3 Marks Question

Question 13 Marks

Which is greater in $\frac{-1}{4}, \frac{1}{4}$

Answer

Since the denominators are the same comparing the numerators
$1 > -1$
Thus,$\frac{1}{4}>-\frac{1}{4}$

Question 23 Marks

Which is greater in $\frac{2}{3}, \frac{5}{2}$

Answer

We need to make the denominators of $3\ \&\ 2$ to common denominators. Thus we find the $LCM$ of $2\ \& \ 3$
$\frac{2}{3}=\frac{2 \times 2}{3 \times 2}=\frac{4}{6} . . . [LCM (3, 2) = 6]$
$\frac{5}{2}=\frac{5 \times 3}{2 \times 3}=\frac{15}{6}$
$\because$$\frac{15}{6}>\frac{4}{6}$ $\therefore$ $\frac{5}{2}>\frac{2}{3}$
Or
$2\over 3$ and $5\over 2$
cross multiplying the numerators we have
$2\times2$ and $5\times3$
$4$ and $15$
$\because 4< 15$
$\therefore$ $2\over 3$<$5\over 2$

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Question 33 Marks

Is the pair represent the same rational number $\frac{-5}{-9} \text { and } \frac{5}{-9}$?

Answer

We have, $\frac{-5}{-9} \text { and } \frac{5}{-9}$
Now,
We have to check if the two given are the same rational number.
Thus,
$\frac{-5}{-9} = \frac{5}{9}$
And,
$\frac{5}{-9}=-\frac{5}{9}$
Clearly,
We can see that,
$\frac{5}{9} \neq-\frac{5}{9}$
Hence, It does not represent the same rational number pair.

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Question 43 Marks

List five rational numbers between $–2$ and $–1.$

Answer

We need to make the whole numbers as a rational number by multiplying and dividing the numerator and the denominator with the same number
Thus, We have,
$-2 = -\frac{2}{1}=\frac{-2 \times 10}{1 \times 10}=-\frac{20}{10}$
$- 1 = -\frac{1}{1}=\frac{-1 \times 10}{1 \times 10}=\frac{-10}{10}$
So, $-\frac{20}{10}<-\frac{19}{10}<-\frac{18}{10}<-\frac{17}{10}<-\frac{16}{10}<-\frac{15}{10}<-\frac{10}{10}$
or $- 2 <-\frac{19}{10}<-\frac{18}{10}<-\frac{17}{10}<-\frac{16}{10}<-\frac{15}{10}<-1$
$\therefore$ five rational numbers between $–2$ and $–1$ are
$-\frac{19}{10},-\frac{18}{10},-\frac{17}{10},-\frac{16}{10}$ and $-\frac{15}{10}$

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