# Rational Numbers

Chapters

- Chapter-1-Rational-Numbers
- Chapter-2-Linear-Equations-in-One-Variable
- Chapter-3-Understanding-Quadrilaterals
- Chapter-4-Practical-Geometry
- Chapter-5-Data-Handling
- Chapter-6-Squares-and-Square-Roots
- Chapter-7-Cubes-and-Cube-Roots
- Chapter-8-Comparing-Quantities
- Chapter-9-Algebraic-Expressions-and-Identities
- Chapter-10-Visualising-Solid-Shapes
- Chapter-11-Mensuration
- Chapter-12-Exponents-and-Powers
- Chapter-13-Direct-and-Inverse-Proportions
- Chapter-14-Factorisation
- Chapter-15-Introduction-to-Graphs
- Chapter-16-Playing-with-Numbers

- Chapter-1-Rational-Numbers
- Chapter-2-Linear-Equations-in-One-Variable
- Chapter-3-Understanding-Quadrilaterals
- Chapter-4-Practical-Geometry
- Chapter-5-Data-Handling
- Chapter-6-Squares-and-Square-Roots
- Chapter-7-Cubes-and-Cube-Roots
- Chapter-8-Comparing-Quantities
- Chapter-9-Algebraic-Expressions-and-Identities
- Chapter-10-Visualising-Solid-Shapes
- Chapter-11-Mensuration
- Chapter-12-Exponents-and-Powers
- Chapter-13-Direct-and-Inverse-Proportions
- Chapter-14-Factorisation
- Chapter-15-Introduction-to-Graphs
- Chapter-16-Playing-with-Numbers

- Solutions
- PDF Download
- Question Papers
- Videos

Solutions

(i) -2/5 x 3/5 + 5/2 - 3/5 x 1/6

(ii) 2/5 x (-3/7) - 1/6 x 3/2 + 1/14 x 2/5

Solution.

Solution.

(i) x=11/15 (ii)x=-13/17

Solution

- (i)-13
- (ii) -13/19
- (iii) 1/5
- (iv) -5/8 x -3/7
- (v) -1 x -2/5
- (vi) -1

Solution.

- (i)-4/5 x (1)=1 x -4/5= - 4/5
- (ii) - 13/17 x -2/7 = -2/7 x -13/17
- (iii) -19/29 x 29/-19 = 1

Solution.

- (i) 1 is the multiplicative identity
- (ii) Commutativity of multiplication
- (iii) Multiplicative inverse.

Solution.

Reciprocal of -7/16 is -1/67 Now, 6/13×-16/7=6×(-16)/13×7=-96/91

Solution. Associativity.

Solution.

-1 1/8=-9/8

Now, 8/9×-9/8=-1=1

So, No ; 8/9 is not the multiplicative inverse of -1 1/8(=-9/8) because the product of 8/9 and -13(-) and -1 1/8(=-9/8) is not 1.

Solution.

Yes ; 0.3 is the multiplicative inverse of 10/3 because

3/10×10/3=3×10/10×3=30/30=1

- (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.

Solution.

- (i) The rational number "0" does not have a reciprocal.
- (ii) The rational numbers 1 and (-1) are equal to their own reciprocals.
- (iii) The rational number 0 is equal to its negative.

- (i) Zero has....reciprocal.
- (ii) The numbers....and...are their own reciprocals.
- (iii) The reciprocal of - 5 is......
- (iv) Reciprocal of 1x, where x?0
- (v) The product of two rational numbers is always a....
- (vi) The reciprocal of a positive rational number is....

Solution.

- (i) Zero has no reciprocal.
- (ii) The numbers 1 and -1 are their own reciprocals.
- (iii) The reciprocal of - 5 is ?15
- (iv) Reciprocal of 1x, where x?0 is x.
- (v) The product of two rational numbers is always a rational number.
- (vi) The reciprocal of a positive rational number is positive.

PDF Download

Question Papers

Videos