How do I determine if ratios are equivalent?
We will look at how to calculate equivalent ratios shortly, first lets look at how to use the free online equivalent ratio calculator:
- Enter a Ratio into the equivalent ratio calculator, for example, you could enter 7:25
- Select the number of equivalent ratios that you would like to see in the table of results
- The equivalent ratio calculator will calculate as you type and produce a lis of equivalent ratios in a table below the calculator
How do you determine whether the ratios are equivalent?
equivalent ratios: Two ratios are equivalent if you can multiply each of the numbers in the first ratio by the same factor to get the numbers in the second ratio. Each of these is a pair of equivalent ratios. For each pair, explain why they are equivalent ratios or draw a diagram that shows why they are equivalent ratios.
How to identify equivalent ratios?
Methods to Find the Equivalent Ratios
- Making the consequents the same
- Finding the decimal form of both the ratios
- Cross multiplication method
- Visual method
How do you write equivalent ratios?
n = numerator. d = denominator. a = multiplier. In our equivalent ratio formula, we can see that by multiplying both the numerator and denominator by the same amount (a) that we maintain the relationship with all equivalent ratio and our initial ratio from which we started the calculation.
What is equivalent ratio?
Equivalent ratios are those that can be simplified or reduced to the same value. In other words, two ratios are considered equivalent if one can be expressed as a multiple of the other. Some examples of equivalent ratios are 1:2 and 4:8, 3:5 and 12:20, 9:4 and 18:8, etc.
What is the Definition of Equivalent Ratios?
Two or more ratios are equivalent if they have the same value when reduced to the lowest form. For example, 1:2, 2:4, 4:8 are equivalent ratios. All three ratios have the same value 1:2 when reduced to the simplest form.
How are Proportional Quantities Described by Equivalent Ratios?
A set of equivalent ratios represent proportional quantities. For example, we can say that 2:3 and 4:6 are in proportion. Proportion is nothing but the equality of ratios. This is how proportional quantities can be described by equivalent ratios.
How to Find Missing Numbers in Equivalent Ratios?
To find missing values in equivalent ratios, we have to first find the multiplying factor by equating the values of antecedents and consequents, and then we find the missing number. For example, if it is given that 1:4 and x:16 are equivalent ratios and we have to ding the missing value x. Here, the values of consequents are known to us, i.e 4 and 16. We multiply 4 by 4 to get 16. So, 4 us the multiplying factor in this case. So, we will multiply the antecedent of the first ratio 1 by 4 to find x. Therefore, the value of x is 4 such that 1:4 and 4:16 are equivalent ratios.
How to find unit rate?
Unit rates and equivalent ratios are related to each other. Unit rates can be found by using the concept of equivalent ratios. For example, if it is given that a car covers 70 miles in 2 hours. In the ratio, it can be expressed as 70:2. We can find the unit rate (distance covered in 1 hour), by finding the equivalent ratio of 70:2 such that 2 will be reduced to 1. For that, we need to multiply both the terms by 2 to get 35:1. This is the required unit rate. Similarly, we can also find equivalent ratios from a given unit rate by multiplying the terms with a natural number. This is how unit rates and equivalent ratios are related to each other.
What is the required value of x in 2:3?
Therefore, 2:3 and 10:15 are equivalent ratios, and the required value of x is 15.
What is the formula for 2:3?
Solution: It is given that 2:3 = 10:x. It means that we have to multiply 2:3 with a natural number such that the answer will be of form 10:x, where x is any natural number. Let us look at the antecedents 2 and 10. If we multiply 2 by 5, we get 10. It means we will have to multiply 3 with 5.
How to make equivalent ratios?
We can create equivalent ratios by multiplying or dividing both the numerator and denominator of a given ratio by the same number. To unlock this lesson you must be a Study.com Member.
When we multiply, we create equivalent ratios?
So when we’re dealing with a ratio, if we’re multiplying (or dividing) both parts of it by the same number, we’re creating equivalent ratios.
What happens when you multiply the same ratio?
So when you multiply both parts of a ratio by the same number, you make an equivalent ratio. All we’re really doing is making equivalent fractions, which are two different fractions that are equal. We could, in fact, multiply the numerator and denominator by any number and get an equivalent fraction.
Why are ratios 60/1 and 120/2 equivalent?
In fact, they’re called equivalent ratios, which are ratios that express the same relationship between two numbers. The ratios 60/1 and 120/2 are equivalent because the relationship between the two parts of the ratios didn’t change.
How far did Michelle run in the new ratio?
The distance Michelle ran in this new ratio is 3 meters. So when Johnny had run 1 meter, Michelle had run 3 meters. Look out, Johnny!
What is a ratio in driving?
A ratio is a relationship between two numbers (usually involving some kind of measurement). For example, when people drive, they travel at a certain speed. We usually refer to that speed as miles per hour. That’s a ratio because it’s a relationship between distance and time. So if you’re driving 60 mph, that means that for each hour you drive, …
Is 3/20 a reduced form of 9/60?
1. Yes, the 3/20 is a reduced form of 9/60
Definition Of Equivalent Ratios
If two ratios have the same value when simplified, then they are called Equivalent Ratios.
More About Equivalent Ratios
Equivalent ratios can be obtained by multiplying or dividing both sides by the same non-zero number.
Example of Equivalent Ratios
1/3 and 2/6 are equivalent ratios since they represent the same fraction.
The two ratios 8 : 24 and 4 : 12 are equivalent.
There are 10 dolls for every 40 children in a preschool. Then the ratio of the number of children to that of the dolls = 40:10 = 4:1
What is the equivalence ratio of plastic?
The equivalence ratio (ER) is perhaps the most important parameters in improving the quality of gas yield in air gasification of plastic [14]. It can be defined as the actual air–fuel ratio (used in the gasification) to the stoichiometric air–fuel ratio for combustion. Its significance was reported by Xiao et al. [15], where it was revealed that ER has more pronounced effects on gas yield and reactor temperature in the gasification of PP than bed height and fluidization velocity. However, it should be noted that the equivalence ratio should not be too high. This is because increasing the ER introduces more air in the gasifier, improves the oxidation reaction with rate more than that of reforming and cracking reactions [16], and eventually enhances formation of more CO 2, H 2 O, and N 2. On the other hand, concentrations of CO and H 2 reduce. However, the reduction in hydrogen concentration with increasing ER may not be high in plastic waste as in the case of biomass. This is because plastic waste has more volatile matter and, accordingly, more tar than biomass. Therefore, cracking and adsorption of the tar at a higher ER maintains a higher operating temperature and leads to more H 2 production [17]. Results by Kim et al. [17] showed that concentrations of CH 4 and heavier hydrocarbons were observed to reduce with increasing ER due to enhanced oxidation reaction. Methane reduced significantly from 15.7% to 3.64% when ER was increased from 0.21 to 0.61. Conversely, reduction in the equivalence ratio enhances evolutions of H 2, CO, CH 4, and other hydrocarbons. This was the case as presented in the gasification of PP by Toledo et al. [18]. It was reported by the authors that while ER was reduced from 0.38 to 0.25, H 2 increased by 33%, CO increased by 70%, and CH 4 increased by 30%, heavier hydrocarbons (C 2 H 2, C 2 H 4, and C 2 H 6) increased by 75%. It should be noted that reducing ER increases tar formation due to a reduction in bed temperature, but the reduction can be compensated for by increasing the freeboard temperature in fluidized bed system.
What is the ER value of a gasifier?
The quality of gas obtained from a gasifier strongly depends on the ER value, which must be significantly below 1.0 to ensure that the fuel is gasified rather than combusted. However, an excessively low ER value (<0.2) results in several problems, including incomplete gasification, excessive char formation, and a low heating value of the product gas. On the other hand, too high an ER (>0.4) results in excessive formation of products of complete combustion, such as CO 2 and H 2 O, at the expense of desirable products, such as CO and H 2. This causes a decrease in the heating value of the gas. In practical gasification systems, the ER value is normally maintained within the range of 0.20 to 0.30. Figure 6.20 shows the variation in carbon conversion efficiency of a circulating fluidized-bed gasifier for wood dust against the equivalence ratio. The efficiency increases with ER and then it starts declining. The optimum value here is 0.26, but it may change depending on many factors.
What is the effect of ER on gasification?
The reduction of high heating value gases like H 2 and CH 4 and heavier hydrocarbons, in addition to the dilution effects of N 2, reduces the heating value of the product gas with increasing ER. Effects of ER on the gasification of mixed plastic comprising PVC, PE, PP, PS, PMMA, and PET in air gasification were also reported by Cho et al. [19]. Their results showed that lower heating value reduced from 13.42 to 7.05 MJ/Nm 3 when the ER was increased from 0.21 to 0.41. A similar result was reported by Xiao et al. [15], with higher heating value reducing from 11.3 to 5.17 MJ/Nm 3 when ER was increased from 0.2 to 0.45 in the air gasification of PP. Although increasing ER reduces H 2 and CO evolution, the overall gas yield increases, and char and tar yield reduce. This is because, with an increase in ER, the bed temperature increases, and a higher amount of gas will be formed in such case during the pyrolysis stage of gasification. The high bed temperature also improves tar cracking, produces light hydrocarbons, and enhances char reactions through the water–gas shift and Boudouard reactions [15]. An increase in the ER from 0.2 to 0.31 in the air gasification of PE by Arena et al. [20] led to a reduction in the tar yield from 14.6 to 7 kg/h. In summary, the equivalence ratio in plastic waste gasification should not be too high to avoid production of syngas with low H 2 and CO concentrations. Also, tar removal may be achieved by other means, like bed additives and thermal cracking.
How is the amount of air supplied in a gasifier determined?
In a combustor, the amount of air supplied is determined by the stoichiometric (or theoretical) amount of air and its excess air coefficient. In a gasifier, the air supply is only a fraction of the stoichiometric amount. The stoichiometric amount of air may be calculated based on the ultimate analysis of the fuel.
What is the ER in combustion?
Equivalence ratio (ER) is defined as the air to biomass weight, in relation to the stoichiometric air to biomass weight needed for complete combustion [97].
Is the hydrocarbon to oxygen ratio equal?
The two values are not equal and to compare it to the equivalence ratio, the hydrocarbon-to-oxidizer ratio of ethane and oxygen mixture needs to be determined from the stoichiometric reaction of ethane and oxygen:
What Are Equivalent Ratios?
A ratio is a mathematical way of comparing two quantities. The first quantity to be compared is written first, and the second quantity to be compared is written second. For example, at 8 AM, there are 5 red cars and 2 blue cars in a parking lot. In this case, the ratio of red cars to blue cars is 5 to 2. To express this in ratio form, it can be written in two different ways, 5:2 or 5/2. The ratio of blue cars to red cars is 2 to 5, which can be written 2:5 or 2/5.
Why are ratios considered equivalent?
The ratios are considered to be equivalent because the numerator and denominator are changed in proportion. Equivalent ratios are multiples or factors of each other. Two ratios are equivalent if: When multiplying the numerator and denominator of one ratio by the same number you get the other ratio.
How to find the second ratio of a number?
Multiply OR divide the numerator and denominator by the same number to get the second ratio.
How to find equivalent ratio?
To find an equivalent ratio, multiply the numerator and denominator of the ratio by the same number OR divide the numerator and denominator of the ratio by the same number.
Why are 5/2 and 10/3 not equivalent?
The ratios 5/2 and 10/3 are NOT equivalent because you cannot derive the second ratio by multiplying both numbers of the first ratio by the name number. In this case the ratios did NOT change in proportion.
What is the ratio of red cars to blue cars?
At 5 PM, there are 10 red cars and 4 blue cars, so the ratio of red cars to blue cars is 10:4 or 10/4. Comparing this to the ratio in the morning, we can say that in mathematical terms the ratio 5/2 and 10/4 are equivalent ratios. This is because the values of the ratios are equal. You can derive 10/4 from 5/2 by dividing both numbers by 2. And you can derive 5/2 from 10/4 by multiplying both numbers by 2. In this case the ratios changed in proportion, as reflected in the following equivalent ratios table..
When the numerator and denominator of the first ratio are multiplied by the same number, you?
In mathematical terms, we can find the following pattern: when the numerator and denominator of the first ratio are multiplied by the same number 3, you get the second ratio. And when the numerator and denominator of the second ratio are divided by the same number 3, you get the first ratio.
What is equivalent ratio?
Equivalent ratios demonstrate a proportional relationship between two quantities. A ratio simply compares one number to another. An equivalent ratio means that the proportional relationship stays the same.
Where Can You Identify Equivalent Ratios?
Equivalent ratios on sixth-grade common core worksheets can show up as fractions or whole numbers separated by a colon, such as 2:3 or 4:6.
How much does a fraction equal in simplest form?
We know each of these fractions has the same ratio between the numerators and the denominators. They all equal ½ when put in simplest form.
How to Find Equivalent Ratios?
As we know, two or more ratios are equivalent if their simplified forms are the same. Thus, to find a ratio equivalent to another we have to multiply the two quantities, by the same number.
What are the two equivalent ratios of 4:5?
Hence, the two equivalent ratios of 4 : 5 are 8 : 10 and 12 : 15.
What is ratio in math?
In Mathematics, a ratio compares two quantities named as antecedent and consequent, by the means of division. For example, when we cook food, then each ingredient has to be added in a ratio. Thus, we can say, a ratio is used to express one quantity as a fraction of another quantity.
What is the symbol for ratio?
A ratio is usually expressed with the symbol ‘: ’. The comparison or simplified form of two quantities of the same kind is referred to as ratio.
When the comparison of two different ratios is same, the such ratios are called?
When the comparison of two different ratios is same, the such ratios are called equivalent ratios. For example, 1:2 and 3:6 are equivalent.
Can a ratio be expressed as a fraction?
We can also express the ratio as a fraction. If a:b, is a ratio, then a/b is its fraction form. Thus, we can easily compare two or more equivalent ratios in the form of equivalent fractions.
Is a given ratio equivalent to a simplified form?
Thus, we can see all the above fractions are equivalent since their simplified forms are the same. Therefore, the given ratios are also equivalent to each other.
Definition of Ratio
Examples of Equivalent Ratio
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Let us see some examples of equivalent ratios. For example, when the first and the second term of the ratio \(2:5\) are multiplied by \(2,\) we get \((2×2):(5×2)\) or \(4:10.\) Here, \(2:5\) and \(4:10\) are equivalent ratios. Similarly, when both the terms of the ratio \(4:10,\) are divided by \(2,\) it gives the ratio as \(2:5.\) If we multiply both the terms of \(1:6\) by \(100,\) we will get, \(…
Methods to Find The Equivalent Ratios
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To find the equivalent fractions, first, we should represent the given ratios in fraction form and then simplify them to see whether they are equivalent ratios or not. Simplification of the ratios can be done till both the antecedent and the consequent are still be whole numbers. There are some different methods to check if the given ratios are equivalent or not. 1. Making the consequents t…
Making The Consequents of The Ratios The Same
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The consequents of the ratios \(3:5\) and \(6:10\) are \(5\) and \(10.\) To make the process simple, we will represent it in fraction form that is \(\frac{3}{5}\) and \(\frac{6}{10}.\) The least common multiple (LCM) of the denominators \(5\) and \(10\) is \(10\). Now make the denominators of both fractions \(10,\) by multiplying them with suitable numbers. \( \Rightarro…
Finding The Decimal Form of Both The Ratios
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In this method, we find the decimal form of both the ratios after converting it to fraction form by actually dividing them. We have to check whether \(\frac{3}{5}\) and \(\frac{6}{10}\) have the same value. So, first, find the decimal value of each ratio. \( \Rightarrow \frac{3}{5} = 0.6\) \( \Rightarrow \frac{6}{{10}} = 0.6\) The decimal values of both the fractions are the same, i.e., \(0.…
Solved Examples – Equivalent Ratios
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Q.1. Are the ratios \(2:7\) and \(4:12\) equivalent? Ans: Given ratios are \(2:7\) and \(4:12.\) The fraction form of the given ratios are \(\frac{2}{7}\) and \(\frac{4}{12}\). Then, we will cross multiply and get, \(2 \times 12\,{\rm{\& }}\,7 \times 4\) \( \Rightarrow 24 \ne 28\) Therefore, \(2:7\) and \(4:12\) are not equivalent ratios. Q.2. Are the ratios \(1:6\) and \(2:12\) equivalent? …
Summary
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In this article, we learnt in detail about ratios, equivalent ratios, and how to check the equivalent ratios. We have learned that to find the equivalent ratios of a given ratio, we need to write the fraction form of it. Then, we will multiply the numerator and the denominator of a fraction by the same non-zero number. The equivalent ratio of a given ratio does not change the value of the rat…
Frequently Asked Questions (FAQ) – Equivalent Ratios
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The most frequently asked queries about equivalent ratios are answered below: We hope this detailed article on equivalent ratios has helped you in your studies. If you have any doubt or queries, you can comment down below and we will be more than happy to help you.
Equivalent Ratios – Definition
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A ratio that is obtained by dividing or multiplying the numerator and denominator of a ratio by the same number is known as an Equivalent Ratio. The equivalent ratio is similar to the concept of Equivalent Fractions. The equivalence of two ratios is also known as proportion. If the antecedent and consequent values are different, but still, if we re…
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How to Find Equivalent Ratios?
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In order to find equivalent ratios, we need to make a multiplication or division of both the terms of the given ratio which needs to be done by the same non-zero number. It is important to learn how to determine the equivalent ratios of a ratio by writing the ratio in the form of fractions. When it comes to finding equivalent ratios, two cases might come up. One is to check and identify whet…
Equivalent Ratios Examples with Solutions
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Problem 1:Find the value of x and y using the ratio value of 12:20. Solution: As given in the question the ratio value is 12:20. Now, we need to find the values of x and y. First, let us consider the two ratios that are, 12/20 = x/5 = 12×5 = 20x x 60 = 20 x x = 60/20 = 30. Hence, the value of x is 30. Next, in order to find the value of y. We have to consider the 1st and 3rd ratios. Here it will be…
FAQs on Equivalent Ratios
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1. What are Equivalent Ratios? The Equivalent Ratios states that when the comparison of two different ratios is the same, then such ratios are called Equivalent Ratios. 2. How do we find the Equivalent Ratio? In order to find equivalent ratios, we need to make a multiplication or division of both the terms of the given ratio which needs to be done by the same non-zero number. It is imp…