Chapter 4: Fractions and Decimals

Ans: Given,

By the end of the year 2007 Metro trains was saved

$33000$  tonnes of CNG

$3300$ tonnes of diesel

$21000$ tonnes of petrol

$\dfrac{{{\text{ The quantity of diesel saved }}}}{{{\text{ The quantity of petrol saved }}}} = \dfrac{{3300}}{{21000}}$

$= \dfrac{{3300 \div 300}}{{21000 \div 300}}$

$= \dfrac{{11}}{{70}}$

Ans:  $\dfrac{{{\text{ The quantity of diesel saved }}}}{{{\text{ The quantity of CNG saved }}}} = \dfrac{{3300}}{{33000}}$

$= \dfrac{{3300 \div 3300}}{{33000 \div 3300}}$

$= \dfrac{1}{{10}}$

The quantity of diesel saved to quantity of petrol is $\dfrac{{11}}{{70}}$ 

The quantity of diesel saved to the quantity of CNG is $\dfrac{1}{{10}}$

Ans: From the given table it is clear that Milk provides the least energy and Rice provides the maximum

Ratio of the least energy to the maximum energy

$\dfrac{{{\text{ The least energy }}}}{{{\text{ The maximum energy }}}} = \dfrac{3}{{5.3}} = \dfrac{{3 \times 10}}{{5.3 \times 10}} = \dfrac{{30}}{{53}}$

The least energy as a fraction of maximum energy is $\dfrac{{30}}{{53}}$.

Ans: Total fill required of a cup of milk is 1

Given that Cup is $\dfrac{1}{3}$ full of milk

The remaining part of the cup which is still to be filled by milk 

$= 1 - \dfrac{1}{3} = \dfrac{{3 - 1}}{3}$

$= \dfrac{2}{3}$

The part of cup is still to be filled by milk to make it full is $\dfrac{2}{3}$.

Ans: Mary bought $3\dfrac{1}{2}{\text{m}}$ of lace

She used $1\dfrac{3}{4}{\text{m}}$ of lace for her new dress

Left lace $=$ bought $3\dfrac{1}{2}{\text{m}}$ of lace $ - $ used $1\dfrac{3}{4}{\text{m}}$ of lace

Rewrite the fraction in same denominator

$= \dfrac{{7 \times 2}}{{2 \times 2}}{\text{m}} - \dfrac{7}{4}{\text{m}} = \dfrac{{14m - 7m}}{4}$

$= \dfrac{7}{4}m = 1\dfrac{3}{4}m$ of lace

The lace left with her is $\dfrac{7}{4}m$.

Ans: Sunita had gained $= 1\dfrac{1}{4}{\text{g}} = \dfrac{5}{4}{\text{kg}}$

Earlier her weight was $46\dfrac{3}{8}{\text{kg}} = \dfrac{{371}}{8}{\text{kg}}$

Her total weight on Monday

$= \dfrac{{371}}{8}{\text{kg}} + \dfrac{5}{4}{\text{kg}}$

$= \dfrac{{371}}{8}{\text{kg}} + \dfrac{{5 \times 2}}{{4 \times 2}}{\text{kg}}$

$= \dfrac{{371}}{8}{\text{kg}} + \dfrac{{10}}{8}{\text{kg}}$

$= \dfrac{{(371 + 10)}}{8}{\text{kg}} = \dfrac{{381}}{8}{\text{kg}}$

$= 47\dfrac{5}{8}{\text{kg}}$

Her weight on Monday was $47\dfrac{5}{8}$

Ans: Monday Sunil purchased $12\dfrac{1}{2}$ liters of juice $= \dfrac{{25}}{2}$ liters

Tuesday Sunil purchased $14\dfrac{3}{4}$ liters of juice $= \dfrac{{59}}{4}$ liters

Total quantity of juice Sunil purchased in two days $= \left( {\dfrac{{25}}{2} + \dfrac{{59}}{4}} \right)$ litres

$= \left( {\dfrac{{25 \times 2}}{{2 \times 2}} + \dfrac{{59}}{4}} \right)$ litres 

$= \left( {\dfrac{{50}}{4} + \dfrac{{59}}{4}} \right)$ litres

$= \left( {\dfrac{{50 + 59}}{4}} \right)$ litres 

$= \dfrac{{109}}{4}$ litres

$= 27\dfrac{1}{4}$ litres

Litres of juice he purchased in two days is $27\dfrac{1}{4}$

Ans: Total quantity of juice $= 5\dfrac{1}{2}$ litres $= \dfrac{{11}}{2}$ litres

Nazima gave to her friends $= 2\dfrac{3}{4}$ litres $= \dfrac{{11}}{4}$ litres

The required quantity of juice she is left with 

$= \left( {\dfrac{{11}}{2} - \dfrac{{11}}{4}} \right)$ litres 

$= \left( {\dfrac{{11 \times 2}}{{2 \times 2}} - \dfrac{{11}}{4}} \right)$ litres

$= \left( {\dfrac{{22 - 11}}{4}} \right)$ litres

 $= \dfrac{{11}}{4}$ litres

$= 2\dfrac{3}{4}$ litres

The litre of juice left with her is $2\dfrac{3}{4}$ litres

Ans: Total length of wood $150\dfrac{1}{4}{\text{cm}} = \dfrac{{601}}{4}{\text{cm}}$

Wood used by carpenter $40\dfrac{1}{5}{\text{cm}} = \dfrac{{201}}{5}{\text{cm}}$

Remaining piece of wood length

$= \left( {\dfrac{{601}}{4} - \dfrac{{201}}{5}} \right){\text{cm}} = \left( {\dfrac{{601 \times 5}}{{4 \times 5}} - \dfrac{{201 \times 4}}{{5 \times 4}}} \right){\text{cm}}$

$= \left( {\dfrac{{3005}}{{20}} - \dfrac{{804}}{{20}}} \right){\text{cm}}$

$= \dfrac{{2201}}{{20}}{\text{cm}}$ or $110\dfrac{1}{{20}}{\text{cm}}$

The length of the remaining piece is $110\dfrac{1}{{20}}{\text{cm}}$

Ans: Nasir travel $3\dfrac{1}{2}{\text{km}}$ in a bus $= \dfrac{7}{2}{\text{km}}$

Walked $1\dfrac{1}{8}{\text{km}}$ to reach a town $= \dfrac{9}{8}{\text{km}}$

Total distance covered by Nasir

  $\left( {\dfrac{7}{2} + \dfrac{9}{8}} \right){\text{km}}$

   $= \dfrac{{(7 \times 8) + (9 \times 2)}}{{2 \times 8}}{\text{km}}$

   $= \dfrac{{56 + 18}}{{16}}{\text{km}}$ 

   $= \dfrac{{74}}{{16}}{\text{km}}$

   $= \dfrac{{74 \div 2}}{{16 \div 2}}{\text{km}}$

   $= \dfrac{{37}}{8}{\text{km}}$

   $= 4\dfrac{5}{8}{\text{km}}$ 

The distance he travelled to reach the town is $\dfrac{{37}}{8}{\text{km}}$ or $4\dfrac{5}{8}{\text{km}}$

Ans: The weight of fish caught by Neetu $3\dfrac{3}{4}{\text{kg}} = \dfrac{{15}}{4}{\text{kg}}$

The weight of fish caught by Narendra $2\dfrac{1}{2}{\text{kg}} = \dfrac{5}{2}{\text{kg}}$

Neetus fish weigh more than that of Narendra by

  $\dfrac{{15}}{4}{\text{kg}} - \dfrac{5}{2}{\text{kg}} = \dfrac{{15}}{4}{\text{kg}} - \dfrac{{5 \times 2}}{{2 \times 2}}{\text{kg}}$

   $= \dfrac{{15}}{4}{\text{kg}} - \dfrac{{10}}{4}{\text{kg}}$ 

   $= \dfrac{{(15 - 10)}}{4}{\text{kg}}$

   $= \dfrac{5}{4}{\text{kg or }}1\dfrac{1}{4}{\text{kg}}$ 

Neetu fish weighed $\dfrac{5}{4}{\text{kg}}$ or $1\dfrac{1}{4}{\text{kg}}$ more than Narendra.