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9th Grade Math Problems with Answers

Free 9th grade math problem with answer are provided for students practice of the subject. The students get an idea or an overview on  the topic before attending the exam. Work solution is provided on different topic of class 9th like rationalize, percentage, solving the equation, graph,etc.

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We have given a set of 9th grade maths problem with answer.


1.   Rationalism the denominator:

   $\frac{2\sqrt{3} + 3\sqrt{3}}{2\sqrt{3} - 3\sqrt{2}}$

Solution
     =  $\frac{2\sqrt{3} + 3\sqrt{3}}{2\sqrt{3} - 3\sqrt{2}}$ * $\frac{2\sqrt{3} + 3\sqrt{2}}{2\sqrt{3} + 3\sqrt{2}}$

       =   $\frac{4*3+9*2+2*2\sqrt{3}*3\sqrt{2}}{(2\sqrt{3})^2-(3\sqrt{2})^2}$

         =    $\frac{12+18+12\sqrt{6}}{12-18}$

         =    $\frac{30+12\sqrt{6}}{-6}$

 2.  The sum of the squares of the two larger of three consecutive even integers is 14 less than 2 times the square of the smaller one. Find the even numbers.

 Solution: -
       Let the numbers be x,x – 2 , x and x + 2. 

      Given the sum of the square of the integers is 14  less than 2 times the square of the smaller one.
      That is x2+ (x + 2)= 2(x - 2)- 14
      x+ x2 + 4x + 4 = 2(x- 4x + 4 - 14
      2x2 + 4x + 4 = 2x- 8x + 8 - 14   subtract 2x2 on both side   
      4x + 4 = -8x - 6     add -4x on both side  
      4x + 4 - 4x = -8x -6 - 4x 
      4 = -12x - 6     subtracting 4 on both side 
      0 = -12x - 10 add 10 on both side 
     10 = -12x       divide by constant term -12 on both side 

    $\frac{10}{-12}= x$

    $\frac{-5}{6}= x$

3.  Solve the linear equation to find the value of x

      $\frac{5x}{4}$ + 3x = 18
      
 Solution:
       Step 1:   take the LCM and simplify  LHS  

         $\frac{5x+12x}{4}$ = 18 
  
                     $\frac{17x}{4}$ = 18 
         
        Step 2: multiply by a constant  term $\frac{4}{17}$ on both side to simplify the equation.    
            
              $\frac{17x}{4}*\frac{4}{17}$ = 18 * $\frac{4}{17}$ 

                   x = $\frac{18 * 4}{17}$

                   x = $\frac{72}{17}$ 

 
4.    What is the standard form of equation
        The standard form of equation is ax+ bx + c  = 0

 5.     Find the circumference of a circular disk whose area is 100pi square centimeters. 
         Solution: Given area of  a circular disk = 100πc2
         Area of circle  = πr2                  assign the value of area in the equation
         100π = πr2                              divide by a constant term π on both side
         100= r2                                    taking square root on both side of equation
         √100 = √ r2
         10 = r
          the radius of circular disk = 10cm
          we have the formula for circumference of circle,  C = 2 πr
          C = 2* π*10              assign the value of  π = 22/7
             = 62.89  
          circumference of a circular disk  = 62.89 cm 

  6.  Find an equation of the line containing (- 4,5) and perpendicular to the line 5x - 3y = 4.
       Solution:  Given perpendicular to the line 5x - 3y = 4.
       writing  the equation in the form of slope of the equation y = m x+b,
       5x - 3y = 4.   subtract  by 5x on  both side
       - 3y = 12 - 5x       divide by constant number 3 on both side
       - y = 4 -  $\frac{5}{3}$ x taking – as common 
       y =  $\frac{5}{3}$ x  -4
       the equation in the form of y = mx+b
       the slope of equation = (m ) = $\frac{5}{3}$
       the y-intercept = (b) = - 4