Write three rational numbers that lie between the two given numbers- 1 27-67 2 45-23 3 -23-45 4 79- -59 5 -34-54 6 78-53 7 57-117 8 0-34

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Standard IX

Mathematics

Rational Numbers

Write three r...

Question

Write three rational numbers that lie between the two given numbers:
$(1) \frac{2}{7}, \frac{6}{7}$

$(2) \frac{4}{5}, \frac{2}{3}$

$(3) - \frac{2}{3}, \frac{4}{5}$

$(4) \frac{7}{9}, - \frac{5}{9}$

$(5) \frac{- 3}{4}, \frac{+ 5}{4}$

$(6) \frac{7}{8}, \frac{- 5}{3}$

$(7) \frac{5}{7}, \frac{11}{7}$

$(8) 0, \frac{- 3}{4}$

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$Name the multiplication property of rational numbers shown below: (i) \frac{3}{5} \times \frac{- 8}{9} = \frac{- 8}{9} \times \frac{3}{5} (i i) \frac{- 3}{4} \times (\frac{5}{7} \times \frac{- 8}{15}) = (\frac{- 3}{5} \times \frac{5}{7}) \times \frac{- 8}{15} (i i i) \frac{4}{5} \times (\frac{3}{- 8} + \frac{- 4}{7}) = \frac{4}{5} \times \frac{3}{- 8} + \frac{4}{5} \times \frac{- 4}{7} (i v) \frac{- 7}{5} \times \frac{5}{- 7} = 1 (v) \frac{8}{- 9} \times 1 = 1 \times \frac{8}{- 9} = \frac{8}{- 9} (v i) \frac{- 3}{4} \times 0 = 0$

Write the following rational numbers in ascending order:

(i) (ii) (iii)

Using commutativity and associativity of addition of rational numbers, express each of the following as a rational number:

(i) $\frac{2}{5} + \frac{7}{3} + \frac{- 4}{5} + \frac{- 1}{3}$

(ii) $\frac{3}{7} + \frac{- 4}{9} + \frac{- 11}{7} + \frac{7}{9}$

(iii) $\frac{2}{5} + \frac{8}{3} + \frac{- 11}{15} + \frac{4}{5} + \frac{- 2}{3}$

(iv) $\frac{4}{7} + 0 + \frac{- 8}{9} + \frac{- 13}{7} + \frac{17}{21}$

Fill in the blanks:

$(i) - 4 \times \frac{7}{9} = \frac{7}{9} \times$ ___

$(i i) \frac{5}{11} \times \frac{- 3}{8} = \frac{- 3}{8} \times$ ___

$(i i i) \frac{1}{2} \times (\frac{3}{4} + \frac{- 5}{12}) = \frac{1}{2} \times$ ____ $+ (\times) \frac{- 5}{12}$

$(i v) \frac{- 4}{5} \times \frac{5}{7} \times$ ___ $= (\frac{- 4}{5} \times \frac{5}{7}) \times \frac{- 8}{9}$

Q. Study the following number line and answer the questions that follow.
2 5 9 1 7 2 5 1 9 7 3 9 5 2 4 6 8 1 9 7 5 2 7 3 1 9 7 8 5 2 6 5 4 1 9 7 8 2 0 1 0 9 7 8 5 1 9 7 3 5 1 6 9 7 2 1 7 3 7 9 5 1

How many times is number '3' preceded by number '7' and not followed by an even number?

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Write three rational numbers that lie between the two given numbers:(1)27,67(2)45,23(3)−23,45(4)79,−59(5)−34,+54(6)78,−53(7)57,117(8)0,−34