11.8 Using Expressions Practically
NCERT Class 6 Mathematics Text book for Blind Students made Screen Readable by Professor T K Bansal.
We have already come across practical situations in which expressions are useful. Let us remember some of them.
| Situation (described in ordinary language) | Variable | Statements using expressions |
|---|---|---|
| 1. Sarita has 10 more marbles than Anita. | Let Anita have x marbles. | Sarita has (x + 10) marbles. |
| 2. Bhaarat is 3 years younger than Rajeev. | Let Rajeev’s age be x years. | Bhaarat’s age is (x − 3) years. |
| 3. Bikash is twice as old as Rajeev. | Let Rajeev’s age be x years. | Bikash’s age is 2x years. |
| 4. Rajeev’s father’s age is 2 years more than 3 times Rajeev’s age. | Let Rajeev’s age be x years. | Rajeev’s father’s age is (3x + 2) years. |
| 5. How old will be Susan 5 years from now? | Let y be Susan’s present age in years. | Five years from now Susan will be (y + 5) years old. |
| 6. How old was Susan 4 years ago? | Let y be Susan’s present age in years. | Four years ago, Susan was (y − 4) years old. |
| 7. Price of wheat per kg is ₹ 5 less than price of rice per kg. | Let price of rice per kg be ₹ p. | Price of wheat per kg is ₹ (p − 5). |
| 8. Price of oil per litre is 5 times the price of rice per kg. | Let price of rice per kg be ₹ p. | Price of oil per litre is ₹ 5p. |
| 9. The speed of a bus is 10 km/hour more than the speed of a truck going on the same road. | Let the speed of the truck be y km/hour. | The speed of the bus is (y + 10) km/hour. |
Try to find more such situations. You will realise that there are many statements in ordinary language, which you will be able to change to statements using expressions with variables. In the next section, we shall see how we use these statements using expressions for our purpose.
EXERCISE 11.4
Q1. Answer the following:
(a) Take Sarita’s present age to be y years
(i) What will be her age 5 years from now?
(ii) What was her age 3 years back?
(iii) Sarita’s grandfather is 6 times her age. What is the age of her grandfather?
(iv) Grandmother is 2 years younger than grandfather. What is grandmother's age?
(v) Sarita’s father’s age is 5 years more than 3 times Sarita’s age. What is her father's age?
(b) The length of a rectangular hall is 4 meters less than 3 times the breadth of the hall. What is the length, if the breadth is b meters?
(c) A rectangular box has height h cm. Its length is 5 times the height and breadth is 10 cm less than the length. Express the length and the breadth of the box in terms of the height.
(d) Meena, Beena and Leena are climbing the steps to the hill top. Meena is at step s, Beena is 8 steps ahead and Leena 7 steps behind. Where are Beena and Meena? The total number of steps to the hill top is 10 less than 4 times what Meena has reached. Express the total number of steps using s.
(e) A bus travels at v km per hour. It is going from Daspur to Beespur. After the bus has travelled 5 hours, Beespur is still 20 km away. What is the distance from Daspur to Beespur? Express it using v.
Q2. Change the following statements using expressions into statements in ordinary language.
(For example, Given Salim scores r runs in a cricket match, Nalin scores (r + 15) runs. In ordinary language - Nalin scores 15 runs more than Salim.)
(a) A notebook costs ₹ p. A book costs ₹ 3 p.
(b) Tony puts q marbles on the table. He has 8 q marbles in his box.
(c) Our class has n students. The school has 20 n students.
(d) Jagdish is z years old. His uncle is 4 z years old and his aunt is (4z − 3) years old.
(e) In an arrangement of dots there are r rows. Each row contains 5 dots.
Q3.
(a) Given Maanav’s age to be x years, can you guess what (x − 2) may show?
(Hint : Think of Maanav’s younger brother.)
Can you guess what (x + 4) may show? What (3 x + 7) may show?
(b) Given Sara’s age today to be y years. Think of her age in the future or in the past.
What will the following expression indicate? y + 7, y − 3, y + 4 1/2, y − 2 1/2.
(c) Given: n students in the class like football, what may 2n show? What may n/2 show?
(Hint: Think of games other than football).