How to Calculate Ratios

To calculate a ratio, divide one quantity by another and simplify the fraction if possible. This shows how many times one quantity is compared to another. Make sure both quantities are in the same units before you start.

Example: We have 10 apples and 20 oranges, and you want to find the ratio of apples to oranges.

To find the ratio of apples to oranges, you simply divide the number of apples by the number of oranges:

Ratio = (Number of Apples) / (Number of Oranges)

Given that there are 10 apples and 20 oranges, the ratio is:

Ratio = 10 apples / 20 oranges

Now, let’s simplify this ratio:

Ratio = (10 ÷ 10) apples / (20 ÷ 10) oranges = 1 apple / 2 oranges

So, the ratio of apples to oranges is 1:2.

Example: What is the ratio of 15 oranges to 5 apples?

To find the ratio of oranges to apples, you simply divide the number of oranges by the number of apples:

Ratio = (Number of Oranges) / (Number of Apples)

Given that there are 15 oranges and 5 apples, the ratio is:

Ratio = 15 oranges / 5 apples

Now, let’s simplify this ratio:

Ratio = (15 ÷ 5) oranges / (5 ÷ 5) apples = 3 oranges / 1 apple

So, the ratio of oranges to apples is 3:1.

How to Find the Ratio of Two Things

Finding the ratio of two things involves comparing them quantitatively. Count each item, then express their relationship as a ratio. This is explained in the example below,

Example: Find the ratio of 8 cats to 12 dogs.

To find the ratio of cats to dogs, you simply divide the number of cats by the number of dogs:

Ratio = (Number of Cats) / (Number of Dogs)

Given that there are 8 cats and 12 dogs, the ratio is:

Ratio = 8 cats / 12 dogs

Now, let’s simplify this ratio:

Ratio = (8 ÷ 4) cats / (12 ÷ 4) dogs = 2 cats / 3 dogs

So, ratio of cats to dogs is 2:3.

How to Convert Ratios With Different Units

To convert ratios with different units, you must first convert one of the units so both are the same. Then, calculate the ratio as usual. This is explained in the example below,

Example: Convert and find the ratio of 2 kilometers to 500 meters.

To compare the ratio of kilometers to meters, we need to ensure both quantities are in the same unit. Let’s convert 2 kilometers to meters:

1 kilometer = 1000 meters

So, 2 kilometers equals:

2 kilometers × 1000 meters/kilometer = 2000 meters

Now, we have 2000 meters and 500 meters. The ratio is:

Ratio = (Number of Kilometers) / (Number of Meters)

Ratio = 2 kilometers / 500 meters

Ratio = (2000 meters / 500 meters)

Ratio = 4

So, the ratio of 2 kilometers to 500 meters is 4:1.

Solving Ratios That Include Decimals

When working with ratios that include decimals, treat the decimals as regular numbers. You may multiply both sides to eliminate decimals for simplicity. This is explained in the example below,

Example: Find the ratio of 1.5 to 3.

To find the ratio of 1.5 to 3, we simply write it as a fraction:

Ratio = 1.5 / 3

Now, let’s simplify this fraction:

Ratio = (1.5 ÷ 1.5) / (3 ÷ 1.5) = 1 / 2

Using Ratios to Solve the Direct Proportions of Quantity

To use ratios for direct proportions, set up a ratio equation and solve for the unknown. This shows how quantities are directly related. This is explained in the example below,

Example: If the ratio of flour to sugar is 2:1, how much sugar do you need for 4kg of flour?

Since the ratio of flour to sugar is 2:1, for 4kg of flour, you would need:

Equivalent parts of sugar = (4 kg of flour) / (2 parts of flour) = 2 kg

Amount of sugar needed = (2 kg) × (1 part of sugar) = 2 kg

So, for 4 kg of flour, you need 2 kg of sugar.

How to Divide a Number by a Ratio

Dividing a number by a ratio means splitting the number according to the ratio parts. This is explained in the example below,

Example: Divide $50 into a ratio of 3:2.

To divide $50 into a ratio of 3:2, first, we need to find the total number of parts in the ratio, which is 3 + 2 = 5.

Next, we divide the total amount of money by the total number of parts to find the value of each part.

Value of each part = Total amount / Total number of parts = $50 / 5 = $10

Now, we multiply the value of each part by the respective parts in the ratio to find out how much each portion receives:

For the part representing the ratio of 3: 3 parts × $10 per part = $30

For the part representing the ratio of 2: 2 parts × $10 per part = $20

So, dividing $50 into a ratio of 3:2 results in $30 for the first part and $20 for the second part.

How to Use Ratios to Find an Unknown Number

Using ratios to find an unknown number involves setting up a proportion based on a known ratio. This is explained in the example below,

Example: If the ratio of boys to girls is 4:3 and there are 12 girls, how many boys are there?

To find out how many boys there are when the ratio of boys to girls is 4:3 and there are 12 girls

Total parts = 4 (boys) + 3 (girls) = 7 parts

Value of each part = Total girls / Number of parts for girls = 12 / 3 = 4

Number of boys = Number of parts for boys × Value of each part = 4 × 4 = 16

So, there are 16 boys.

How to Find a Ratio

To find a ratio, compare two quantities by dividing them and simplifying the result. This is explained in the example below,

Example: What is the ratio of 30 minutes to 2 hours?

To find the ratio of 30 minutes to 2 hours, we need to ensure both quantities are in the same units. Since 1 hour is equal to 60 minutes, we can convert 2 hours to minutes:

2 hours × 60 minutes/hour = 120 minutes

Now, we have both quantities in minutes:

Ratio = (Number of Minutes) / (Number of Minutes)

Ratio = 30 minutes / 120 minutes

To simplify this ratio, we can divide both numbers by their greatest common divisor, which is 30:

Ratio = (30 ÷ 30) minutes / (120 ÷ 30) minutes = 1 minute / 4 minutes

So, the ratio of 30 minutes to 2 hours is 1:4.

A ratio is a mathematical expression that compares two or more numbers. It shows the relative sizes or quantities of one value to another. It is expressed in the form of a fraction or with a colon, such as 3:1 or 3/1, indicating that for every unit of the second quantity, there are three units of the first.

In this article, you will get a step-by-step guide on how to calculate ratios.