Division in Given Ratio Practice Problems & Solutions

Master dividing quantities in specific ratios with step-by-step practice problems. Learn ratio division methods, solve real-world examples, and build confidence.

📚Practice Dividing Quantities in Given Ratios
  • Divide money, objects, and quantities using specific ratios like 2:3 or 5:1
  • Apply the three-step method: add ratio parts, find unit value, multiply
  • Solve problems using variables and algebraic equations with one unknown
  • Use table organization method to systematically solve ratio division problems
  • Work with real-world scenarios like sharing inheritance or distributing resources
  • Check answers by verifying totals match original quantities

Understanding Division in a given ratio

Complete explanation with examples

What is division in a given ratio?

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 100100 Dollars in a 2:32:3 ratio.
So, the quantity is 100100 , and the ratio provided is 2:32:3 .

In order to do so, let's follow there simple steps:

  1. Add the parts of the ratio. In our case: 2+3=52 + 3 = 5 .
    Now we know that we need to divide the quantity to 55 .
  2. Divide the total amount by 55 . In our case: 100:5=20100:5=20
    So we get 2020 Dollars per part.
  3. Multiply each of the ratio side by the part.
    So: 202=4020\cdot2=40 , 320=603\cdot20=60 .

And so the 100100 Dollars is divided into 4040 Dollars and 6060 Dollars , maintaining the 2:32:3 ratio.

Diagram demonstrating division in a given ratio: total quantity of $100 divided in the ratio 2:3, resulting in $40 and $60. A simple visualization for understanding ratio-based division, featured in a math tutorial on dividing quantities in specific ratios.

Detailed explanation

Practice Division in a given ratio

Test your knowledge with 27 quizzes

During a swimming contest, four swimmers completed different distances in varying times:

Swimmer A - 50m in 25 seconds.

Swimmer B - 75m in 50 seconds.

Swimmer C - 20m in 10 seconds.

Swimmer D - 100m in 80 seconds.

Which swimmer had the fastest pace?

Examples with solutions for Division in a given ratio

Step-by-step solutions included
Exercise #1

What is the ratio between the number of fingers and the number of toes?

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Identify the number of fingers, which is typically 10.
  • Step 2: Identify the number of toes, which is also typically 10.
  • Step 3: Write the ratio of fingers to toes.
  • Step 4: Simplify the ratio.

Now, let's work through each step:
Step 1: The typical number of fingers on a human is 10 10 .
Step 2: The typical number of toes on a human is 10 10 .
Step 3: The ratio of fingers to toes is 10:10 10:10 .
Step 4: Simplifying this ratio 10:10 10:10 gives us 1:1 1:1 .

Therefore, the solution to the problem is 1:1 1:1 , which corresponds to answer choice 4.

Answer:

1:1 1:1

Exercise #2

In a basket, there are 15 apples and 10 oranges. What is the ratio of apples to oranges?

Step-by-Step Solution

To find the ratio of apples to oranges, divide the number of apples by the number of oranges.
Therefore, apples:oranges=1510=3:2 \text{apples:oranges} = \frac{15}{10} = 3:2 .
Thus, the ratio of apples to oranges is 3:2 3:2 .

Answer:

3:2 3:2

Exercise #3

A recipe calls for 400g of flour and 200g of sugar. What is the ratio of flour to sugar in the recipe?

Step-by-Step Solution

To find the ratio of flour to sugar, divide the amount of flour by the amount of sugar.
Thus, we have flour:sugar=400200=2:1 \text{flour:sugar} = \frac{400}{200} = 2:1 .
Therefore, the ratio of flour to sugar is 2:1 2:1 .

Answer:

3:2 3:2

Exercise #4

A tank fills with water at a rate of 20 liters every 5 minutes.
What is the flow rate of the water in liters per minute?

Step-by-Step Solution

The total volume of water that fills the tank is 20 20 liters over 5 5 minutes. The flow rate is given by the volume divided by time:
Flow Rate=Total VolumeTime=205=4 \text{Flow Rate} = \frac{\text{Total Volume}}{\text{Time}} = \frac{20}{5} = 4
Thus, the water flows at a rate of 4 4 liters per minute.

Answer:

4 4 liters/minute

Exercise #5

On one tree, 8 oranges grow in 4 days.
What is the growth rate of the oranges?

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Identify the total number of oranges that grow, which is 8.
  • Step 2: Note the total number of days in which the 8 oranges grow, which is 4 days.
  • Step 3: Apply the formula for the growth rate: Growth rate=Total number of orangesTotal number of days\text{Growth rate} = \frac{\text{Total number of oranges}}{\text{Total number of days}}.
  • Step 4: Calculate the growth rate by dividing 8 by 4.

Now, let's work through each step:
Step 1: The problem gives us a total of 8 oranges.
Step 2: These oranges grow over a period of 4 days.
Step 3: Using the formula, we find the growth rate: 84=2\frac{8}{4} = 2 oranges per day.

Therefore, the solution is that the growth rate is 2 oranges per day.

Answer:

2 oranges per day

Frequently Asked Questions

What is division in a given ratio?

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Division in a given ratio means splitting a total quantity into parts that maintain a specific proportional relationship. For example, dividing $100 in a 2:3 ratio results in $40 and $60, maintaining the original proportion.

How do you divide a number in a given ratio step by step?

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Follow these three steps: 1) Add the ratio parts together (e.g., 2+3=5), 2) Divide the total by this sum (e.g., 100÷5=20), 3) Multiply each ratio part by this result (2×20=40, 3×20=60).

What are the two main methods for solving ratio division problems?

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The two main methods are: 1) Using one variable (X) where you set up equations like 5X + 3X = 112, and 2) Using a table to organize data systematically with columns for names, ratios, and amounts.

How do you check if your ratio division answer is correct?

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Verify your answer by: 1) Adding the divided parts to ensure they equal the original total, 2) Checking that the ratio between parts matches the given ratio, 3) Cross-multiplying to confirm proportional relationships.

What real-world situations use division in given ratios?

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Common applications include: dividing inheritance among heirs, sharing business profits between partners, distributing resources in recipes, allocating budget amounts, and splitting costs according to agreed proportions.

Can you divide in ratios with more than two parts?

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Yes, ratios can have multiple parts like 2:3:5. Use the same method: add all parts (2+3+5=10), divide the total by this sum, then multiply each part by the result to find individual amounts.

What's the difference between ratio and proportion in division problems?

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A ratio (like 3:7) shows the relationship between quantities, while proportion involves equal ratios. In division problems, you use the given ratio to create proportional parts that maintain the same relationship.

How do you solve ratio division word problems with variables?

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Set up variables for each part (like 5X and 3X for a 5:3 ratio), create an equation using the total (5X + 3X = total), solve for X, then multiply back to find each individual amount.

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