Comparing Quantities & Rational Numbers Class Notes (Class 7th, 2025)

# All in one Class 7th Maths 2025 by Physics Wallah ## Introduction This document is a set of notes for a class 7th maths course. It is titled "All in one Class 7th Maths 2025" and is produced by Physics Wallah. The course is taught by Priyanshu Shukla sir and is intended to be a one-shot review...

# All in one Class 7th Maths 2025 by Physics Wallah ## Introduction This document is a set of notes for a class 7th maths course. It is titled "All in one Class 7th Maths 2025" and is produced by Physics Wallah. The course is taught by Priyanshu Shukla sir and is intended to be a one-shot review of all the important concepts in the syllabus. ## Topics Covered The document covers the following topics: 1. All concepts in one shot. 2. Comparing Quantities * Percentage * Ratios To Percentages * Increase Or Decrease As Percent * Buying and Selling - Profit and Loss * Simple Interest 3. Rational Numbers ## Comparing Quantities ### Percentage The word "per cent" is an abbreviation of the Latin phrase "per centum," which means per hundred or hundredths. Therefore, the term per cent means out of hundred or for every hundred. For example, "x percent" is written as *x%* and *x%* = x/100. ### How to Calculate Percentage Percentage = (Parts/Whole) x 100% For example, to calculate the percentage of 445 out of 500: * (445/500) x 100% = 89% ### Ratios to Percents To express a ratio in percentage form, we need to express the given ratio in the form of a fraction. For example, to convert the ratio *a:b* into percentage. * (a/(a+b)) x 100% ### Increase or Decrease as Percent To calculate increase or decrease in terms of percentage, we use the following formulas: * Percentage increase = (Increase in quantity/Original quantity) x 100% * Percentage decrease = (Decrease in quantity/Original quantity) x 100% ### Buying and Selling - Profit and Loss * **Cost Price** is the price at which an article is purchased. It is abbreviated as C.P. * **Selling Price** is the price at which an article is sold. It is abbreviated as S.P. **Profit:** If the selling price (S.P.) of an article is greater than the cost price (C.P.), then the difference between the selling price and cost price is called profit. * Gain = S.P - C.P * Gain % = (Gain/CP) x 100% **Loss:** If the selling price (S.P.) of an article is less than the cost price (C.P.), then the difference between the cost price (C.P.) and the selling price (S.P.) is called loss. * Loss = CP - S.P * Loss% = (Loss/CP) x 100% **Basic Formula:** * If S.P > C.P, then there's a profit. * Profit = S.P - C.P * Profit% = (Profit/CP) x 100% * If S.P < CP, then there's a loss. * Loss = CP - SP * Loss% = (Loss/CP) x 100% **IMPORTANT:** C.P & S.P are always calculated on COST-PRICE. ### Simple Interest Whenever we borrow money from a lending source, we pay some extra money for the service. This extra money is called **Interest**. The borrowed money is called **Principal**. **Simple Interest** is calculated simply on the original principal. When interest is added to the principal, the sum is called the **Amount**. * S.I = (P x R x T)/ 100 * **P = Principal** * **R = Rate of interest** * **T = Time in years** ## Rational Numbers A rational number is a number that can be expressed as a fraction p/q, where p and q are integers and q is not equal to zero. * A **natural number** is a rational number. All natural numbers can be expressed as a fraction with a denominator of 1. For example, 3 = 3/1 * An **integer** is a rational number. All integers can be expressed as a fraction with a denominator of 1. For example, -3 = -3/1. * Zero is a rational number. It can be expressed as 0/1. **Equivalent Rational Numbers:** Two rational numbers are equivalent if they represent the same value. The simplest way to check if two rational numbers are equivalent is to multiply or divide both the numerator and denominator by the same non-zero number. **Standard Form of a Rational Number:** A rational number is in standard form when its denominator is positive and it is in its lowest terms. **Representing Rational Numbers on a Number Line:** 1. To represent a rational number on a number line, divide the unit segment between 0 and 1 into as many equal parts as there are units in the denominator of the rational number. 2. Then mark the point that represents the numerator on the number line. **Comparing Rational Numbers:** * **Same denominators:** Compare the numerators. The rational number with the greater numerator is the greater rational number. * **Different denominators:** * **First Method:** Convert both rational numbers into equivalent rational numbers with the same denominator and then compare. * **Second Method:** Cross-multiplication. **Rational Numbers Between Two Rational Numbers:** To find the rational numbers between two rational numbers, we have to make their denominator same, then we can find the rational numbers. **Operations on Rational Numbers:** * **Addition:** If the denominators are the same, add the numerators and keep the same denominator. If the denominators are different, convert them to have a common denominator. * **Subtraction:** If the denominators are the same, subtract the numerators and keep the same denominator. If the denominators are different, convert them to have a common denominator. * **Multiplication:** Multiply the numerators and multiply the denominators. * **Division:** Multiply the first rational number with the reciprocal of the second rational number.