{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3: Fraction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 3.1, Page number 3.4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "the descending order for 1st case is [0.8571428571428571, 0.8333333333333334, 0.75, 0.625]\n",
      "the descending order for 2nd case is [0.6, 0.5, 0.42, 0.3]\n",
      "the descending order for 3rd case is [0.5833333333333334, 0.4722222222222222, 0.3333333333333333, 0.3125]\n",
      "the descending order for 4th case is [0.9326923076923077, 0.8125, 0.7142857142857143, 0.6]\n",
      "the descending order for 5th case is [0.02824858757062147, 0.023297491039426525, 0.02197802197802198, 0.02016498625114574]\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "numbers1=[5/6,3/4,5/8,6/7];\n",
    "numbers2=[1/2,3/5,3/10,21/50];\n",
    "numbers3=[7/12,5/16,17/36,1/3];\n",
    "numbers4=[3/5,5/7,13/16,97/104];\n",
    "numbers5=[2/91,5/177,22/1091,13/558];\n",
    "\n",
    "#Calculation\n",
    "a1=sorted(numbers1,reverse=True);     #descending order for 1st case\n",
    "a2=sorted(numbers2,reverse=True);     #descending order for 2nd case\n",
    "a3=sorted(numbers3,reverse=True);     #descending order for 3rd case\n",
    "a4=sorted(numbers4,reverse=True);     #descending order for 4th case\n",
    "a5=sorted(numbers5,reverse=True);     #descending order for 5th case\n",
    "\n",
    "#Result\n",
    "print \"the descending order for 1st case is\",a1\n",
    "print \"the descending order for 2nd case is\",a2\n",
    "print \"the descending order for 3rd case is\",a3\n",
    "print \"the descending order for 4th case is\",a4\n",
    "print \"the descending order for 5th case is\",a5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 3.2, Page number 3.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "required amount is 900.0 Rs\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "p1=5/12;     #part\n",
    "p2=3+(3/4);   #part\n",
    "a=100;    #amount(Rs)\n",
    "\n",
    "#Calculation\n",
    "x=p2*a/p1;     #required amount(Rs)\n",
    "\n",
    "#Result\n",
    "print \"required amount is\",x,\"Rs\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 3.3, Page number 3.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "required fraction is 0.1\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "n=5*12;     #number of bananas\n",
    "fp=6;    #fraction part\n",
    "\n",
    "#Calculation\n",
    "rf=fp/n;    #required fraction\n",
    "\n",
    "#Result\n",
    "print \"required fraction is\",rf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 3.4, Page number 3.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "number of absentees is 12.0\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "n=40;    #number of students\n",
    "np=7/10;   #number of students present\n",
    "\n",
    "#Calculation\n",
    "na=(1-np)*n;   #number of absentees\n",
    "\n",
    "#Result\n",
    "print \"number of absentees is\",na"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 3.5, Page number 3.6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "savings is 1400.0 Rs\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "ps=2/7;    #part of savings\n",
    "al=1000;   #amount left(Rs) \n",
    "\n",
    "#Calculation\n",
    "s=al/(1-ps);     #savings(Rs)\n",
    "\n",
    "#Result\n",
    "print \"savings is\",s,\"Rs\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 3.6, Page number 3.6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "total number of pages is 320.0\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "abyb=3/8;     \n",
    "xbyy=4/5;\n",
    "pl=40;     #pages left\n",
    "\n",
    "#Calculation\n",
    "p=pl/((1-abyb)*(1-xbyy));    #total number of pages\n",
    "\n",
    "#Result\n",
    "print \"total number of pages is\",p"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 3.7, Page number 3.6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "total salary is 8000.0 Rs\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "abyb=2/5;     \n",
    "xbyy=3/10;\n",
    "mbyn=1/8;\n",
    "ba=1400;     #balance amount(Rs)\n",
    "\n",
    "#Calculation\n",
    "ts=ba/(1-(abyb+xbyy+mbyn));     #total salary(Rs)\n",
    "\n",
    "#Result\n",
    "print \"total salary is\",ts,\"Rs\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 3.8, Page number 3.6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "total salary is 4400.0 Rs\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "abyb=1/3;     \n",
    "xbyy=1/4;\n",
    "mbyn=1/5;\n",
    "ba=1760;     #balance amount(Rs)\n",
    "\n",
    "#Calculation\n",
    "ts=ba/((1-abyb)*(1-xbyy)*(1-mbyn));     #total salary(Rs)\n",
    "\n",
    "#Result\n",
    "print \"total salary is\",ts,\"Rs\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 3.9, Page number 3.7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "total salary is 4800.0 Rs\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "abyb=1/3;     \n",
    "xbyy=1/4;\n",
    "mbyn=1/5;\n",
    "ba=1760;     #balance amount(Rs)\n",
    "\n",
    "#Calculation\n",
    "ts=ba/((1-abyb)*(1-(xbyy+mbyn)));     #total salary(Rs)\n",
    "\n",
    "#Result\n",
    "print \"total salary is\",ts,\"Rs\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 3.10, Page number 3.7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "total length of pole is 1050.0 cm\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "L=250;    #length in mud(Rs)\n",
    "p=(4/7)-(1/3);    #part in mud\n",
    "\n",
    "#Calculation\n",
    "Tl=L/p;     #total length of pole(cm)\n",
    "\n",
    "#Result\n",
    "print \"total length of pole is\",Tl,\"cm\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 3.11, Page number 3.7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "journey still left is 36.0 km\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "dt=60;    #distance travelled(km)\n",
    "dp=5/8;   #part travelled \n",
    "\n",
    "#Calculation\n",
    "x=dt*(1-dp)/dp;     #journey still left(km)\n",
    "\n",
    "#Result\n",
    "print \"journey still left is\",x,\"km\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 3.12, Page number 3.8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "amount to be added is 77.375\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=0.685;\n",
    "b=325;\n",
    "c=300;\n",
    "\n",
    "#Calculation\n",
    "x=c-(a*b);     #amount to be added\n",
    "\n",
    "#Result\n",
    "print \"amount to be added is\",x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 3.13, Page number 3.8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "length above water is 4.0 m\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "abyb=0.15;     \n",
    "xbyy=0.65;\n",
    "l=20;     #length of pole(m)\n",
    "\n",
    "#Calculation\n",
    "L=l*(1-(abyb+xbyy));     #length above water(m)\n",
    "\n",
    "#Result\n",
    "print \"length above water is\",L,\"m\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 3.14, Page number 3.8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "wife's share of money is 5625.0 Rs\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "abyb=0.375;     \n",
    "xbyy=0.4;\n",
    "ba=3375;     #balance amount(Rs)\n",
    "\n",
    "#Calculation\n",
    "ts=ba/(1-(abyb+xbyy));     #total salary(Rs)\n",
    "ws=abyb*ts;        #wife's share of money(Rs)\n",
    "\n",
    "#Result\n",
    "print \"wife's share of money is\",ws,\"Rs\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 3.15, Page number 3.8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "fraction between 1/3 and 4/5 is 5/8\n",
      "fraction between 2 and 7/2 is 3.0\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "from fractions import Fraction\n",
    "\n",
    "#Variable declaration\n",
    "#a=1/3\n",
    "a1=1;\n",
    "a2=3;\n",
    "#b=4/5\n",
    "b1=4;\n",
    "b2=5;\n",
    "x1=2;\n",
    "x2=1;\n",
    "#y=7/2\n",
    "y1=7;\n",
    "y2=2;\n",
    "\n",
    "#Calculation\n",
    "f1=(a1+b1)/(a2+b2);       #fraction between 1/3 and 4/5\n",
    "f2=(x1+y1)/(x2+y2);       #fraction between 2 and 7/2\n",
    "\n",
    "#Result\n",
    "print \"fraction between 1/3 and 4/5 is\",Fraction(f1)\n",
    "print \"fraction between 2 and 7/2 is\",f2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 3.16, Page number 3.8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "the three fractions are 0.545454545455 5/8 0.692307692308\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "from fractions import Fraction\n",
    "\n",
    "#Variable declaration\n",
    "#a=1/3\n",
    "a1=1;\n",
    "a2=3;\n",
    "#b=4/5\n",
    "b1=4;\n",
    "b2=5;\n",
    "\n",
    "#Calculation\n",
    "f11=a1+b1;    #numerator of 1st fraction\n",
    "f12=a2+b2;    #denominator of 1st fraction\n",
    "f1=f11/f12;   #1st fraction\n",
    "f21=a1+f11;   #numerator of 2nd fraction\n",
    "f22=a2+f12;   #denominator of 2nd fraction\n",
    "f2=f21/f22;   #2nd fraction\n",
    "f31=f11+b1;   #numerator of 3rd fraction\n",
    "f32=f12+b2;   #denominator of 3rd fraction \n",
    "f3=f31/f32;   #3rd fraction \n",
    "\n",
    "#Result\n",
    "print \"the three fractions are\",f2,Fraction(f1),f3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 3.17, Page number 3.9"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "15/46 is lesser than 1/3\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=22/63;\n",
    "b=4/11;\n",
    "c=15/46;\n",
    "d=33/98;\n",
    "e=1/3;\n",
    "\n",
    "#Calculation\n",
    "if(a<e):\n",
    "    print \"22/63 is lesser than 1/3\"\n",
    "if(b<e):\n",
    "    print \"4/11 is lesser than 1/3\"\n",
    "if(c<e):\n",
    "    print \"15/46 is lesser than 1/3\"\n",
    "if(d<e):\n",
    "    print \"33/98 is lesser than 1/3\"        "
   ]
  }
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