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- These tests focus on the basics of Maths and are meant to indicate your preparation level for the subject.
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## Basic Maths: Test 27

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*Basic Maths: Test 27*.You scored %%SCORE%% out of %%TOTAL%%.You correct answer percentage: %%PERCENTAGE%% .Your performance has been rated as %%RATING%% Your answers are highlighted below.

Question 1 |

$ \frac{4\frac{9}{13}}{4+\frac{3}{3+\frac{1}{2}}}$

is equal to ?

is equal to ?

1.7 | |

1.5 | |

2.4 | |

0.96 |

Question 1 Explanation:

We will solve this step by step

$ \begin{array}{l}\frac{\frac{61}{13}}{4+\frac{3}{3+\frac{1}{2}}}\\=\frac{\frac{61}{13}}{4+\frac{3}{\frac{6+1}{2}}}\\=\frac{\frac{61}{13}}{4+\frac{6}{7}}\\=\frac{\frac{61}{13}}{\frac{28+6}{7}}\\=\frac{61}{13}\times \frac{7}{34}=\frac{427}{442}=0.96\end{array}$

So the right answer for the question is option (d).

$ \begin{array}{l}\frac{\frac{61}{13}}{4+\frac{3}{3+\frac{1}{2}}}\\=\frac{\frac{61}{13}}{4+\frac{3}{\frac{6+1}{2}}}\\=\frac{\frac{61}{13}}{4+\frac{6}{7}}\\=\frac{\frac{61}{13}}{\frac{28+6}{7}}\\=\frac{61}{13}\times \frac{7}{34}=\frac{427}{442}=0.96\end{array}$

So the right answer for the question is option (d).

Question 2 |

$ \frac{9}{26}$ is equal to

$ \displaystyle \frac{1}{5+\frac{1}{7+\frac{1}{17}}}$ | |

$ \displaystyle \frac{1}{2+\frac{1}{1+\frac{1}{8}}}$ | |

$ \displaystyle \frac{1}{3+\frac{1}{1+\frac{1}{2+\frac{1}{4}}}}$ | |

$ \displaystyle \frac{1}{16+\frac{1}{8+\frac{1}{2+\frac{1}{9}}}}$ |

Question 2 Explanation:

The fraction can be written by hit and trail method

$ \begin{array}{l}\frac{1}{2+\frac{1}{1+\frac{1}{8}}}\\=\frac{1}{2+\frac{1}{\frac{8+1}{8}}}=\frac{1}{2+\frac{8}{9}}\\=\frac{1}{\frac{18+8}{9}}=\frac{9}{26}\end{array}$

$ \begin{array}{l}\frac{1}{2+\frac{1}{1+\frac{1}{8}}}\\=\frac{1}{2+\frac{1}{\frac{8+1}{8}}}=\frac{1}{2+\frac{8}{9}}\\=\frac{1}{\frac{18+8}{9}}=\frac{9}{26}\end{array}$

Question 3 |

Simplyfy

$ 1+\frac{5}{2+\frac{3}{5-\frac{1}{2}}}-\frac{1}{2}\,\left( 20\div 2 \right)$

$ 1+\frac{5}{2+\frac{3}{5-\frac{1}{2}}}-\frac{1}{2}\,\left( 20\div 2 \right)$

-1/2 | |

0 | |

-17/8 | |

1/3 |

Question 3 Explanation:

$ \begin{array}{l}1+\frac{5}{2+\frac{3}{5-\frac{1}{2}}}-\frac{1}{2}\,\times 10\\=1+\frac{5}{2+\frac{6}{9}}-5\\=1+\frac{5}{2+\frac{2}{3}}-5\\=1+\frac{5}{\frac{8}{3}}-5\\=1+\frac{5\times 3}{8}-5\\=\frac{15}{8}-4=\frac{15-32}{8}=\frac{-17}{8}\end{array}$

Question 4 |

$ \displaystyle \begin{array}{l}\frac{\left[ \left( 5+\frac{1}{9+\frac{1}{9}} \right)\times \left( 5+\frac{1}{9+\frac{1}{9}} \right)-\left( 5-\frac{1}{9+\frac{1}{9}} \right)\times \left( 5-\frac{1}{9+\frac{1}{9}} \right) \right]}{\left[ \left( 5+\frac{1}{9+\frac{1}{9}} \right)+\left( 5-\frac{1}{9+\frac{1}{9}} \right) \right]}\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\end{array}$

$ \displaystyle \frac{40}{101}$ | |

$ \displaystyle \frac{9}{41}$ | |

$ \displaystyle \frac{21}{101}$ | |

$ \displaystyle \frac{20}{100}$ |

Question 4 Explanation:

We will solve this equation in sections

Let us consider first

Let us suppose

$ \begin{array}{l}5+\frac{1}{9+\frac{1}{9}}=\frac{419}{82}=a\\5-\frac{1}{9+\frac{1}{9}}=\frac{401}{82}=b.\\if\,you\,see\,\,it\,\,is\,\,a\,\,formula\,\,of\,\,\\\frac{{{a}^{2}}-{{b}^{2}}}{\left( a+b \right)}=\frac{\left( a+b \right)\left( a-b \right)}{\left( a+b \right)}\\=\left( a-b \right)\\=\frac{419}{82}-\frac{401}{82}=\frac{18}{82}=\frac{9}{41}\end{array}$

So the right answer for this question is option b

Let us consider first

Let us suppose

$ \begin{array}{l}5+\frac{1}{9+\frac{1}{9}}=\frac{419}{82}=a\\5-\frac{1}{9+\frac{1}{9}}=\frac{401}{82}=b.\\if\,you\,see\,\,it\,\,is\,\,a\,\,formula\,\,of\,\,\\\frac{{{a}^{2}}-{{b}^{2}}}{\left( a+b \right)}=\frac{\left( a+b \right)\left( a-b \right)}{\left( a+b \right)}\\=\left( a-b \right)\\=\frac{419}{82}-\frac{401}{82}=\frac{18}{82}=\frac{9}{41}\end{array}$

So the right answer for this question is option b

Question 5 |

$ 1+\frac{3}{2+\frac{1}{5}}=?$

$ \frac{26}{11}$ | |

$ \frac{13}{6}$ | |

$ \frac{15}{6}$ | |

$ \frac{11}{26}$ |

Question 5 Explanation:

The given fraction can be simplified by

Expression

$ =1+\frac{3}{2+\frac{1}{5}}$

$ =1+\frac{3}{2+\frac{1}{5}}=1+\frac{15}{11}=\frac{11+15}{11}=\frac{26}{11}$

Therefore the answer for the question is option a

Expression

$ =1+\frac{3}{2+\frac{1}{5}}$

$ =1+\frac{3}{2+\frac{1}{5}}=1+\frac{15}{11}=\frac{11+15}{11}=\frac{26}{11}$

Therefore the answer for the question is option a

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