Simple Ratio: Basic Formula, Rules and Examples

Simple Ratio compares two quantities of the same kind by division. This page explains ratio notation, the basic ratio formula, equivalent ratios, simplest form, comparison methods and division of a quantity in a given ratio. It also includes short methods and simple ratio questions with clear calculations.

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What Is a Simple Ratio?

A simple ratio shows the relative relationship between two quantities of the same unit or kind. It is written as a:b and means a divided by b, where b is not zero.

In the ratio a:b, a is the first term and b is the second term. Both terms may be multiplied or divided by the same non-zero number without changing the ratio. For example, 12:18 becomes 2:3 after dividing both terms by their greatest common divisor, 6.

Simple Ratio Formula & Tricks

Important Formulas

Basic ratio formula
a:b = a/b

The ratio of a to b is the quotient of a divided by b, with b not equal to zero.

Equivalent ratio
a:b = (ka):(kb), k ≠ 0

Multiplying or dividing both terms by the same non-zero number gives an equivalent ratio.

Simplest form
Simplest ratio = (a ÷ gcd(a,b)):(b ÷ gcd(a,b))

Divide both terms by their greatest common divisor to reduce the ratio.

Division in a given ratio
First share = T × a/(a+b); Second share = T × b/(a+b)

A total T divided in the ratio a:b has a+b equal parts.

Quick Tricks

Convert quantities to the same unit first

A ratio can be formed only after both quantities use the same unit. Convert larger units into smaller units when convenient, then reduce the ratio.

Example: 2 m:50 cm = 200 cm:50 cm = 4:1.
Use total parts for sharing questions

For a total divided in the ratio a:b, add the ratio terms first. Divide the total by a+b to find one part.

Example: ₹840 in the ratio 3:4 gives 7 parts. One part is ₹120, so the shares are ₹360 and ₹480.
Cross-multiply to compare two ratios

For positive ratios a:b and c:d, compare ad and bc. The larger cross-product represents the larger ratio.

Example: To compare 5:8 and 3:5, compare 5 × 5 = 25 with 8 × 3 = 24. Therefore, 5:8 is larger.

Simple Ratio Concepts

Writing a Ratio in Simplest Form

Reduce a ratio to simplest form by dividing both terms by their greatest common divisor.

The common divisor must be applied to both terms. The resulting terms have no common factor greater than 1. For example, 36:48 becomes 3:4 because both terms are divided by 12.

Example: 45:60 = (45 ÷ 15):(60 ÷ 15) = 3:4.

Equivalent Ratios

Equivalent ratios have the same value even though their terms may be different.

Multiplying or dividing both terms by the same non-zero number preserves the ratio. If a:b = c:d, then ad = bc. Thus, 4:7 and 20:35 are equivalent because both terms of 4:7 are multiplied by 5.

Example: 3:5 = 6:10 = 15:25.

Comparing Two Ratios

Compare ratios by converting them to fractions or by cross-multiplication.

For positive ratios a:b and c:d, compare a/b and c/d. Cross-multiplication avoids decimal calculations: if ad > bc, then a:b > c:d; if ad < bc, then a:b < c:d.

Example: Compare 7:12 and 5:9. Since 7 × 9 = 63 and 12 × 5 = 60, 7:12 is greater.

Dividing a Quantity in a Ratio

To divide a total T in the ratio a:b, use a+b total parts and assign a parts and b parts respectively.

The value of one part is T/(a+b). The two shares are Ta/(a+b) and Tb/(a+b). For more than two terms, add all ratio terms to get the total number of parts.

Example: Divide 560 in the ratio 3:5. One part = 560/8 = 70, so the shares are 210 and 350.

Simple Ratio Video Lessons

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Duplicate, Triplicate and Sub-Duplicate Ratios

Learn the definitions and application of duplicate, triplicate, and sub-duplicate ratios, with clear methods for understanding how these special ratios are formed and used.

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Practice Simple Ratio Questions

Practise published questions related to this topic.

1A shopkeeper sells an item for ₹225.6 after giving two successive discounts of 90% and 50% on its marked price. Had he not given any discount, he would have earned a profit of 41%. What is the cost price (in ₹) of the item?→ 2The ratio of two numbers is 7 : 9 and their Highest Common Factor is 3. What are the two numbers?→ 3If x = √100 ÷ √25+√64, then what is the value of 2x?→ 4An officer checks the cost ratio: √18 ÷ √2 .Simplify.→ 53 different pieces of iron with lengths 81 cm, 54 cm and 36 cm. Rods are to be made by cutting these pieces. Each rod should be of same length. No iron is to be wasted. What is the length (in cm) of longest such rod?→ 6The square root of 7 + 4√3 is:→ 7Which number should replace both the '*' in ((*)/21) × ((*)/189) = 1?→ 8Which is the least number exactly divisible by 5, 7, 9 and 21?→ 9Solve √(30-√(30-√(30-....)))→ 10The marked price of an item is 10% higher than the cost price and a discount of 10% is given on the marked price. What is the percentage gain or loss to the business owner in this sale?→

Simple Ratio Quick Quiz

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Quick Revision Notes

Simple Ratio Revision Points

Remember these rules and formulas when solving simple ratio questions.

  • A ratio compares quantities of the same kind and unit.
  • a:b means a/b, with the second term non-zero.
  • Multiply or divide both terms by the same non-zero number to obtain an equivalent ratio.
  • Reduce a ratio by dividing both terms by their greatest common divisor.
  • For a total T divided in a:b, the shares are Ta/(a+b) and Tb/(a+b).
  • Convert units before forming a ratio.
  • To compare a:b and c:d, compare ad with bc.

Simple Ratio FAQs

What is the basic ratio formula?

The basic ratio formula is a:b = a/b, where a and b are the quantities being compared and b is not zero.

How do you simplify the ratio 24:36?

The greatest common divisor of 24 and 36 is 12. Dividing both terms by 12 gives 24:36 = 2:3.

How do you divide ₹1,200 in the ratio 2:3?

Total parts = 2+3 = 5, so one part is ₹1,200/5 = ₹240. The shares are ₹480 and ₹720.

Can quantities with different units be written directly as a ratio?

No. Convert them to the same unit first. For example, 3 m:75 cm = 300 cm:75 cm = 4:1.

How can two ratios be compared without converting them to decimals?

Use cross-multiplication. To compare a:b and c:d, compare ad and bc. The ratio with the larger cross-product is greater when all terms are positive.

What is the difference between a ratio and its reciprocal?

The reciprocal of a:b is b:a. For example, the reciprocal of 2:5 is 5:2; these ratios are generally not equal.

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