Ratio Calculator

For a ratio A:B = C:D, Calculate the fourth value(D) in the ratio by providing the three numbers (A, B, C).

Ratio is essentially a fraction of two numbers. Like a fraction, it is made up of two parts, the numerator and the denominator. For example, a pizza is cut into 6 slices and 5 of them have been eaten. If we want to know the ratio of slices eaten compared to the entire pizza, then we plug the number of slices eaten as the numerator and the total number of slices as the denominator, which is 5/6.

Ratios can be scaled up to larger, equivalent ratios where the numbers involved are much bigger. For example, we might want to scale up the ratio 5/6 to another equivalent ratio with the denominator 72. To do this, we set up a relation between the two ratios, where they are equal to each other, and we need to solve for the missing number. For the new equivalent ratio, the missing number may be the numerator or the denominator. This process of equating the two ratios is known as setting up a proportion.

We consider a pair of equivalent ratios, A/B and C/D.

The ratio can be used to find D when A, B and C are known. The equivalent ratios can be written as

$$ {A\over B} = {C \over D} $$

To find D, we use the formula

$$ D = C * {B \over A} $$

For example, if A = 3, B = 8 and C = 12, then

$$ D = 12 * {8\over3} = 32 $$

Hence, the ratios 3/8 and 12/32 are equivalent to each other.

However, if A, B, and D are known, and C needs to be calculated, then the formula is

$$ C = D*{A\over B} $$

For example, if A = 3, B = 8 and D = 24, then

$$ C = 24*{3\over8} = 9 $$

Hence, the equivalent ratios are 3/8 and 9/24.

Given below are some rules followed by ratios.

i) If two ratios A/B and C/D are equal, then

• a) Invertendo $$ {B\over A} = {D\over C} $$
• b) Alternendo $$ {A \over C} = {B\over D} $$
• c) Componendo $$ {{A+B}\over B} = {{C+D}\over D} $$
• d) Dividendo $$ {{A-B}\over B} = {{C-D}\over D} $$

ii) The ratio remains the same if both the numerator and denominator are multiplied or divided by the same non-zero number.

$$ {A\over B} = {xA \over xB}, x \ne 0 \; and \; {A\over B} = {{A\over y}\over {B\over y}}, y \ne 0 $$

iii) Ratios can be compared just like real numbers.

• $$ {A\over B} = {C \over D} \, is \, equivalent \,to \,AD \;= \;BC $$
• $$ {A\over B} > {C\over D} \;means \, that \, AD > BC $$
• $$ {A\over B} < {C \over D} \; means \, that \, AD < BC$$

Let us assume that we have a ratio of 5/6 and we want to scale it up to another equivalent ratio with the denominator 72. To do this, we set up a relation between the two ratios, where they are equal to each other, and we need to solve for the missing number. The steps for this are as follows:

Write the ratios in terms of fractions, and label the missing part of the new number with some variable.

Make the fractions equal to each other. This is called forming a proportion.

Try to isolate the variable by cross-multiplying.

Solve for the variable using one of the ratio formulas. The answer obtained is the required number.

Consider the example described above. For the fraction having 72 as denominator, the numerator is named ‘x’. Therefore,

$$ {5\over 6} = {x \over 72} $$

$$ 5*72 = 6x $$

$$ {{5*72}\over 6} = x $$

$$ x = 60 $$

Hence, the new fraction is 60/72. The fractions 5/6 and 60/72 are equal to each other.

Ratios help to describe mathematical relationships in real-life situations. Some examples are as follows.

1) Ratios are frequently used in cooking and baking. Every recipe mentions the exact quantity of each ingredients to be used in order to prepare a good meal. Messing up this ratio might affect the overall outcome. For example, for making brownies, two of the ingredients are flour and milk. The recipe requires 2 cups of flour and 1 cup of milk. This can be visualized as a ratio of 1 cup milk to 2 cups flour.

2) While grocery shopping, one might observe that different quantities of the same item are priced differently. For example, 500 ml of milk costs INR 25, whereas 1 litre of milk costs INR 50. The pricing and quantity might also vary according to the brands of the same product. For example, for brand A, a 200g box of muesli costs INR 220, and a different brand B has a 400g box of muesli priced at INR 350. By dividing the price of each box by the corresponding quantity of muesli, one can obtain a relationship between the cost and the quantity. In the second example, the brand B is cheaper, because 1g of muesli costs INR 0.875, whereas for brand A, 1g of muesli costs INR 1.1.

3) Ratios are also extremely useful for drawing relationships between distance and time. For example, the distance between Bangalore and Mysore is 143.6 km. While travelling from Bangalore to Mysore by car, where the average speed of the car is 60 kmph, the time taken to reach Mysore can be calculated by finding the ratio of the total distance by the speed. This ratio tells us that it takes approximately 2.39 hours to travel.

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