Question 11 Mark
Find the product $\frac{-6}{5} \times \frac{9}{11}$
Answer
View full question & answer→$\frac{-6}{5} \times \frac{9}{11}=\frac{-6 \times 9}{5 \times 11}=\frac{-54}{55}$
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Question 21 Mark
Find the product $\frac{3}{10} \times$-9
Answer
View full question & answer→$\frac{3}{10} \times-9=\frac{3 \times(-9)}{10}=\frac{-27}{10}=-2 \frac{7}{10}$
Question 31 Mark
Find the product $\frac{9}{2} \times\left(\frac{-7}{4}\right)$
Answer
View full question & answer→$\frac{9}{2} \times\left(\frac{-7}{4}\right)=\frac{9 x-7}{2 \times 4}=\frac{-63}{8}=-7 \frac{7}{8}$
Question 41 Mark
Find $-2 \frac{1}{9}-6$
Answer
View full question & answer→$-2 \frac{1}{9}-6=\frac{-19}{9}-6$
=$\frac{-19}{9}+(-6)=\frac{-19}{9}+\frac{(-6)}{1}$
$LCM$ of $9$ and $1$ is $9.$
$-6\over 1$=$-6\times9\over 1 \times 9$=$-54\over 9$
Thus, $\frac{-19}{9}+\frac{(-6)}{1}=\frac{-19}{9}+\frac{(-54)}{9}$
$\frac{-19+(-54)}{9}=\frac{-73}{9}=-8 \frac{1}{9}$
=$\frac{-19}{9}+(-6)=\frac{-19}{9}+\frac{(-6)}{1}$
$LCM$ of $9$ and $1$ is $9.$
$-6\over 1$=$-6\times9\over 1 \times 9$=$-54\over 9$
Thus, $\frac{-19}{9}+\frac{(-6)}{1}=\frac{-19}{9}+\frac{(-54)}{9}$
$\frac{-19+(-54)}{9}=\frac{-73}{9}=-8 \frac{1}{9}$
Question 51 Mark
Find the sum $\frac{-2}{3}$+0
Answer
View full question & answer→Any number added to zero will give the same number
$\frac{-2}{3}+0=\frac{-2}{3}$
$\frac{-2}{3}+0=\frac{-2}{3}$
Question 61 Mark
Find the sum $\frac{5}{4}+\left(\frac{-11}{4}\right)$
Answer
View full question & answer→Here,
$\frac{5}{4}+\left(\frac{-11}{4}\right)$
$=\frac{5-11}{4}$
$=\frac{-6}{4}$
$\frac{5}{4}+\left(\frac{-11}{4}\right)$
$=\frac{5-11}{4}$
$=\frac{-6}{4}$
Question 71 Mark
Which is greater in $-3 \frac{2}{7},-3 \frac{4}{5}$
Answer
View full question & answer→To find the greater rational number we need to have a common denominator, so the $LCM$ of $7$and $5$is $35$
$-3 \frac{2}{7}=-\frac{23}{7}=\frac{-23 \times 5}{7 \times 5}=\frac{-115}{35}. . . .[LCM (7, 5) = 35]$
$-3 \frac{4}{5}=\frac{-19}{5}=\frac{-19 \times 7}{5 \times 7}=\frac{-133}{35}$
$\because$$\frac{-115}{35}>\frac{-133}{35}$
$\therefore -3 \frac{2}{7}>-3 \frac{4}{5}$
Or
$-23\over 7$and$-19\over 5$
Cross multiplying the numerators we have
$-23 \times 5$ and $-19 \times 7$
$-115$ and $-133$
$-115 > -133$
$\therefore -3 \frac{2}{7}>-3 \frac{4}{5}$
$-3 \frac{2}{7}=-\frac{23}{7}=\frac{-23 \times 5}{7 \times 5}=\frac{-115}{35}. . . .[LCM (7, 5) = 35]$
$-3 \frac{4}{5}=\frac{-19}{5}=\frac{-19 \times 7}{5 \times 7}=\frac{-133}{35}$
$\because$$\frac{-115}{35}>\frac{-133}{35}$
$\therefore -3 \frac{2}{7}>-3 \frac{4}{5}$
Or
$-23\over 7$and$-19\over 5$
Cross multiplying the numerators we have
$-23 \times 5$ and $-19 \times 7$
$-115$ and $-133$
$-115 > -133$
$\therefore -3 \frac{2}{7}>-3 \frac{4}{5}$
Question 81 Mark
Which is greater in $\frac{-3}{4}, \frac{2}{-3}$
Answer
View full question & answer→To find the greater rational number we need to have a common denominator, so the $LCM$ of $4$ and $3$ is $12.$
Therefore,$\frac{-3}{4}=\frac{-3 \times 3}{4 \times 3}=\frac{-9}{12}$
$\frac{2}{-3}=\frac{2 \times 4}{-3 \times 4}=\frac{8}{-12}=\frac{-8}{12}. . . [LCM (4,3) = 12]$
$\because$$\frac{-8}{12}>\frac{-9}{12}$
$\therefore$ $\frac{2}{-3}>\frac{-3}{4}$
Therefore,$\frac{-3}{4}=\frac{-3 \times 3}{4 \times 3}=\frac{-9}{12}$
$\frac{2}{-3}=\frac{2 \times 4}{-3 \times 4}=\frac{8}{-12}=\frac{-8}{12}. . . [LCM (4,3) = 12]$
$\because$$\frac{-8}{12}>\frac{-9}{12}$
$\therefore$ $\frac{2}{-3}>\frac{-3}{4}$
Question 91 Mark
Rewrite the rational numbers in the simplest form $\frac{-8}{10}$
Answer
View full question & answer→We can simplify the given fraction $-\frac{8}{10}$as follows:
$\frac{-8}{10}=\frac{-4 \times 2}{5 \times 2}=\frac{-4}{5}$
Therefore, $\frac{-4}{5}$ is the simplest form of the given fraction.
$\frac{-8}{10}=\frac{-4 \times 2}{5 \times 2}=\frac{-4}{5}$
Therefore, $\frac{-4}{5}$ is the simplest form of the given fraction.
Question 101 Mark
Rewrite the rational number $\frac{-44}{72}$ in the simplest form.
Answer
View full question & answer→We can simplify the given fraction $\frac{-44}{72}$ as follows
$\frac{-44}{72}=\frac{-11 \times 4}{18 \times 4}=\frac{-11}{18}$
Thus, $\frac{-11}{18}$ is the simplest form of the given fraction.
$\frac{-44}{72}=\frac{-11 \times 4}{18 \times 4}=\frac{-11}{18}$
Thus, $\frac{-11}{18}$ is the simplest form of the given fraction.
Question 111 Mark
Rewrite the rational number $\frac{25}{45}$ in the simplest form.
Answer
View full question & answer→The $HCF$ of $25$ and $45$ is $5$. The numbers $25 \& 45$ come in the same table $5$
Thus, its simplest form would be $\frac{25 \div 5}{45 \div 5}=\frac{5}{9}$
Thus, its simplest form would be $\frac{25 \div 5}{45 \div 5}=\frac{5}{9}$
Question 121 Mark
Rewrite the rational number $\frac{-8}{6}$in the simplest form.
Answer
View full question & answer→The $HCF$ of $8$ and $6$ is $2.$ The numbers $8 \& 6$ come in the same table $2$
Thus, its simplest form would be $\frac{-8 \div 2}{6 \div 2}=\frac{-4}{3}$
Thus, its simplest form would be $\frac{-8 \div 2}{6 \div 2}=\frac{-4}{3}$
Question 131 Mark
Draw the numbers line and represent rational number $\frac{7}{8}$ on it.
View full question & answer→Question 141 Mark
Draw the numbers line and represent the rational number $\frac{-7}{4}$on it.
Answer
$-7\over 4 $$=-1$$3\over 4$ie $-1$ and$3\over 4$
Thus it will be represented after $-1$
$\frac{7}{4}=\frac{-4-3}{4}=\frac{-4}{4}-\frac{3}{4}=-1-\frac{3}{4}$
View full question & answer→$-7\over 4 $$=-1$$3\over 4$ie $-1$ and$3\over 4$
Thus it will be represented after $-1$
$\frac{7}{4}=\frac{-4-3}{4}=\frac{-4}{4}-\frac{3}{4}=-1-\frac{3}{4}$
Question 151 Mark
Draw the numbers line and represent rational number$\frac{-5}{8}$on it.
View full question & answer→Question 161 Mark
Draw the number line and represent rational numbers $\frac{3}{4}$ on it:
Answer
View full question & answer→We can observe that the fraction represents $3$ parts out of $4.$
Thus, each space between two integers will be divided into four equal parts.
Hence,
$\frac{3}{4}$ can be represented on the number line as:
Thus, each space between two integers will be divided into four equal parts.
Hence,
$\frac{3}{4}$ can be represented on the number line as:
Question 171 Mark
Give four rational numbers equivalent to $\frac{4}{9}$.
Answer
View full question & answer→Four rational numbers equivalent to $\frac{4}{9}$are
$\frac{4 \times 2}{9 \times 2}=\frac{8}{18}$
$\frac{4 \times 3}{9 \times 3}=\frac{12}{27}$
$\frac{4 \times 4}{9 \times 4}=\frac{16}{36}$
$\frac{4 \times 5}{9 \times 5}=\frac{20}{45}$
Therefore, $\frac{8}{18}, \frac{12}{27}, \frac{16}{36}$and are four rational numbers equivalent to$\frac{4}{9}$
$\frac{4 \times 2}{9 \times 2}=\frac{8}{18}$
$\frac{4 \times 3}{9 \times 3}=\frac{12}{27}$
$\frac{4 \times 4}{9 \times 4}=\frac{16}{36}$
$\frac{4 \times 5}{9 \times 5}=\frac{20}{45}$
Therefore, $\frac{8}{18}, \frac{12}{27}, \frac{16}{36}$and are four rational numbers equivalent to$\frac{4}{9}$
Question 181 Mark
Give four rational numbers equivalent to $\frac{5}{-3}$
Answer
View full question & answer→Four rational numbers equivalent to $\frac{5}{-3}$are,
$\frac{5 \times 2}{-3 \times 2}=\frac{10}{-6} \quad \frac{5 \times 3}{-3 \times 3}=\frac{15}{-9}$
$\frac{5 \times 4}{-3 \times 4}=\frac{20}{-12}$and $\frac{5 \times 5}{-3 \times 5}=\frac{25}{-15}$
Therefore, $\frac{10}{-6} \frac{15}{-9} \frac{20}{-12}$ ,and $\frac{25}{-15}$are four rational numbers equivalent to $\frac{5}{-3}$
$\frac{5 \times 2}{-3 \times 2}=\frac{10}{-6} \quad \frac{5 \times 3}{-3 \times 3}=\frac{15}{-9}$
$\frac{5 \times 4}{-3 \times 4}=\frac{20}{-12}$and $\frac{5 \times 5}{-3 \times 5}=\frac{25}{-15}$
Therefore, $\frac{10}{-6} \frac{15}{-9} \frac{20}{-12}$ ,and $\frac{25}{-15}$are four rational numbers equivalent to $\frac{5}{-3}$
Question 191 Mark
Give four rational numbers equivalent to$\frac{-2}{7}$
Answer
View full question & answer→Four rational numbers equivalent to $\frac{-2}{7}$are
$\frac{-2 \times 2}{7 \times 2}=\frac{-4}{14}$, $\frac{-2 \times 3}{7 \times 3}=\frac{-6}{21}$
$\frac{-2 \times 4}{7 \times 4}=\frac{-8}{28}$and $\frac{-2 \times 5}{7 \times 5}=\frac{-10}{35}$
$\therefore$$\frac{-4}{14}, \frac{-6}{21}, \frac{-8}{28}$ and $\frac{-10}{35}$ are four rational numbers equivalent to $\frac{-2}{7}$
$\frac{-2 \times 2}{7 \times 2}=\frac{-4}{14}$, $\frac{-2 \times 3}{7 \times 3}=\frac{-6}{21}$
$\frac{-2 \times 4}{7 \times 4}=\frac{-8}{28}$and $\frac{-2 \times 5}{7 \times 5}=\frac{-10}{35}$
$\therefore$$\frac{-4}{14}, \frac{-6}{21}, \frac{-8}{28}$ and $\frac{-10}{35}$ are four rational numbers equivalent to $\frac{-2}{7}$
Question 201 Mark
Do $\frac{4}{-9}$ and $\frac{-16}{36}$ represent the same rational number?
Answer
View full question & answer→Yes, because $\frac{4}{-9}=\frac{4 \times(-4)}{9 \times(-4)}=\frac{-16}{36}$ or $\frac{-16}{36}=\frac{-16\div-4}{35 \div-4}=\frac{-4}{-9}$.
Question 211 Mark
Reduce to standard form: $\frac{-3}{-15}$
Answer
View full question & answer→The $HCF$ of $3$ and $15$ is $3.$
Hence, $\frac{-3}{-15}=\frac{-3 \div(-2)}{-15 \div(-3)}=\frac{1}{5}$
Hence, $\frac{-3}{-15}=\frac{-3 \div(-2)}{-15 \div(-3)}=\frac{1}{5}$
Question 221 Mark
Reduce to standard form: $\frac{36}{-24}$
Answer
View full question & answer→The $HCF$ of $36$ and $24$ is $12.$
Therefore, its standard form would be obtained by dividing by $–12.$
$\frac{36}{-24}=\frac{36 \div(-12)}{-24 \div(-12)}=\frac{-3}{2}$
Therefore, its standard form would be obtained by dividing by $–12.$
$\frac{36}{-24}=\frac{36 \div(-12)}{-24 \div(-12)}=\frac{-3}{2}$