Ratio calculator

Solution:

180 = 60 + 120

60:120 = 1:2

Solve ratios or proportions a:b=c:d for the missing value. Missing value mark as variable x (or other a-z). We also accept decimals and some basic mathematical operations. Ratios enter in the form such as:

1/x = 3/8
180 = 1:2 divide a number in the ratio
2:x = 4:5
x/2 = 3:5
2.2/x = 5.5/6.6
5/6 = x:12
-8/5 = 12/y
-8/5 = (y+1)/12
A ratio in math is a way to compare two or more quantities by showing the relative sizes of the quantities. It expresses how much of one quantity there is compared to another. Ratios are used in many real-world situations, such as cooking, mixing ingredients, scaling maps, and comparing proportions.

Key Concepts of Ratios

1. Definition:
- A ratio compares two or more numbers or quantities. It is written in the form a : b or ab , where a and b are the quantities being compared.

2. Simplification:
- Ratios can be simplified by dividing both terms by their greatest common divisor (GCD). For example:
- The ratio 6 : 9 can be simplified to 2 : 3 by dividing both terms by 3.

3. Types of Ratios:
- Part-to-Part Ratio: Compares one part of a whole to another part of the same whole. For example, in a group of 5 boys and 3 girls, the ratio of boys to girls is 5 : 3 .
- Part-to-Whole Ratio: Compares one part of a whole to the entire whole. For example, in the same group, the ratio of boys to the total number of children is 5 : 8 .

4. Equivalent Ratios:
- Ratios that represent the same relationship but are written with different numbers. For example:
- 2 : 3 is equivalent to 4 : 6 or 6 : 9 .

5. Proportions:
- A proportion is an equation that states that two ratios are equal. For example:
- 23 = 46 is a proportion.

How to Write and Use Ratios

Example 1:

Writing a Ratio
- Suppose there are 4 apples and 6 oranges. The ratio of apples to oranges is:

4 : 6 or 46

- This can be simplified to:

2 : 3 or 23

Example 2:

Using Ratios in Real Life
- A recipe calls for 2 cups of flour and 1 cup of sugar. The ratio of flour to sugar is:

2 : 1

- If you want to double the recipe, the ratio remains the same, but the quantities become:

4 cups of flour : 2 cups of sugar

Applications of Ratios

1. Scaling:
- Ratios are used to scale objects up or down. For example, if a map has a scale of 1 : 100,000 , 1 cm on the map represents 100,000 cm in real life.

2. Mixing:
- Ratios are used to mix ingredients in recipes, paints, or chemicals. For example, a paint mixture might use a ratio of 3 : 1 (3 parts paint to 1 part thinner).

3. Finance:
- Ratios are used in finance to compare quantities, such as debt-to-income ratio or price-to-earnings ratio.

4. Probability:
- Ratios are used to express probabilities. For example, the probability of rolling a 3 on a six-sided die is 1 : 6 .

Summary

A ratio is a mathematical tool for comparing quantities. It can be written in the form a : b or ab , simplified, and used in various real-world applications. Understanding ratios is essential for solving problems involving proportions, scaling, mixing, and more.