Fractions Test

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Fractions Test - 13

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Weekly Quiz Competition

Question 1
1 / -0

The lowest form of $$\displaystyle \frac { 30 }{ 60 } $$ is -

A
$$\displaystyle \frac { 1 }{ 2 } $$

B
$$\displaystyle \frac { 6 }{ 12 } $$

C
$$\displaystyle \frac { 15 }{ 30 } $$

D
$$\displaystyle \frac { 10 }{ 20 } $$

Solution

lowest form of $$\dfrac{30}{60}$$ is
$$\dfrac{30}{60}=\dfrac{3}{6}=\dfrac{1}{2}$$
Question 2
1 / -0

The sum of $$\displaystyle \frac { 8 }{ 14 } and \frac { 6 }{ 14 } $$

A
$$\displaystyle \frac { 1 }{ 7 } $$

B
$$\displaystyle \frac { 2 }{ 14 } $$

C
One

D
None of these

Solution

$$\displaystyle \frac { 8 }{ 14 } + \frac {6} {14} = \frac {14} {14} = 1 $$
Question 3
1 / -0

Re-arrange suitably and find the sum of the following
$$\displaystyle\frac{-4}{7}+\displaystyle\frac{7}{6}+\displaystyle\frac{2}{7}+3+\displaystyle\frac{-11}{6}$$.

A
$$\displaystyle\frac{43}{21}$$

B
$$\dfrac{43}{42}$$

C
$$\dfrac{23}{42}$$

D
$$\dfrac{23}{21}$$

Solution

Re-arranging and grouping the numbers in pairs in such a way that each group contains a pair of rational numbers with equal denominators, we have

$$\cfrac{-4}{7}+\cfrac{7}{6}+\cfrac{2}{7}+3+\cfrac{-11}{6}$$
$$=\begin{pmatrix}\cfrac{-4}{7}+\cfrac{2}{7}\end{pmatrix}+\begin{pmatrix}\cfrac{7}{6}+\cfrac{-11}{6}\end{pmatrix}+3$$

$$=\cfrac{(-4)+2}{7}+\cfrac{7+(-11)}{6}+3=\cfrac{-2}{7}+\cfrac{(-4)}{6}+3$$
$$=\cfrac{(-2)}{7}+\cfrac{(-2)}{3}+3\begin{bmatrix}\therefore\cfrac{-4}{6}=\cfrac{-2}{3}\end{bmatrix}$$

$$=\begin{pmatrix}\cfrac{(-2)}{7}+\cfrac{(-2)}{3}\end{pmatrix}+3$$
$$=\cfrac{(-2)\times3+(-2)\times7}{21}+3=\cfrac{(-6)+(-14)}{21}+3$$

$$=\cfrac{(-20)}{21}+\cfrac{3}{1}=\cfrac{(-20)+3\times21}{21}$$
$$=\cfrac{(-20)+63}{21}=\cfrac{43}{21}$$
Question 4
1 / -0

Simplify $$\displaystyle\frac{-3}{10}+\displaystyle\frac{7}{15}+\displaystyle\frac{3}{-20}+\displaystyle\frac{-9}{10}+\displaystyle\frac{13}{15}+\displaystyle\frac{13}{-20}$$

A
$$\displaystyle\frac{-2}{3}$$

B
$$\dfrac{3}{5}$$

C
$$\dfrac45$$

D
$$\dfrac13$$

Solution

Re-arranging and grouping the numbers in pairs such that each group

contains a pair of rational numbers with equal denominators, we have

$$\displaystyle\frac{-3}{10}+\displaystyle\frac{7}{15}+\displaystyle\frac{3}{-20}+\displaystyle\frac{-9}{10}+\displaystyle\frac{13}{15}+\displaystyle\frac{13}{-20}$$

$$=\begin{pmatrix}\displaystyle\frac{-3}{10}+\displaystyle\frac{-9}{10}\end{pmatrix}+\begin{pmatrix}\displaystyle\frac{7}{15}+\displaystyle\frac{13}{15}\end{pmatrix}+\begin{pmatrix}\displaystyle\frac{3}{-20}+\displaystyle\frac{13}{-20}\end{pmatrix}$$

$$=\begin{pmatrix}\displaystyle\frac{-3}{10}+\displaystyle\frac{-9}{10}\end{pmatrix}+\begin{pmatrix}\displaystyle\frac{7}{15}+\displaystyle\frac{13}{15}\end{pmatrix}+\begin{pmatrix}\displaystyle\frac{-3}{20}+\displaystyle\frac{-13}{20}\end{pmatrix}$$

$$=\displaystyle\frac{(-3)+(-9)}{10}+\displaystyle\frac{7+13}{15}+\displaystyle\frac{(-3)+(-13)}{20}$$

$$=\displaystyle\frac{-12}{10}+\displaystyle\frac{20}{15}+\displaystyle\frac{-16}{20}$$

$$=\displaystyle\frac{-6}{5}+\displaystyle\frac{4}{3}+\displaystyle\frac{-4}{5}$$ [Expressing each rational in lowest terms]

$$=\begin{pmatrix}\displaystyle\frac{-6}{5}+\displaystyle\frac{-4}{5}\end{pmatrix}+\displaystyle\frac{4}{3}$$

$$=\displaystyle\frac{(-6)+(-4)}{5}+\displaystyle\frac{4}{3}=\displaystyle\frac{-10}{5}+\displaystyle\frac{4}{3}$$

$$=-2+\displaystyle\frac{4}{3}=\displaystyle\frac{-6+4}{3}=\displaystyle\frac{-2}{3}$$
Question 5
1 / -0

$$\displaystyle 3 \dfrac { 6 }{ 10 } = \dfrac { ? }{ 10 } $$
Find $$?$$

A
$$63$$

B
$$26$$

C
$$36$$

D
$$62$$

Solution

since we are given a mixed fraction so the resulting fraction will be:
$$=\dfrac { (3\times10)+6 }{ 10 } $$
$$=\dfrac{36}{10}$$
Question 6
1 / -0

............. $$\displaystyle -\frac { 3 }{ 8 } = \frac { 3 }{ 8 }$$

A
1

B
0

C
$$\displaystyle \frac { 4 }{ 3 }$$

D
$$\displaystyle \frac { 3 }{4 }$$

Solution

Answer=3/8+3/8
=3/4
Question 7
1 / -0

The difference between $$\displaystyle \frac { 14 }{ 29 } and \frac {6} {29} $$ is

A
$$\displaystyle \frac { 16 }{ 29 } $$

B
$$\displaystyle \frac { 8 }{ 29 }$$

C
$$\displaystyle \frac { 11 }{ 58 } $$

D
$$8$$

Solution

Difference =$$\displaystyle \frac { 14 }{ 29 } - \frac {6} {29} = \frac {8} {29} $$
Question 8
1 / -0

Subtract $$\displaystyle \frac {8} {10}\ from\ \frac {11} {25}$$

A
$$\displaystyle \dfrac {18} {50} $$

B
$$\displaystyle -\dfrac {9} {25} $$

C
$$\displaystyle \dfrac {25} {9} $$

D
$$\displaystyle \dfrac {50} {18} $$

Solution

subtract 8/10 from 11/25
= 11/25 - 8/10
=- 9/25
Question 9
1 / -0

$$ \displaystyle \frac{4}{5} $$+ $$ \displaystyle \frac{2}{5} $$- $$ \displaystyle \frac{1}{5} $$ is equal to

A
1

B
$$ \displaystyle \frac{1}{5} $$

C
-5

D
None of these

Solution

$$ \displaystyle \frac{4}{5} $$+ $$ \displaystyle \frac{2}{5} $$- $$ \displaystyle \frac{1}{5}=\dfrac{4+2-1}{5}=\dfrac{5}{5}=1 $$
Question 10
1 / -0

$$\displaystyle \frac { 20 }{ 25 } = \frac {?} {5} $$

A
$$2$$

B
$$5$$

C
$$4$$

D
$$6$$

Solution

$$\displaystyle \frac { 20 }{ 25 } =\frac { 20\div 5 }{ 25\div 5 } =\frac { 4 }{ 5 } $$

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Re-Attempt Weekly Quiz Competition

Fractions Test - 13

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Fractions Test - 13

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Question 1

$$\displaystyle \frac { 1 }{ 2 } $$

$$\displaystyle \frac { 6 }{ 12 } $$

$$\displaystyle \frac { 15 }{ 30 } $$

$$\displaystyle \frac { 10 }{ 20 } $$

Solution

Question 2

$$\displaystyle \frac { 1 }{ 7 } $$

$$\displaystyle \frac { 2 }{ 14 } $$

One

None of these

Solution

Question 3

$$\displaystyle\frac{43}{21}$$

$$\dfrac{43}{42}$$

$$\dfrac{23}{42}$$

$$\dfrac{23}{21}$$

Solution

Question 4

$$\displaystyle\frac{-2}{3}$$

$$\dfrac{3}{5}$$

$$\dfrac45$$

$$\dfrac13$$

Solution

Question 5

$$63$$

$$26$$

$$36$$

$$62$$

Solution

Question 6

1

0

$$\displaystyle \frac { 4 }{ 3 }$$

$$\displaystyle \frac { 3 }{4 }$$

Solution

Question 7

$$\displaystyle \frac { 16 }{ 29 } $$

$$\displaystyle \frac { 8 }{ 29 }$$

$$\displaystyle \frac { 11 }{ 58 } $$

$$8$$

Solution

Question 8

$$\displaystyle \dfrac {18} {50} $$

$$\displaystyle -\dfrac {9} {25} $$

$$\displaystyle \dfrac {25} {9} $$

$$\displaystyle \dfrac {50} {18} $$

Solution

Question 9

1

$$ \displaystyle \frac{1}{5} $$

-5

None of these

Solution

Question 10

$$2$$

$$5$$

$$4$$

$$6$$

Solution

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