Comparing Quantities

Class 7 Maths

1. Comparing Quantities

2. Ratios The ratio is used to compare two quantities. These quantities must have the same units. The ratio is represented by “:”, which is read as “to”. We can write it in the form of “fraction”.

3. Equivalent Ratios The equivalent ratio is like the equivalent fractions so to find the equivalent ratio we need to write it in the form of a fraction. To find the equivalent ratio we need to multiply or divide the numerator and denominator with the same number.

4. Proportion Proportion shows the equality between two ratios. If two ratios are in proportion then these must be equal.

5. Unitary Method The unitary method is a method in which you find the value of a unit and then the value of a required number of units.

6. Percentage The percentage is another way of comparisons. In ratios we have to make the denominator same then only we can compare them but in percentage, we can compare by calculating the percentage of the given quantity.

7. Percentage if the total is not a hundred If the total number of quantity is not hundred i.e. the denominator is not hundred then to find the percentage we need to make the denominator 100.

8. Fractions to Percentage (%) Fractional numbers have different denominator and to convert them into percentage we have to multiply the fraction with the 100%.

9. Converting decimals to percentage To convert the decimal into a percentage, first, we need to convert the decimal into fraction then multiply it by 100%.

10. Parts always add to give a whole If we know the one part of a whole then we can find the other part because all the parts together form a whole or 100%.

11. Fun with estimation With the help of percentage, we can estimate the parts of an area. Here the percentage of each 1/2 half of pizza is 50%

12. Use of Percentages Interpreting percentages To use the percentages in real life we must be able to interpret the percentage. Example  If we say that Seema is spending 20% of her income then it means that Seema is spending Rs. 25 out of every Rs. 100 she earns.

13. Converting percentages to “How many”. Example If 20% of students get a distinction out of 45 students in a class, then how many students got the distinction? Solution The number of students got distinction = [20/100] × 45 = 9. Hence, 9 students out of 45 got the distinction.

14. Ratios to percent Ratio to percentage conversion helps us in obtaining accuracy in mixtures of elements, or while calculating the percentage score in a test. At times you are given parts of a quantity in the form of ratios. They can also be represented in the form of percentages.

15. Increase or decrease as Percent Sometimes we have to find the increase or decrease in certain quantities as a percentage. Like the increase in population, decrease in sale etc.

16. Cost Price and Selling Price Cost price is the price at which you buy some product. It is written as C P Selling price is the price at which you sell something. It is written as SP. These are the factors which tell us that the sale of some product is profitable or not.

17. Profit or loss percentage The profit and loss can be converted into a percentage. It is always calculated on the cost price.

18. How to find SP if CP and profit or loss % is given?

19. How to find CP if SP and profit or loss % is given

20. Simple Interest When we borrow some money from the bank then we have to pay some interest to the bank. The money which we borrow is called the Principal. The amount which we have to pay to the bank to use that money is called interest. At the end of the year we return the money to the bank with interest, that money is called Amount. Amount = Principal + interest

21. Where, SI = Simple interest P = Principal R = Rate of Interest T = time period

22. Calculate the simple interest for 3 years when the principal amount is 200 and interest rate is 10% for 1 year. Solution: Given: P = 200; R = 10%; T = 3 yrs Simple Interest = 200×10×3100=60Amount = P + SI = Rs. (200 + 60) = Rs. 260