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. For any two rational number x and y which of the following is/ are correct, if x is positive and y is negative
2. x< y II) x=y   III) x>y
3. Which of the following statement is true:  a) 1 and -1 are reciprocal of themselves   b) Zero has no reciprocal c) The product of two rational number is a rational number  d) Absolute value of a rational number is either positive or 0.   e) There are countless rational numbers with absolute value less than 5.  f) The absolute value of 0 is 0.
4. Represent the following rational numbers on the number line: a)-3/4     b) 31/-6     c) -1/2    d) ¾
5. Write the following rational numbers in the standard form: a) 5/15     b) -24/40     c) 33/-77    d) -45/-105
6. Add: 1) 3/7 and -9/7    2) 5/9 and 7/-9   3) 2/5, 5/-9 and -6/15
7. Subtract : 1) (-3/4) from (1/2)    2) (5/8) from (-3/14)
8. Find the product of : 1) 5/9, -2/5     2) -5, -3/15
9. Multiply, and give the product in the standard form: 1) -6/25 by 50/24     2) 3/11 by 22   3) 21/5 by -15/21     4) -36 by -5/9
10. The product of two rational numbers is 6. If one of them is 8, find the other number.
11. Find three rational numbers between and represent them on number line:  1) -5 and 8     2) ( -1/3 ) and (1/2)

#### understanding:

1. Compare the following rational numbers:
1) -9/27, 6/-18     2) -5/7, 10/-6
3) 3/-8, -15/40     4) -11/7, 33/21
2. Arrange the following rational numbers in the descending order:
1) 2/-3, -4/9, -5/12, 7/-18
2) 3/-4, -5/12, -7/16, 9/-24
3. Arrange the following rational numbers in the ascending order:
1) 2/5, 1/3, 3/4, 1/6      2) 5/6, 7/8, 11/12, 3/1
4. Fill in the blanks by the correct symbol >, = or < :
1) | 3/4| ———| ½|     2) |-1/2| —– | -3/4 |
5. Show the rational number correctly on the number line [ -2/9  + 1/9]
6. Simplify the following:
1) (2/3) + (-4/5) + I + (-2/3) + (-11/5)
2)(5/8) + (-8/9) + 0 + (-13/3) + (17/24)
7. Simplify:  1) -2 + ( 3 / 8 ) + ( – 1 / 5 )     2) (2/3) + ( -7/11) + (-1/4 )    3) [-18 1/3 * 2 8/11]-[4 5/7 * 2 1/3)

#### Application:

1. The sum of two rational numbers is (-3/7). If one of the number is (-5/8) find the other.
2. The sum of two rational numbers is (-5/8). If one of the number is (-6/11), find the other number.
3. To which number should (2/3) be added to give (-11/4)?
4. What should be added to (-7/20) to get (-2/5)?
5. By what number should (-6/11) be multiplied to get (-32/11)?
6. From which number should (-11/4) be subtracted to give (-11/4)?
7.  Verify the property a × b = b × a by taking :
1) a = (-12/7), b = (-21/5)    2) a = 0 , b = (-13/3)
8. Verify the property a × ( b × c ) = (a × b) × c by taking
1) a = (7/5), b = (-9/4), c = (1/2)
2) a = 1, b = (-13/5), c = (3/5)
9. Verify the property a×(b + c)=(a × b)+(a × c) by taking:
1) a = (1/3), b = 0, c = (-7/6)
2) a = -2, b = (9/5), c = (-2/15
10. Verify that a + b = b + a by taking:  (1) a = -7/5, b = 2/7     (2) a = -1 , b = -2/3
11. Verify that (a + b)+c=a+(b + c) by taking :  (1) a = -2 , b = -2/3 , c = -3/4    (2) a = -12, b = -9/11, c = 7/-12

Word Problems:

1. A box is to be filled with mangoes, each weighing 1/10 kg. The weight of the box should not exceed 3/5 kg. Find the maximum number of mangoes than can be put inside.
2. 3/20 of delegation is from India, ¼ are from Britain, 3/10 are from Germany and the rest are Americans. If there are 1200 members in the delegation, then calculate how many Americans are there?