clear understanding of the whole concept. A ratio is a comparison of different quantities of the same unit and it can be described as a fraction. Here, the ratio of X and Y is defined as X: Y = X/Y. In the ratio, the quantity X is called the antecedent and the quantity Y is the consequent.

Practice the questions given below on Dividing Quantity in Given Ratios and answer all complex problems with ease. The 6th Grade Math Dividing a Quantity into a Given Ratio Word Problems gives a step-to-step explanation so that you don’t feel bored and difficult to study & solve the questions.

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### What is meant by Dividing a Quantity in Given Ratio?

Dividing a quantity in a given ratio 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 or three parts based on a given Ratios.

### Problems on How do I Divide a Number into a Ratio

**Problem 1:**

Divide ₹ 3876 in the ratio of 4/5:1(3/5)

**Solution:**

Given the ratio 4/5: 1(3/5 )i.e., 4/5: 8/5.

First, find the sum value of the given ratios.

The ratio becomes 4: 8 = 4+8 = 12.

Let the common multiple be x.

12x = 3876

x = 387612

⇒ x = 323

Now, 4x = 4×323 = 1292.

Next, the value is 8x = 8×323 = 2584.

Hence, the ratio is divided into ₹1292 and ₹2584.

**Problem 2:
**A bag contains red and black marbles in the ratio of 2 : 3. If there are 40 red marbles, find the total number of marbles in the bag?

**Solution:
**As given in the question,

The ratio of red marbles and black marbles is 2:3.

So, the total number of red marbles is 40.

First, find the sum value of the given ratio.

The sum ratio value is 2+3 = 5.

Let x be the number of marbles in the bag.

Now, find the x value.

2/5 x X = 40

2x/5 = 40

2x = 40 x 5 = 200.

x = 200/2 = 100.

Therefore, the total number of marbles in a bag is 100.

**Problem 3:
**If 4x = 7y = 2z, find the ratio of x: y: z.

**Solution:**

In the Given question, the equation is 4x = 7y = 2z.

Now, we will find the ratios.

Let 4x = 7y

So, x = 7y/4 —- (i)

Next, 7y = 2z

⇒ z = 7y/2 —- (ii)

Now, from the equation (i) and (ii) the ratio is

x: y: z = 7y/4: y : 7y/2.

x: y: z = 7/4: 1 : 7/2

The value is x: y: z = 7: 4: 14

Therefore, the ratio of x: y: z is 7: 4: 1.

**Problem 4:**

Sam and John worked together on a project and received $250 for their completed work. Sam worked for 2 days and John worked for 3 days, and they agree to divide the money between them in the ratio of 2: 3. How much the amount should each receive?

**Solution:
**In the given question, the value is 250 and the ratio is 2:3.

First, find the total of the given ratio.

The sum of the given ratio is 2+3 = 5.

Now, there are 5parts. In that, the smaller amount is 2.

So, the smaller amount is 2/5 x 250.

i.e., 2x 50 = 100.

So, Sam’s share is $100 and the remaining amount is John’s share which is $150.

**Problem 5:**

A number is divided into two parts in the ratio of 4: 9. If the larger part is 270, then what are the actual number and the smaller part?

**Solution:**

The given ratio is 4: 9.

So, the numbers are 4k and 9k.

Given that, the larger part of the number is 270.

Now, we need to find the value of k.

i.e., 9k = 270.

k = 270/9.

Therefore k = 30.

Next, the number is 4k.

substitute the k value in 4k. We get,

4k = 4 × 30 = 120.

Hence, the smaller part number is 120 and the actual number is 390(i.e., 270+120 = 390).

**Problem 6:**

Four workers worked for 7 hours, 6 hours, 5 hours, and 6 hours. The total wages amount is ₹14640 was divided among the four workers according to the number of hours worked. How much did they get for the hours they worked?

**Solution:**

Let the hours of the workers worked to be in the ratio of 7: 6: 5: 6.

The sum of the ratio is 7+6+5+6 = 24hours

Now, find the amount per hour i.e., Total wage / Hours worked = ₹14640/24 = ₹610 per hour

The wage of the first worker is 7×₹610 = ₹4270

The wage of the second worker is 6×₹610 = ₹3660

The wage of the third worker is 5×₹610 = ₹3050

The wage of the fourth worker is 6×₹610 = ₹3660

Therefore, the amount of each worker is ₹4270, ₹3660, ₹3050, and ₹3660.

**Problem 7:**

What is the value of a : b : c : d? If a : b = 2 : 3 , b : c = 4 : 5 , and c : d = 6 : 7.

**Solution: **

Given in the question, the value is a:b=2:3, b:c=4:5, c:d=6:7.

Now, find the value of a:b:c:d.

First, find the value of a:b i.e, 2×8:3×8 =16:24.

Next, the value of b:c is 4×6:5×6 = 24:30.

The value of c:d is 6×5:7×5 = 30:35.

So, the value of a:b:c:d is 16:24:30:35.

**Problem 8:**

Divide $260 among A, B, and C in the ratio of 1/2: 1/3: 1/4.

**Solution:
**Given that, the value is $260 and the ratios are 1/2:1/3:1/4.

First of all, we need to convert the given ratio into its simple form.

So, the L.C.M. of denominators 2, 3, and 4 is 12.

Therefore, 1/2 : 1/3 : 1/4 = 1/2 × 12 : 1/3 × 12 : 1/4 × 12 = 6 : 4 : 3

Now, find the sum of the given ratios that is 6 + 4 + 3 = 13.

Next, the A’ share is 6/13 of $260 = $6/13 × 260 = $120.

The B’ share is 4/13 of $260 = $4/13 × 260 = $80.

The C’ share is 3/13 of $260 = $3/13 × 260 = $60.

Hence, the shares of A are $120, B is $80 and C is $60.

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### FQAs on Dividing a Quantity in a given Ratio

**1. Why do we divide ratios?**

In mathematics, a ratio is a comparison of two or more numbers that indicates their sizes in relation to each other. A ratio will compare two quantities by division, with the dividend or number being divided as the antecedent and the divisor or number that is dividing named as the consequent.

**2. What are the steps for dividing a quantity in a given ratio?**

The following are the steps for dividing a quantity in a given ratio:

- Step 1: First, find the sum of the ratio’s values.
- Step 2: Next, divide by the sum of the ratio.
- Step 3: Now, multiply with the quotient.

**3. What happens when you divide a ratio?**

When dividing ratios, we are essentially dividing a whole number into a number of smaller numbers and assigning those in proportion to the specified ratio by multiplying.

**4. How do you share in a given ratio?**

The Sharing in a given ratio is,

1. First, add all the ratios to find the total number of parts.

2. Next, divide the total amount by the number of parts.

3. Then, multiply by the ratio to find each value.

4. Now, add up all these values to check with the original value.