mathematics

class VII

#### Key Concepts

rational numbers, fractions, properties of rational numbers, equivalent rational numbers, word problems, comparing rational number, number line, operation in rational numbers

#### essential questions

1. How do I apply the rules of mathematical operations to rational numbers?
2. How are rational numbers useful in life?
3. How does a number's relationship to zero affect its value?
4. What does the sign of a rational number say about the direction from its initial position?
5. How do we use the context to determine what approach we use to solve?
6. What are the properties of rational numbers? How are they useful?
7. How are adding and subtracting related?
8. At a quick glance, how do you know if your answer is positive or negative?

#### Remembering:

1. The additive inverse of -1/3  – (-1/3) is ____ a) 1/3  b) 0   c) -1/3   d) none of these
2. What is the quotient when a non zero rational number is divided by its additive inverse. a) 0 b) -1  c) 1  d) none of these
3. Mark True or false: a) rational number remains unchanged, if its numerator and denominator are multiplied by the same non zero integers. b) On dividing numerator and denominator of a common divisor, it changes                                                                                                                    c) For any rational number a,b, c which among the following is false: a) a× b = b× a    b) a×(b-c)= a×b – a×c  c) a×(b÷c)= a×b ÷ a×c    d) a×(b÷ c) = a×b ÷ a×c
4. ___and __ are reciprocal of itself. a) 0,1   b) 0,-1  c) 1,-1  d) none
5.  Divide the sum o -1/3 and 5/6 by the sum of 1/-4 and 3/8 : a) 3/8  b) 1/2  c) 4  d) 1/4
6. If p/q and r/s are rational numbers then, p/q is mulitplicative inverse of r/s, if a) p/q= r/s   b) p/q+ r/s = 1   c) p/q× r/s =1   d) p/q+ r/s= 0
7. State whether true or false: i) Zero is the smallest rational number ii) Every integer is a rational number iii) The quotient of two integer is always a rational number  iv) Every fraction is a rational number  v) Every rational number is a fraction
8. List five rational numbers between -2 and -1
9. List five rational numbers between -4/5 and -2/3
10. Which of the following is true: a) -3/5 lies to the left of 0 on the number line  b) -13/7 lies to right of 0 on the number line  c) -18/-13 lies to the left of 0 on the number line  iv) 1/3 and -5/2 lie on opposite sides of 0 on the number line.
11. 33/-55 in standard form is: a) 3/-5  b) -3/5  c) -33/55  d) none of these
12. Find the multiplicative inverse of the following: a) 18  b) -16 c) 13/25

#### understanding:

1. For what value of ‘a’ the number -11 ⁄ a  is not a rational number: a) -1  b) 1  c) 0  d) 10
2. Find the value of -9/5 + (-8/5) ÷ 5/2 × -5/4     a) -1   b) -3   c) 2   d) -8
3. The sum of 3 rational numbers is -1/5. if two of the numbers are 3/10 and -2/5, find the 3rd number.
4. Which of the following is not equivalent to -6/21: a) 20/-70    b) 10/-35  c) -9/24   d) -26/91
5. Find the value: [ -2/7 – 5/7]× [ 8/3÷4/9]
6. Divide the difference of 3/7 and 2/5 by the product of 4/ and 25/2.
7. Fill in the blanks: i) -9/5 =?/ 20= 27/? =-45/?  ii) -6/11=-18/? =?/44
8. Which of the following are equal: i) 8/-12 and -10/15  ii)  -3/9 and 7/-21  iii)  -8/-14 and 15/21
9. Subtract -3/5 from its reciprocal.
10. Find the sum of : [ -5/9 +-7/12 +11/18]
11. Simplify i) 7/24 × -48  ii) -19/36  × 16  iii) -3/4 × 4/3    iv) -9/16 × -64/27   v) ( 13/8×12/13)+ (-4/9 ×3/-2)

#### Application:

1. By what number should we multiply -5/4 to get 7/2?
2. The product of two rational numbers is -7/8.  If one of the numbers is 1/-6. Find the other. a) 37/8   b) -42/8  c) 21/4  d) -7/48
3. From a rope of 40m 50cm, pieces of equal size are cut. If each pieces is of 2 ¼ m long, find the number of pieces cut off?
4. The product of two rational number is 10. If one of the number is -8, find the other.
5. If 24 pairs of trousers of equal size can be prepared with 54 m cloth. What length cloth is required for each pair of trousers.
6. A car is moving at an average speed of 56  4/5 km/hour. How much distance will it cover in 7½  hours?
7. Find the cost of 3 1/3 m of cloth at Rs 40 ½ per meter.
8. Find x such that: i) -1/5 =8/x   ii) 7/-3 =x/6  iii) 3/5= x/-25  iv) 13/6= -65/x  v) 16/x= -4   vi)-48/x=2

#### Analysis:

1. Rahul walks 2/3 km from a place P towards east and then from there 1  5/6 km towards west. What is his position from P?