Ratio calculator
Solution:
x = 10
5/6 = 10:12
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.
Ratio questions and word problems
- Garden
The square garden area is 2/9 of a triangle garden with sides 160 m, 100 m, and 100 m. How many meters of fencing are needed to fence a square garden?
- Plan of the village
The plan of the municipality in 1:1000 scale has plotted garden with dimensions 25 mm and 28 mm. Determine the area of gardens in ares in reality.
- Pumps
Pump drawing water at velocity 3.5 liters per second from a construction trench takes 35 minutes. a) Find out how many minutes the water would run out of the trench pump that draws 7.4 liters of water per second. b) What pumping velocity would you have ha
- Glass
At the glass shop, we have to cut eight sheets of glass. Each was shaped as a square with sides of 18 cm. We paid 44 CZK. How much is 1 m² of glass?
- Flowerbed
The family has tulips on a square flower bed of 6 meters. Later, they added a square terrace with a side of 7 meters to their house. One vertex of the terrace lay exactly in the middle of a tulip bed, and one side of the terrace was divided by the side of
- Switzerland - summerjob
Zuzka and Hanka used to work in a cherry orchard to earn money for a sightseeing trip to Switzerland. They brushed 15 trees every day and harvested the entire orchard in 10 days. How long would it take them to harvest the entire orchard if they brushed 20
- Unknown amount of money
Damian and Denis split an unknown amount in the ratio of 5:4. Damian got six euros more than Denis. Calculate an unknown amount. Determine how much money Damian got and how much Denis got.
- Length 4992
The part is 230 meters long. What will its image length be on the plan at a scale of 1:2500?
- Length 6208
How does the volume of a cube change if we double the length of its edge?
- Geometric progression 4
There is a number sequence: 8,4,√2,4,2√2 Prove that the sequence is geometric. Find the common ratio and the following three members.
- Distance 7296
The cyclist covered a certain distance in 9 hours. How many hours does a car need to travel four times more if it moves three times faster?
- Determine 7488
The lengths of the edges of the two cubes are in the ratio 2:3. Determine how many times the surface of the larger cube is larger than the surface of the smaller cube.
- Six percents
6% of the base is 21. How much is 28% of this base?
- A recipe 3
A recipe calls for 1/2 cup of ingredient A for every 1 2/3 cups of ingredient B. You use 4 cups of ingredient A. How many cups of ingredient B do you need?
- Complementary 81152
In a certain polygon, the ratio of the sum of the sizes of its internal angles and the sum of the sizes of the complementary angles is 2:5. How many vertices does this polygon have?
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