5 Mark Question

Question 15 Marks

A piece of wire is of length $12\frac{3}{4}\text{m}.$ If it is cut into two pieces in such a way that the length of one piece is $5\frac{1}{4}\text{m},$ what is the length of the other piece?

Answer

A piece of wire of length $12\frac{3}{4}\text{m}.$ one piece is $5\frac{1}{4}\text{m},$
$12\frac{3}{4}=\frac{51}{4}\text{ and }5\frac{1}{4}=\frac{21}{4}$
Let the length of other piece be x m.
$\frac{51}{4}=\text{x}+\frac{21}{4}$
$\Rightarrow\text{x}=\frac{51}{4}-\frac{21}{4}$
$\Rightarrow\text{x}=\frac{51-21}{4}$
$\Rightarrow\text{x}=\frac{30}{4}$
$\Rightarrow\text{x}=\frac{15}{2}$
$\Rightarrow\text{x}=7\frac{1}{2}$

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Question 25 Marks

A rectangular sheet of paper is $12\frac{1}{2}\text{cm}$ long and $10\frac{2}{3}\text{cm}$ wide. Find its perimeter.

Answer

A rectangular piece of paper is $12\frac{1}{2}\text{cm}$ long and $10\frac{2}{3}\text{cm}$ wide,
$12\frac{1}{2}=\frac{25}{2}\text{ and }10\frac{2}{3}=\frac{32}{3}$
Perimeter = 2(length + width)
Perimeter $=2\Big(\frac{25}{2}\text{cm}+\frac{32}{3}\text{cm}\Big)$
Perimeter $=2\Big(\frac{75}{6}+\frac{64}{6}\Big)\text{cm}$
Perimeter $=2\Big(\frac{139}{6}\Big)\text{cm}$
Perimeter $=\frac{139}{3}$
Perimeter $=46\frac{1}{3}$

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Question 35 Marks

Waht should be added to $5\frac{4}{15}$ to get $12\frac{3}{5}?$

Answer

We have,
$5\frac{4}{15}=\frac{79}{15}$
$12\frac{3}{5}=\frac{63}{5}$
Let x be the number added to $\frac{79}{15}$ to get $\frac{63}{5}$
$=\frac{79}{15}+\text{x}=\frac{63}{5}$
$\Rightarrow\text{x}=\frac{63}{5}-\frac{79}{15}$
Taking out the LCM of 5 and 15 we get,
3 × 5 = 15
Now, we convert the given fraction to equivalent fractions by making the denominators 15, we get,
$\Rightarrow\text{x}=\frac{63\times3}{5\times3}-\frac{79}{15}$
$\Rightarrow\text{x}=\frac{189}{15}-\frac{79}{15}$
$\Rightarrow\text{x}=\frac{189-79}{15}$
$\Rightarrow\text{x}=\frac{110}{15}$
$\Rightarrow\text{x}=\frac{22}{3}$

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Question 45 Marks

Arrange the following fraction in descending order:
$\frac{2}{7},\frac{11}{35},\frac{9}{14},\frac{13}{28}$

Answer

We have,
$\frac{2}{7},\frac{11}{35},\frac{9}{14},\frac{13}{28}$
Taking the LCM of 7, 35, 14 and 28, we get
7 × 5 × 2 × 2 = 140
Now, we convert the given fractions to equivalent fractions by making the denominators 140
$\frac{2\times20}{7\times20},\frac{11\times4}{35\times4},\frac{9\times10}{14\times10},\frac{13\times5}{28\times5}$
$\frac{40}{140},\frac{44}{140},\frac{90}{140},\frac{65}{140}$
As we know 40 > 44 > 65 > 90
Therefore, $\frac{90}{140}<\frac{65}{140}<\frac{44}{140}<\frac{40}{140}$
Hence, $\frac{9}{14}<\frac{13}{28}<\frac{11}{35}<\frac{2}{7}$

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Question 55 Marks

Arrange the following fractions in ascending order:
$\frac{4}{6},\frac{3}{8},\frac{6}{12},\frac{5}{16}$

Answer

We have,
$\frac{4}{6},\frac{3}{8},\frac{6}{12},\frac{5}{16}$
Taking the LCM of 6, 8, 12 and 16, we get
2 × 2 × 2 × 2 × 3 = 48
Now, we convert the given fractions to equivalent fractions by making the denominators 48,
$\frac{4\times8}{6\times8},\frac{3\times6}{8\times6},\frac{6\times2}{12\times2},\frac{5\times3}{16\times3}$
$=\frac{32}{48},\frac{18}{48},\frac{12}{48},\frac{15}{48}$
We know that 12 < 15 < 18 < 32
Therefore, $\frac{12}{48}<\frac{15}{48}<\frac{18}{48}<\frac{32}{148}$
Hence, $\frac{6}{12}<\frac{5}{16}<\frac{3}{8}<\frac{4}{6}$

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Question 65 Marks

Arrange the following fraction in descending order:
$\frac{4}{5},\frac{7}{10},\frac{11}{15},\frac{17}{20}$

Answer

We have,
$\frac{4}{5},\frac{7}{10},\frac{11}{15},\frac{17}{20}$
Taking the LCM of 5, 10, 15 and 20, we get
5 × 2 × 2 × 3 = 60
Now, we convert the given fractions to equivalent fractions by making the denominators 48,
$\frac{4\times12}{5\times12},\frac{7\times6}{10\times6},\frac{11\times4}{15\times4},\frac{17\times3}{20\times3}$
$\frac{48}{60},\frac{42}{60},\frac{44}{60},\frac{51}{60}$
As we know 51 > 48 > 44 > 42
Therefore,
$\frac{51}{60}<\frac{48}{60}<\frac{44}{60}<\frac{42}{60}$
Hence, $\frac{17}{20}<\frac{4}{5}<\frac{11}{15}<\frac{7}{10}$

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Question 75 Marks

Suman studies for $5\frac{2}{3}$ hours daily. She devotes $2\frac{4}{5}$ hours of her time lor Science and Mathematics. How much time does she devote for other subjects?

Answer

Given,
Suman studies for $5\frac{2}{3}$ i.e., $\frac{17}{3}$ hours daily
She devotes $5\frac{2}{3}$ i.e., $\frac{17}{3}$ hours of her time for science and Mathematics. Let x be time she devotes for other subject.
$\frac{17}{3}=\text{x}+\frac{14}{5}$
$\Rightarrow\text{x}=\frac{17}{3}-\frac{14}{5}$
Taking out the LCM of 3 and 5 we get,
3 × 5 = 15
Now, we convert the given fractions to equivalent fractions by making the denominators 48, we get,
$\Rightarrow\text{x}=\frac{17\times5}{3\times5}-\frac{14\times3}{5\times3}$
$\Rightarrow\text{x}=\frac{85}{15}-\frac{42}{15}$
$\Rightarrow\text{x}=\frac{85-42}{15}\text{hours}$
$\Rightarrow\text{x}=\frac{43}{15}\text{hours}$
$\Rightarrow\text{x}=2\frac{13}{15}\text{hours}$

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Question 85 Marks

Arrange the following fractions in ascending order:
$\frac{3}{8},\frac{5}{6},\frac{6}{8},\frac{2}{4},\frac{1}{3}$

Answer

$\frac{3}{8},\frac{5}{6},\frac{6}{8},\frac{2}{4},\frac{1}{3}$
Taking the LCM of 8, 6, 8, 4 and 3, we get
2 × 4 × 3 = 24
Now, we convert the given fractions to equivalent fractions by making the denominators 24,
$\frac{3\times3}{8\times3},\frac{5\times4}{6\times4},\frac{6\times3}{8\times3},\frac{2\times6}{4\times6},\frac{1\times8}{3\times8}$
$=\frac{9}{24},\frac{20}{24},\frac{18}{24},\frac{12}{24},\frac{8}{24}$
We know that, 8 < 9 < 12 < 18 < 20
Therefore, $\frac{8}{24}<\frac{9}{24}<\frac{12}{24}<\frac{18}{24}<\frac{20}{24}$
Hence, 13 < 38 < 24 < 68 < 56

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Question 95 Marks

Compare the following fractions by using the symbo > or < or =
$\frac{17}{15}\text{ and }\frac{119}{105}$

Answer

We have,
$\frac{17}{15}\text{ and }\frac{119}{105}$
Taking the LCM of 15 and 105, we get
5 × 3 × 7 = 105
Now, we convert the given fractions to equivalent fractions by making the denominators 105,
$\frac{17\times7}{15\times7}\text{ and }\frac{119}{105}$
$\frac{119}{105}\text{ and }\frac{119}{105}$

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Question 105 Marks

In a "magic square", the sum of the numbers in each row, in each column and along the diagonal is the same. Is this a magic square?

$\frac{4}{11}$	$\frac{9}{11}$	$\frac{2}{11}$
$\frac{3}{11}$	$\frac{5}{11}$	$\frac{7}{11}$
$\frac{8}{11}$	$\frac{1}{11}$	$\frac{6}{11}$

Answer

Given,

$\frac{4}{11}$	$\frac{9}{11}$	$\frac{2}{11}$
$\frac{3}{11}$	$\frac{5}{11}$	$\frac{7}{11}$
$\frac{8}{11}$	$\frac{1}{11}$	$\frac{6}{11}$

Along the $1^{\text {st }}$ column=\frac{4}{11}+\frac{3}{11}+\frac{8}{11}=\frac{15}{11}$
Along the $2^{\text {nd }}$ column=\frac{9}{11}+\frac{5}{11}+\frac{1}{11}=\frac{15}{11}$
Along the $3^{\text {rd }}$ column=\frac{2}{11}+\frac{7}{11}+\frac{6}{11}=\frac{15}{11}$
Along the $1^{\text {st }}$ column=\frac{4}{11}+\frac{9}{11}+\frac{2}{11}=\frac{15}{11}$
Along the $2^{\text {nd }}$ row=\frac{3}{11}+\frac{5}{11}+\frac{7}{11}=\frac{15}{11}$
Along the $3^{\text {rd }}$ row=\frac{8}{11}+\frac{1}{11}+\frac{6}{11}=\frac{15}{11}$
Diagonally $=\frac{4}{11}+\frac{5}{11}+\frac{6}{11}=\frac{15}{11}$
And $\frac{2}{11}+\frac{5}{11}+\frac{8}{11}=\frac{15}{11}$
Therefore, the sum of numbers in each row, in row column and along the diagonal is same and the sum is $\frac{15}{11}$

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