mathematics

class VII

#### Key Concepts

linear equation, transposition, LHS and RHS, equality, inequality

#### essential questions

1. What does the number of solutions ( none, one or infinite) of a system of linear equations represent?
2. What are the advantages and disadvantages of solving a system of linear equations graphically versus algebraically?
3. How can systems of equations be used to represent situations and solve problems?

#### Remembering:

1. Find the solution of the equation: a) x + 3 = 0   b) x- 6 = 1   c) 5x =10  d) m/2 = 3   e) 7n +5 =12   f) p+4 = 4  g)  m-1 = 2  h) 2m =4  i) m/3 = 3   j) 4p -2 =10  k) p/2 + 1 =3

#### understanding:

1. Write the following statements in the form of an equation: a) the sum of three times x and 10 is 13 : a) 3x + 10 = 13   b) 3x-10 = 13  c) 3x +13 = 10  d) None
2. If you subtract 3 from 6 times a number you get 9:  a) 3x -6 =9  b) 6x- 3=9   c) 6x +3 = 9  d) 3x + 6 = 9
3. One third of a number plus 2 is 3. a) m/3  –  2 = 3   b) m/3 + 2 =3   c) m/2 – 3= 3   d) m/2 + 3 =3
4. One-fourth of n is 3 more than 2: a) n/4 – 2 = 3  b) n/4 + 2 = 3 c) n/2 -4 =3  d) n/2 +4 =3
5. Taking away 5 from x gives 10 : a) x -5 = 10  b) x+5 =10  c) x-10 =5  d) None
6. The number b divided by 6 gives 5. a) b/6 = 5   b)  b-5 = 6   c) 5b = 6  d) b+ 5 = 6
7. Convert the following equations into statements: i) 2n +5 =10    ii) x -9 =11   iii) y -2 =6   iv) m+ 8 =66  v) p+ 6 =10
8. Write true or false: i) 5 is the solution of the equation 3 x+ 2 =17     ii) 9/5 is the solution for the equation 4x -1 =8    iii) 4x-5 =7 does not have an integer as its soultion     iv) 3/ 2 is the solution of the equation 8x – 5 = 7

#### Application:

1. Solve: i) (3x -1)/5 – x/7 = 3   ii) (2x -3) = 3/10 (5x -12)  iii) (y-1)/3 – (y-2)/4 =1  iv) (x-2)/4 +1/3= x- (2x-1)/3                                   v) (2x -1)/3 – (6x -2)/5 =1/3   vi) 2/7 (x-9)  + x/3 = 3
2. Mohan is 3 year older than Sohan. The sum of their ages is 43 years.
3. If 1 is subtracted from a number and the difference is multiplied by 1/2, the result is 7.
4. A number divided by 2 and then increased by 5 is 9.
5. The interest received by K is Rs 30 more than R. If the total interest received by them is Rs 70, find the interest received by R.
6. After 25years, Ramu will be 5 times as old as he is now. Find his present age.
7. Anamika thought of a number. She multiplied it by 2 and added 5/2 the product and obtained 17 as the result. What is the number she had thought of?
8. In a family, the consumption of wheat is 4 times that of rice. The total consumption.
9. Length of a rectangle is two times its width. The perimeter of the rectangle is 180 cm. Find the dimensions of the rectangle.
10.  In a certain exam, a total of 3768 students secured first division in the years 2006 and 2007. The number of the first division in 2007 exceeded those in 206 by 34. How many students got first division in 2006?
11. Radha got Rs 17,480 as her monthly salary and over time by Rs 10,000. What is her monthly salary?

#### Analysis:

1. The sum of twice a number  and 4 is 18.
2. My younger sister’s age today is 3 times, what it will be 3 years from now minus 3 times what her age was 3 years ago. Find her present age.
3. The sum of 3 consecutive integer is 5 more than the smallest of the integers. Find the integers.
4. One of the two numbers is twice the other. The sum of the numbers is 12. Find the numbers.
5. The perimeter of a rectangle is 40 m. The lenght of the rectangle is 4 m less than 5 times its breadth. Find the length of rectangle.
6. If 45 is added to half a number, the result is triple the number. Find the number.
7. Thrice a number decreased by 5 exceeds twice the number by 1. Find the number.
8.  If one side of square is represented by 18x -20 and the adjacent side is represented by 42 – 13x. Find the length of the side of the square.

#### Evaluation:

1. Follow the instruction and correct the given equation, written in Roman Numerals:

a) Remove two of these matchsticks to make a valid equations: b)  Move one matchstick to make the equation valid. find 2 different solution: 2. What does a duck do when it flies up side down? The answer to this riddle is hidden in equation:

If i+69 =70, then i =?  If 8u= 6u +8, then u = ___

If 4a = -5a + 45, then a =? If 4q + 5= 17 then q =?

If -5t-60 = -70, then t-? if 1/4 s + 98 =100 then s= ?

5/3 p + 9 =24, then p=?  3c =c+12 , then c =?

3 (k+1) =24, then k=?

For riddle’s answer: Substitute the number for the letter in the equation:

1   2 / 3 4 5 6 7 8/ 4 9