# Lessons

# Questions

- Solve the following equations and check your results. (1) 3x = 2x + 18 (2) 5t – 3 = 3t – 5 (3) 5x + 9 = 5 + 3x (4) 4z + 3 = 6 + 2z (5) 2x – 1 = 14 – x (6) 8x + 4 = 3 (x – 1) + 7 (7) x = 4/5(x + 10) (8) 2x/3 + 1 = 7x/15 + 3 (9) 2y + 5/3 = 26/3 - y (10) 3m = 5 m – 8/5
- The organisers of an essay competition decide that a winner in the competition gets a prize of ₹100 and a participant who does not win gets a prize of ₹25. The total prize money distributed is ₹3,000. Find the number of winners, if the total number of participants is 63.
- . I have a total of ₹300 in coins of denomination ₹1, ₹2 and ₹5. The number of ₹2 coins is 3 times the number of ₹5 coins. The total number of coins is 160. How many coins of each denomination are with me?
- Lakshmi is a cashier in a bank. She has currency notes of denominations ₹100, ₹50 and ₹10, respectively. The ratio of the number of these notes is 2:3:5. The total cash with Lakshmi is ₹4,00,000. How many notes of each denomination does she have?
- . A rational number is such that when you multiply it by 5/2 and add 2/3 to the product, you get -7/12. What is the number?
- . Fifteen years from now Ravi’s age will be four times his present age. What is Ravi’s present age?
- Baichung’s father is 26 years younger than Baichung’s grandfather and 29 years older than Baichung. The sum of the ages of all the three is 135 years. What is the age of each one of them?
- The number of boys and girls in a class are in the ratio 7:5. The number of boys is 8 more than the number of girls. What is the total class strength?
- The ages of Rahul and Haroon are in the ratio 5:7. Four years later the sum of their ages will be 56 years. What are their present ages?
- Three consecutive integers are such that when they are taken in increasing order and multiplied by 2, 3 and 4 respectively, they add up to 74. Find these numbers.
- The sum of three consecutive multiples of 8 is 888. Find the multiples.
- Three consecutive integers add up to 51. What are these integers?
- Two numbers are in the ratio 5:3. If they differ by 18, what are the numbers?
- Sum of two numbers is 95. If one exceeds the other by 15, find the numbers.
- The base of an isosceles triangle is 4/3 cm. The perimeter of the triangle is 62/15 cm. What is the length of either of the remaining equal sides?
- The perimeter of a rectangular swimming pool is 154 m. Its length is 2 m more than twice its breadth. What are the length and the breadth of the pool?
- If you subtract 1/2 from a number and multiply the result by 1/2, you get 1/8. What is the number?
- Solve the following equations. (1) x – 2 = 7 (2) y + 3 = 10 (3) 6 = z + 2 (4) 3/7 + x = 17/7 (5) 6x = 12 (6) t/5 = 10 (7) 2x/3 = 18 (8) 1.6 = y/1.5 (9) 7x – 9 = 16 (10) 14y – 8 = 13 (11) 17 + 6p = 9 (12) x/3 + 1 = 7/15
- Find ten rational numbers between 3/5 and 3/4.
- Write five rational numbers greater than -2.
- Find five rational numbers between. (i) 2/3 and 4/5 (ii) -3/2 and 5/3 (iii) 1/4 and 1/2
- Find ten rational numbers between -2/5 and 1/2.
- Write five rational numbers which are smaller than 2.
- . Represent -2/11, -5/11, -9/11 on the number line.
- Represent these numbers on the number line. (i) 7/4 (ii) -5/6
- . Write. (i) The rational number that does not have a reciprocal. (ii) The rational numbers that are equal to their reciprocals. (iii) The rational number that is equal to its negative.
- Is 8/9 the multiplicative inverse of ? 9/8 Why or why not?
- Tell what property allows you to compute 1/3 × (6 × 4/3) as (1/3 × 6) × 4/3.
- Multiply 6/13 by the reciprocal of -7/16.
- Name the property under multiplication used in each of the following. (i) -4/5 × 1 = 1 × -4/5 = -4/5 (ii) -13/17 × -2/7 = -2/7 × -13/17 (iii) -19/29 × 29/-19 = 1
- Find the multiplicative inverse of the following. (i) -13 (ii) -13/19 (iii) 1/5 (iv) -5/8 × -3/7 (v) -1 × -2/5 (vi) -1
- Verify that : -(-x) = x for. (i) x = 11/15 (ii) x = -13/17
- Write the additive inverse of each of the following. (i) 2/8 (ii) -5/9 (iii) -6/-5 (iv) 2/-9 (v) 19/-6
- Using appropriate properties find. (i) -2/3 × 3/5 + 5/2 - 3/5 × 1/6 (ii) 2/5 × (-3/7) - 1/6 × 3/2 + 1/14 × 2/5