Ratio calculator
Solution:
x = 6/5 = 1.2
1.2/2 = 3:5
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
- Sphere cuts
At what distance from the center does the sphere intersect with the radius R = 46 plane if the cut area and area of the main sphere circle are in ratio 2/5?
- Work
The first paver paves the pavement for 27 hours. Second for 27 hours. I started the first paver and, after 4 hours, joined the second. How long will they finish the pavement?
- Bonus
The gross wage was 1222 EUR, including the 14% bonus. How many EUR were bonuses?
- Trapezoid RT
The plot is a rectangular trapezium ABCD, where ABIICD has a right angle at the vertex B side and AB has a length of 36 m. The lengths of the sides AB and BC are in the ratio 12:7. The lengths of the sides AB and CD are in the ratio 3:2. Calculate the con
- Resistances 80352
We connect a 9V battery, 2 light bulbs in parallel, and a switch to the circuit. When the switch is turned on, a current of 0.5 A passes through the first bulb and a current of 8 A through the unbranched part of the circuit. Draw the connection and calcul
- Three-quarters 4216
The machine moves 36 products in half an hour. How many products will move in three-quarters of an hour?
- Cube cut
The edge of the CC' guides the ABCDA'B'C'D'cube, a plane that divides the cube into two perpendicular four-sided and triangular prisms, whose volumes are 3:2. Determine which ratio the edge AB divides by this plane.
- Figure
Figure A is a scale image of Figure B, as shown. (Figure A is 6 inches, and Figure B is x inches, both squares) The scale that maps Figure A onto Figure B is 1:1 1/3. Enter the value f x
- Probability 81964
Calculate the probability of the event that you sit in seats 1 to 30 in the cinema at: a) seat marked with a prime number b) seat marked with an even number c) a seat marked with a number divisible by 3 or 4
- The minute
The minute hand of a clock is 6 cm long. Find the area it sweeps between 2:05 PM and 2:40 PM.
- Kilograms 83204
Nine kilograms of bell metal contain 7 kg of copper, the rest of which is tin. How much copper and how much tin were used to cast five bells? Each of the two larger bells weighed 535kg, and each of the remaining three smaller ones weighed 286kg.
- Components 83328
Divide the number 112 into three components, x, y, and z, so that x: y = 7: 5 and y: z = 3: 4 apply.
- Collecting money
Rs 180 contained in a box of one rupee, 50 Paise and 25 Paise coins in the ratio 2:3:4. What is the number of 50 Paise coins? (One rupee = 100 paisa)
- Greek railwayman
Lewis has worked for the Slovak railways since 2000. His salary is 950 €. His colleague Evgenias works at the Greek State Railways from 1984. Evgenias earns 5700 € per month. Calculate: a) how many times does Evgenias earn more than Lewis? b) how many tim
- Efficiency of rail
With subsidies, is business easy? Calculate how much a rail ticket (x) would cost at today's ticket price € 11 if the government did not subsidize the trains. It is known that it would cost three times today's ticket without subsidies. Calculate the value
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