Olympiad Mathematics - Fractions
Exam Duration: 45 Mins Total Questions : 30
What is the mixed fraction form of \(\frac{41}{12}\)?
- (a)
\(3\frac{1}{2}\)
- (b)
\(3\frac{2}{12}\)
- (c)
\(3\frac{5}{12}\)
- (d)
\(2\frac{14}{12}\)
\(Q\frac{R}{D}=3\frac{5}{12}\)
What is the simplified form of the product of \(\frac{12}{24}\) and \( \frac{36}{72}\)?
- (a)
\(\frac{16}{24}\)
- (b)
\(\frac{3}{5}\)
- (c)
4
- (d)
\(\frac{1}{4}\)
\(\frac{12}{24}\times\frac{36}{72}=\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}\)
Give an example for a proper fraction.
- (a)
\(\frac{28}{13}\)
- (b)
\(\frac{11}{23}\)
- (c)
\(\frac{16}{9}\)
- (d)
\(\frac{14}{3}\)
In a proper fraction, the numerator is less than the denominator.
Raju scored 9 marks in maths test. If the maximum marks of the test is 25. how is Raju's score represented as a fraction?
- (a)
\(\frac{1}{25}\)
- (b)
\(\frac{16}{25}\)
- (c)
\(\frac{9}{25}\)
- (d)
\(\frac{25}{25}\)
Maximum marks = 25
MarkSscored by Raju = 9
\(\therefore\) Raju's score represented as a fraction = \(\frac{9}{25}\)
By how much is \(\frac{19}{20}\)greater than \(\frac{2}{20}?\)
- (a)
\(\frac{21}{20}\)
- (b)
\(\frac{21}{40}\)
- (c)
\(\frac{17}{20}\)
- (d)
\(\frac{17}{40}\)
\(\frac{19}{20}-\frac{2}{20}=\frac{19-2}{20}=\frac{17}{20}\)
Which of these makes a whole?
- (a)
One half
- (b)
Two halves
- (c)
3 halves
- (d)
5 halves
In which of the following does the shaded part represent one fourth of its whole?
- (a)
- (b)
- (c)
- (d)
Two fractions are equivalent if their cross multiplications are
- (a)
0
- (b)
1
- (c)
equal.
- (d)
not equal.
What fraction of the children in the following group are girls?
- (a)
\(\frac{3}{4}\)
- (b)
\(\frac{4}{3}\)
- (c)
\(\frac{3}{7}\)
- (d)
\(\frac{4}{7}\)
Which is the equivalent fraction of \(\frac{2}{3}\)having denominator 18 ?
- (a)
\(\frac{2}{18}\)
- (b)
\(\frac{18}{3}\)
- (c)
\(\frac{12}{18}\)
- (d)
\(\frac{12}{27}\)
Between which numbers does \(\frac{15}{4}\) lie?
- (a)
1 and 2
- (b)
2 and 3
- (c)
3 and 4
- (d)
11 and 12
\(\frac{15}{4}=3\frac{3}{4}\) So \(\frac{15}{4}\) lies between 3 and 4.
What should be placed in the empty space so that the sum of the fractions on each side of the triangle is same?
- (a)
\(\frac{7}{15}\)
- (b)
\(\frac{9}{15}\)
- (c)
\(\frac{6}{15}\)
- (d)
\(\frac{11}{15}\)
\(\frac{1}{15}+\frac{8}{15}+\frac{2}{15}=\frac{11}{15}\)
What fraction of alphabets are made of semicircles and straight lines?
- (a)
\(\frac{1}{7}\)
- (b)
\(\frac{2}{7}\)
- (c)
\(\frac{3}{7}\)
- (d)
\(\frac{4}{7}\)
R
The fraction of alphabets made of semicircles and straight lines is \(\frac{1}{7}\)
Which of the following is an improper fraction?
- (a)
- (b)
- (c)
- (d)
The fraction that represents the figure is \(\frac{1}{1}\)It is an improper fraction.
What fraction of the candles on the cake is lit?
- (a)
\(\frac{4}{6}\)
- (b)
\(\frac{4}{3}\)
- (c)
\(\frac{3}{6}\)
- (d)
\(\frac{1}{4}\)
Total number of candles =6
number of candles lit =4
Hence the fraction =\(\frac{4}{6}\)
\(\frac{5}{6}+\frac{2}{3}-\frac{4}{9}=M\) Determine the value of M.
- (a)
\(1\frac{1}{3}\)
- (b)
\(1\frac{1}{6}\)
- (c)
\(1\frac{1}{9}\)
- (d)
\(1\frac{1}{18}\)
A rope, \(36\frac{1}{3}\) m long, was cut into three parts measuring \(12\frac{2}{5}m,13\frac{1}{2}m\) and \(5\frac{4}{15}\) m respectively. What was the length of the rope left?
- (a)
\(5\frac{1}{6}\)
- (b)
\(7\frac{2}{5}\)
- (c)
\(9\frac{1}{6}\)
- (d)
\(11\frac{2}{5}\)
\(36\frac{1}{3}-[12\frac{2}{5}+13\frac{1}{2}+5\frac{4}{15}]\)
\(\Rightarrow \frac{109}{3}-[\frac{62}{5}+\frac{27}{2}+\frac{79}{15}]\)
\(\Rightarrow \frac{109}{3}-[\frac{62\times6+27\times15+79\times2}{30}]\)
\(\Rightarrow \frac{109}{3}-[\frac{372+405+158}{30}]\)
\(\Rightarrow \frac{109}{3}-\frac{935}{30}=\frac{155}{30}=\frac{31}{6}=5\frac{1}{6}\)
Hari gave Sai Rs.450 if \(\frac{1}{9}\) and \(\frac{2}{5}\) of the money was spent on food and clothes respectively, how much money did Sai spend?
- (a)
Rs. 250
- (b)
Rs. 240
- (c)
Rs. 230
- (d)
Rs. 220
Amount given by Hari = Rs.450
Part of amount spent on food \(=\frac{1}{9}\) of Rs.450
Part of amount spent on clothes \(=\frac{2}{5}\) of Rs.450
Total amount spent
\(=\left(\frac{1}{9}+\frac{2}{5}\right)\) of Rs.450
\(=\frac{23}{45}\times\) Rs.450 = Rs.230
\(\left( 999\frac{1}{7}+999\frac{2}{7}+999\frac{3}{7}+999\frac{4}{7}+999\frac{5}{7}+999\frac{6}{7}\right)=x\) What is the value of X?
- (a)
2997
- (b)
5979
- (c)
5994
- (d)
5997
\(999\frac{1}{7}+999\frac{2}{7}+999\frac{3}{7}+999\frac{4}{7}+999\frac{5}{7}+999\frac{6}{7}\)
\(=\left(999\times6)+(\frac{1}{7}+\frac{2}{7}+\frac{3}{7}+\frac{4}{7}+\frac{5}{7}+\frac{6}{7}\right)\)
\(=5994+\left(\frac{1+2+3+4+5+6}{7}\right)\)
\(=5994+\left(\frac{21}{7}\right)=5994+3=5997\)
The models are shaded to show which of the following?
- (a)
\(\frac{1}{3}=\frac{2}{4}\)
- (b)
\(\frac{1}{4}>\frac{1}{3}\)
- (c)
\(\frac{2}{3}<\frac{2}{4}\)
- (d)
\(\frac{2}{4}<\frac{2}{3}\)
Three equivalent fractions of \(\frac{2}{3}\)are______.
- (a)
\(\frac{2}{6},\frac{3}{6},\frac{4}{12}\)
- (b)
\(\frac{4}{6},\frac{6}{9},\frac{8}{12}\)
- (c)
\(\frac{3}{6},\frac{7}{6},\frac{8}{12}\)
- (d)
\(\frac{4}{6},\frac{8}{6},\frac{3}{6}\)
Equivalent fractions of \(\frac{2}{3}\)are
\(\frac { 2\times 2 }{ 3\times 2 } =\frac { 4 }{ 6 } ,\frac { 2\times 3 }{ 3\times 3 } =\frac { 6 }{ 9 } ,\frac { 2\times 4 }{ 3\times 4 } ,\frac { 8 }{ 12 } \)
i.e.,\(\frac { 4 }{ 6 } ,\frac { 6 }{ 9 } ,\frac { 8 }{ 12 } \)
In which figure does the shaded portion represents?
- (a)
- (b)
- (c)
- (d)
(A) Total number of equal parts = 4 Number of shaded parts = 2
Fraction of shaded portion =\(\frac{2}{4}=\frac{1}{2}\)
(B) Total number of equal parts = 3
Number of shaded parts = 2
Fraction of shaded portion =\(\frac{2}{3}\)
(C) Total number of equal parts = 4
Number of shaded parts = 3
Fraction of shaded portion =\(\frac{3}{4}\)
(D)Total number of equal parts = 6
Number of shaded parts = 4
Fraction of shaded portion = \(\frac{4}{6}=\frac{2}{3}\)
A pasta recipe requires 2\(\frac{2}{3}\)kg cheese. Approximately, how much pasta can be made from a 21 kg cheese?
- (a)
7\(\frac{7}{8}\)
- (b)
7\(\frac{4}{8}\)
- (c)
6\(\frac{7}{8}\)
- (d)
6\(\frac{4}{8}\)
Quantity of cheese required for a pasta
recipe=2\(\frac{2}{3}\)kg \(\frac{8}{3}\)kg
So, quantity of pasta can be made from
21. kg cheese =21\(\div\)\(\frac{8}{3}\)
=21x\(\frac{3}{8}\)=\(\frac{63}{8}\)=7\(\frac{7}{8}\)
Which number should come in place of \(\Box \) ?
\(\frac{4}{9}+\frac{7}{9}+\frac{\Box}{9}=2\frac{1}{9}\)
- (a)
7
- (b)
1
- (c)
8
- (d)
9
We have,\(\frac{4}{9}+\frac{7}{9}+\frac{\Box}{9}=\frac{19}{9}\)
or, \(\frac{4}{9}+\frac{7}{9}+\frac{8}{9}=\frac{19}{9}\)
\(\therefore \Box\)=8
How many more equal sized pieces would you need to make a whole for the given figure?
- (a)
1
- (b)
2
- (c)
4
- (d)
6
Find x if 5\(\frac { 1 }{ 3 } -3\frac { 2 }{ 3 } \div 1\frac { 1 }{ 3 } \div X+3\frac { 1 }{ 5 } \div 1\frac { 1 }{ 5 } \)=7
- (a)
1\(\frac{1}{2}\)
- (b)
2\(\frac{1}{3}\)
- (c)
3\(\frac{1}{4}\)
- (d)
None of these
We have,
5\(\frac { 1 }{ 3 } -3\frac { 2 }{ 3 } \div 1\frac { 1 }{ 3 } \div X+3\frac { 1 }{ 5 } \div 1\frac { 1 }{ 5 } \)=7
\(\Rightarrow \frac { 16 }{ 3 } -\frac { 11 }{ 3 } \div \frac { 4 }{ 3 } \div X+\frac { 16 }{ 5 } \div \frac { 6 }{ 5 } \)=7
\(\Rightarrow \frac { 16 }{ 3 } -\frac { 11 }{ 3 } \times \frac { 4 }{ 3 } \times \frac { 1 }{ X } +\frac { 16 }{ 5 } \times \frac { 5 }{ 6 } \)=7
\(\Rightarrow \frac { 16 }{ 3 } -\frac { 11 }{ 4X } +\frac { 8 }{ 3 } \)=7 \(\Rightarrow \frac { 24 }{ 3 } -\frac { 11 }{ 4X } \)
\(\Rightarrow\)8-7=\(\frac { 11 }{ 4X } \quad \quad \Rightarrow \)4x=11
\(\Rightarrow\)x=\(\frac { 11 }{ 4 } \quad \Rightarrow \)X=2\(\frac{3}{4}\)
Four families went on a picnic. Each family carried a cake for the picnic.\(\frac{3}{4}\)of each cake was eaten. How much cake was eaten in all?
- (a)
\(\frac{3}{8}\)
- (b)
3
- (c)
\(\frac{9}{12}\)
- (d)
1
Fraction eaten from each cake =\(\frac{3}{4}\)
Number of families = 4
\(\therefore\)Fraction of cake was eaten in all
=3x\(\frac{3}{4}\)=3
Aman had 128 trading cards. He gave \(\frac{3}{8}\)of his cards to Mohit and \(\frac{1}{4}\) of his cards to Kushal. How many cards did he give altogether?
- (a)
50
- (b)
65
- (c)
80
- (d)
75
Total number of cards Aman had = 128
Number of cards he gave to Mohit =\(\frac{3}{8}\)x128 = 48
Number of cards he gave to Kushal=\(\frac{1}{4}\)x128=32
\(\therefore\)Total number of cards he gave altogether = 48 + 32 = 80
Sudha planted tomatoes in 1/2 portion of her kitchen garden. She planted spinach in one-fourth of the remaining portion. What fraction of the garden has spinach?
- (a)
\(\frac{1}{2}\)
- (b)
\(\frac{1}{3}\)
- (c)
\(\frac{1}{8}\)
- (d)
\(\frac{1}{5}\)
Let whole garden be denoted by x.
Fraction of garden having tomatoes =\(\frac{X}{2}\)
\(\therefore\)Remaining fraction of garden = x -\(\frac{X}{2}\)=\(\frac{X}{2}\)
Fraction of garden having spinach \(=\frac { 1 }{ 4 } \left( \frac { X }{ 2 } \right) =\frac { X }{ 8 } =\frac { 1 }{ 8 } \)(x)
Which of the following statements is CORRECT?
Statement-1 : Mrs Soni bought 7\(\frac{1}{2}\) litres of milk. Out of this, 5\(\frac{3}{4}\) litres was consumed. 1\(\frac{1}{3}\)litres of milk is left with her.
Statement-2 : Amit reads \(\frac{3}{5}\)of a book. He finds that there are still 80 pages left to be read. Total number of pages in the book is 200.
- (a)
Only Statement-1
- (b)
Only Statement-2
- (c)
Both Statement-1 and Statement-2
- (d)
Neither Statement-1 and nor Statement-2
Statement-1: Total quantity of milk bought =7\(\frac{1}{2}\)=litres=\(\frac{15}{2}\)litres
Quantity of milk consumed =5\(\frac{3}{4}\)litres
=\(\frac{23}{4}\)litres
Quantity of milk left = \(\left( \frac { 15 }{ 2 } -\frac { 23 }{ 4 } \right) \quad \)
\(\left( \frac { 30-23 }{ 4 } \right) \)litres =\(\frac{1}{2}\)litres =1\(\frac{1}{3}\)litres
Statement-2: Let total number of pages in
the book be x.
According to question,
\(\frac{3}{5}\)x+80 = x
\(\Rightarrow\)x-\(\frac{3}{5}\)x=80 \(\Rightarrow\) \(\frac{2X}{5}\)=80 \(\Rightarrow\)x=\(\frac{80\times5}{2}\)
\(\Rightarrow\)x=200
\(\therefore\)Total number of pages = 200
Hence, only statement-2 is true.