How to Calculate Rate

A ratio is a mathematical expression that compares two or more numbers. Ratios can be used to compare quantities and absolute quantities or to compare parts to a sum. Ratios can be calculated and written in different forms, however, the principle that guides their use is the same.

Table of Contents

Understanding What is Ratio?

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Notice how the ratio is used. Ratios are used in academia and life to compare multiple quantities or quantities with each other. The simplest ratio is to compare two values, there are also ratios that compare three or more values. In any case where two or more different numbers and quantities are to be compared, the ratio applies. By describing a quantity relationship, the ratio indicates whether a chemical recipe can be doubled or a recipe can be added. Once you understand the problem, you will often use proportions in your life. ^{[1] X Research Source}

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Understand what the ratio is. As noted above, ratio represents the quantitative relationship of at least two objects to each other. For example, if baking requires two cups of flour and one cup of sugar, you would say that the ratio of flour to sugar is 2/1.

Ratios are used to determine the relationship between quantities, even if they are not directly tied (such as in recipes). For example, if there are 5 girls and 10 boys in the class, the ratio of girls to boys is 5/10. These two quantities do not depend or bind to each other, and will change if the number of students is reduced or added. Ratios are simply for comparing quantities.

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Notice how the ratios are written. Ratios can be written in words or in mathematical notation. ^{[2] X Research Source}

You will often see ratios written in words (as above). Since ratios are often used in a variety of ways, if you’re not working in science or math, you’ll find that’s the most common way of writing ratios.
Ratios are often used with colons. When comparing two quantities, you would use a colon (like 7 : 13) and when comparing two or more quantities you would add a colon between each pair of continuous quantities (like 10 : 2 : 23). . In the classroom example, we can compare the number of boys with the number of girls by the ratio: 5 girls: 10 boys. We can also simply write: 5 : 10.
Ratios are sometimes written as fractions. In the classroom example, the ratio of 5 girls to 10 boys could be simply written as 5/10. However, you should not interpret that ratio as a fraction and must remember that these numbers do not represent the ratio of a part to a sum.

Using Ratio

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Return the scale to its minimalist form. Ratios can be reduced to fractions by removing the common divisors of the terms in the ratio. To minimize the ratio, divide the term in the ratio by the common divisors until it can no longer be divided. However, when doing so, it is important not to forget the original quantity to get that ratio. ^{[3] X Research Sources}

In the class example above, the ratio of 5 girls to 10 boys (5 : 10), both terms have a common divisor of 5. Divide the two terms by 5 (greatest common divisor). best) to get a ratio of 1 girl to 2 boys (or 1: 2). However, we must keep the original quantity in mind even when using the scaled down. The class size is 15, not 3. The minimalist ratio only compares the relationship between the number of boys and girls. There are 1 in 2 boys and 1 girl, not just 2 boys and 1 girl.
Some ratios cannot be minimized. For example, 3:56 cannot be reduced because the two numbers have no common divisor – 3 is prime, and 56 is not divisible by 3.

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Use multiplication or division to “balance” the ratio. A common type of ratio problem is to use ratios to balance the increase or decrease of two proportional numbers. Multiply or divide the terms in the ratio by the same number to get a new ratio that is proportional to the original ratio, so to balance the ratio, multiply or divide the ratio by the scaling factor. ^{[4] X Research Sources}

For example, a baker needs to increase a cake recipe by 3 times. If the ratio of flour to regular sugar was 2/1 (2 : 1), then both numbers would have to be multiplied by 3. The corresponding amount would be 6 cups of flour with 3 cups of sugar (6: 3).
The same procedure can be done in reverse. If the baker needs only half the ingredients for a regular cake recipe, then both quantities are multiplied by 1/2 (or divided by 2). The result will be 1 cup of flour versus 1/2 (0.5) cup of sugar.

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Find the unknown known in advance of two equal ratios. Another type of ratio problem requires finding one unknown in the ratio, given another number in the ratio, and the second ratio being equal to the first. The principle of cross multiplication can solve this problem quite easily. Write the ratio as a fraction, set the two ratios equal, and cross multiply to get the result. ^{[5] X Research Sources}

For example, we have a group of students consisting of 2 boys and 5 girls. If the ratio of boys to girls is calculated, how many boys will there be in a class with 20 girls? To solve this problem, first, we have two ratios, one of which contains unknowns: 2 males : 5 females = x males : 20 females. Converting to a fraction, we have 2/5 and x/20. If we cross multiply, we get 5x=40, solve the problem by dividing both sides of the equation by 5. The final result is x=8.

Error Detection

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Avoid addition or subtraction in word scale problems. Many word problems are written like this: “A recipe calls for 4 potatoes and 5 carrots. If you need to use 8 potatoes, how many carrots are needed to keep the ratio the same. ?” Many students add the same amount to each quantity. You actually need to use multiplication, not addition, to keep the ratio the same. Here is an example of how to do right and wrong when solving this problem:

Wrong way: “8 – 4 = 4, I add 4 potatoes and the recipe. Which means I will also add 4 carrots to the 5 given… Wait! That’s not the right way to do it! I’ll try again.”
Correct way: “8 ÷ 4 = 2, we multiply the number of potatoes by 2. That means we also multiply 5 carrots by 2.5. 5 x 2 = 10, so we need a total of 10 carrots for new recipes”.

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Convert to the same unit. Some problems are more complicated by using different units of measure. Let’s convert to the same unit before finding the ratio. Here is an example of a problem and its solution:

A storekeeper has 500 g of gold and 10 kg of silver. What is the ratio of gold to silver in stock?
Grams and kilograms are not the same thing, so we have to change the units. 1 kg = 1,000 g, so 10 kg = 10 kg x $1,000 yen$ $g$ $first$ $k$ $g$ ${displaystyle {frac {1,000g}{1kg}}}$ ${frac {1,000g}{1kg}}$ = 10 x 1,000 g = 10,000 g.
The storekeeper has 500 g of gold and 10,000 g of silver.
The ratio of gold to silver is $500$ $g$ $DRAW$ $a$ $n$ $g$ $10,000 won$ $g$ $REMOVE$ $a$ $c$ $=$ $5$ $100$ $=$ $first$ $20$ ${displaystyle {frac {500gVang}{10,000gBac}}={frac {5}{100}}={frac {1}{20}}}$ ${frac {500gVang}{10,000gBac}}={frac {5}{100}}={frac {1}{20}}$ .

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Enter the units in the problem. In word scale problems, it’s easier to make a mistake by writing the unit after each value. Remember, the same units will not be recorded on the score. After minimizing the ratio, add the units to the final result.

Example: If you have 6 boxes, 9 out of 3 boxes have marbles, how many marbles are there in all?
How to do it wrong: $6$ $H$ $o$ $p$ $*$ $3$ $H$ $o$ $p$ $9$ $v$ $i$ $e$ $n$ $b$ $i$ $=$ $.$ $.$ $.$ ${displaystyle 6hop*{frac {3hop}{9vienbi}}=…}$ $6hop*{frac {3hop}{9vienbi}}=...$ Wait, nothing is crossed out, the result will be “box x boxes / marbles”. That’s not fair.
The right way to do it:
$6$ $H$ $o$ $p$ $*$ $9$ $v$ $i$ $e$ $n$ $b$ $i$ $3$ $H$ $o$ $p$ $=$ ${displaystyle 6hop*{frac {9vienbi}{3hop}}=}$ $6hop*{frac {9vienbi}{3hop}}=$ $6$ $H$ $o$ $p$ $*$ $3$ $v$ $i$ $e$ $n$ $b$ $i$ $first$ $H$ $o$ $p$ $=$ ${displaystyle 6hop*{frac {3vienbi}{1hop}}=}$ $6hop*{frac {3vienbi}{1hop}}=$
$6$ $H$ $o$ $p$ $*$ $3$ $v$ $i$ $e$ $n$ $b$ $i$ $first$ $H$ $o$ $p$ $=$ ${displaystyle {frac {6hop*3vienbi}{1hop}}=}$ ${frac {6hop*3vienbi}{1hop}}=$ $6$ $*$ $3$ $v$ $i$ $e$ $n$ $b$ $i$ $first$ $=$ ${displaystyle {frac {6*3vienbi}{1}}=}$ ${frac {6*3vienbi}{1}}=$ 18 marbles.

Steps

Understanding What is Ratio?

Using Ratio

Error Detection

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