Question

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Answer 1

Answer:

10. <

Explanation:

-3/7 _ -4/10

-0.428<-0.4

Answer 2

Explanation:

Questions :

9. Represent the following rational numbers on a number line:

$\dfrac{-3}{6}, \; \dfrac{-5}{6},\; \dfrac{5}{6},\;\dfrac{3}{6}$

10. Use >,< or = appropriately, using the property of cross products.

$\dfrac{-3}{7} \boxed {\;\;} \dfrac{-4}{10}$

11.Find 5 rational numbers between  $\dfrac{-5}{7} and \dfrac{-3}{8}$

Solution:

9.  (Figure Attached )

• Divide the portion into equal parts according to the denominator, and mark the point according to the numerator.

eg : In  $\dfrac{-3}{6}$, we simplify it to $\dfrac{-1}{2}$ . -1 >   $\dfrac{-1}{2}$ > 0 .  Here the denomiator = 2, Hence we divide the line between -1 and 0 into 2 equal parts. and mark the point 1 from zero.

• To mark a negative rational number, we mark it from right towards left.

• To mark a positive rational number, we mark it from left  towards right.

10. $\dfrac{-3}{7} \boxed {\;\;} \dfrac{-4}{10}$

To compare the following fractions, their denominators must be equal.

On taking LCM of 7 and 10 = 70

$\dfrac{-3\times 10}{7\times10}$ =  $\dfrac{-30}{70}$

$\dfrac{-4\times7 }{10\times7}$ = $\dfrac{-28}{70}$

Now comparing them,

$\dfrac{-30}{70} \boxed {\; <\;} \dfrac{-28}{70}$                since -28 > -30

∴ $\dfrac{-3}{7} \boxed {\;<\;} \dfrac{-4}{10}$

11. To find a rational number between the 2 fractions.

their denominators mus be equal.

LCM of 7 and 8 = 56

$\dfrac{-5\times8}{7\times8}$ = $\dfrac{-40}{56}$

$\dfrac{-3\times7}{8\times7}$ =  $\dfrac{-21}{56}$

Write 5 integers between -40 and -21 as the numerators .

Hence the rational numbers are  $\dfrac{-22}{56} ,\; \dfrac{-23}{56} , \; \dfrac{-30}{56}, \;\dfrac{-35}{56},\;\dfrac{-39}{56}$

Hence 5 rational numbers between $\dfrac{-5}{7} and \dfrac{-3}{8}$  are

$\dfrac{-11}{28} ,\; \dfrac{-23}{56} ,\;\dfrac{-15}{28} ,\;\dfrac{-5}{8} ,\;\dfrac{-39}{56}$