Ch 7 mathematics
- 2. INTRODUCTION There is a 20 over cricket match going on between India and Zimbabwe. India scores 200 runs with Kohli playing a good knock of 76* runs. Zimbabwe gets bowled out at 100 runs. So India wins by a good margin. That’s a qualitative definition. But by how much did India win? This is answered by the concept of ratios and proportions. So come, let us know more about ratios and proportions.
- 3. GLOSSARY Ratio - the comparison or simplified form of two quantities of the same kind . We make use of ratios to compare two things. The sign used to denote a ratio is ‘:’. Proportion - When two ratios are equal in value, then they are said to be in proportion. In simple words, it compares two ratios. Proportions are denoted by the symbol ‘::’ or ‘=’. Equivalent - two values, numbers or quantities which are the same.
- 4. Today we will learn about RATIO only …… LET’S START
- 5. Ratio a: b ⇒ a/b where a and b could be any two quantities. Here, “a” is called the first term or antecedent, and “b” is called the second term or consequent. Example: In ratio 4:9, is represented by 4/9, where 4 is antecedent and 9 is consequent. If we multiply and divide each term of ratio by the same number (non-zero), it doesn’t affect the ratio. Example: 4:9 = 8:18 = 12:27
- 6. When we compare the relationship between two numbers dealing with a kind, then we use the ratio formula. It is denoted as a separation between the number with a colon (:). Sometimes a division sign is also used to express ratios. For example, we are making a cake, then the recipe sometimes says to mix flour to water in the ratio 2 part 1. That means if you using 2 cups of flour then mix it with 1 cup of water. Both the numbers should be non-zero in order to make a meaning out of the comparison. Some ratios are denoted in percentages and decimals as well. The ratio formula is a:b⇒ab
- 7. EQUIVALENT RATIOS Two ratios that have the same value are called equivalent ratios. To find an equivalent ratio, multiply or divide both quantities by the same number. It is the same process as finding equivalent fractions. The recipe uses 3 cups of flour and 1 cup of butter and she wants to make 3 batches of the recipe. To find how much flour and butter she needs, Angie can use equivalent ratios. TELL HOW . NOW LET’S CHECK THE ANSWER
- 8. ANSWER PLZZZZ.. First, write a ratio for the number of cups of flour and the number of cups of butter. 3 cups of flour ------------------- 1 cups of butter Next, find an equivalent ratio by multiplying the numerator and denominator by 3. 3×3= 9 ------- ----- 1×3= 3 The equivalent ratio tells you that Angie will need 9 cups of flour and 3 cups of butter to make 3 batches of cookies.
- 9. STRENUOUS QUESTION WHICH WILL MAKE UR MIND PUZZELED John weights 65.7 kg. If he reduces his weight in the ratio 5 : 4, find his reduced weight.
- 10. STRENUOUS QUESTION ANSWER Step-by-step explanation Let the previous weight be 5x 5x = 65.7 x = 65.75 x = 13.14 Therefore, the reduce weight = 4 × 13.14 = 52.56 kg
- 12. Proportion is equality of two ratios: e.g. a:b= c:d i.e. Ratio between first and second is equal to ratio between third and fourth term. (ii) a and d are called extreme terms and band c are called mean terms and a xd = bxc (iii) Fourth term is called fourth proportional.
- 13. Continued Proportion Three quantities are called in continued proportion if the ratio between first and second is equal to the ratio between secondand third i. e. a, b,c are in continued proportion if a : b = b:c b the middle term is called the mean proportional between a and c and the third term is called the third proportional to a and b.
- 14. LET’S TEST Find p in each case so that the numbers are in continued proportion. (i) p, 1 , 12, 2 ____ 2 (ii) 16, p, 9
- 15. UR RESULTS !! (i) 1 ____ 8 (ii) 12
- 16. Unitary Method
- 17. Unitary Method The unitary method is used to find the value of a single unit from a given multiple. For example, the price of 40 pens is Rs. 400, then how to find the value of one pen here. It can be done using the unitary method. Also, once we have found the value of a single unit, then we can calculate the value of the required units by multiplying the single value unit.
- 18. NOW LET’S START FROM ONE TRANQUIL QUESTION 12 farmers harvest the crops in the field in 20 hours. How many workers will be required to do the same work in 15 hours?
- 19. NOWSEETHEANSWER 12 farmers need 20 hours to complete the harvesting. Find the number of farmers needed if the work is to be completed in 1 hour: 20 hours = 12 farmers 1 hour = 12 x 20 = 240 farmers Find the number of farmers needed if the work is to be completed in 15 hour: 1 hour = 240 farmers15 hours = 240 ÷ 15 = 16 farmers Answer: 16 farmers are needed to complete the work in 15 hours
- 20. SIMPLEST QUESTION Fifteen post cards cost Rs. 2.25. What will be the cost of 36 post cards? How many postcards can we buy in Rs. 45?
- 21. SOLUTION 15 Post cards = Rs 2.25 1 Post card = 2.25/15 = 0.15 Hence, 36 Post cards 0.15 x 36 = Rs 5.4 Let the no. of post cards bought in 45 rs be x Therefore, 45/x 0.15 x = 45/0.15 = 300
- 23. BYE – BYE !!!! Ok now I have to go . BYE!! STRIVE DONE BY – NANDINI VII-B ROLL NO. 33
- 24. Thank you