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Sagot :
Let's walk through each part of the question step-by-step:
### Section-13
Question 6: Multiply the negative of [tex]\( \frac{2}{3} \)[/tex] by the inverse of [tex]\( \frac{9}{7} \)[/tex]:
- Take the negative of [tex]\( \frac{2}{3} \)[/tex], which is [tex]\( -\frac{2}{3} \)[/tex].
- The inverse of [tex]\( \frac{9}{7} \)[/tex] is [tex]\( \frac{7}{9} \)[/tex].
- Multiplying these two together, we get:
[tex]\[ -\frac{2}{3} \times \frac{7}{9} \approx -0.5185 \][/tex]
Question 7: Write [tex]\( \frac{2}{3}, -\frac{4}{9}, -\frac{8}{11} \)[/tex] in ascending order:
- Convert the fractions to decimals for easier comparison:
- [tex]\( \frac{2}{3} \approx 0.6667 \)[/tex]
- [tex]\( -\frac{4}{9} \approx -0.4444 \)[/tex]
- [tex]\( -\frac{8}{11} \approx -0.7273 \)[/tex]
- Arranging them in ascending order:
[tex]\[ -\frac{8}{11}, -\frac{4}{9}, \frac{2}{3} \][/tex]
Or in decimal form: [tex]\(-0.7273, -0.4444, 0.6667\)[/tex]
### Section-C
Question 8: Write:
(i) A rational number which has no reciprocal:
- The rational number which has no reciprocal is [tex]\( 0 \)[/tex].
(ii) A rational number whose product with a given rational number:
- If we consider the given rational number as [tex]\( 5 \)[/tex], a rational number which gives the same number when multiplied is [tex]\( 1 \)[/tex].
(iii) A rational number which is equal to its reciprocal:
- A rational number that is equal to its reciprocal is [tex]\( 1 \)[/tex].
### Section-D
Question 9:
(i) Find three rational numbers between [tex]\( \frac{3}{7} \)[/tex] and [tex]\( \frac{2}{3} \)[/tex]:
- The midpoint between [tex]\( \frac{3}{7} \)[/tex] and [tex]\( \frac{2}{3} \)[/tex]:
[tex]\[ \text{midpoint} = \frac{\frac{3}{7} + \frac{2}{3}}{2} \approx 0.5476 \][/tex]
- Another point between [tex]\( \frac{3}{7} \)[/tex] and [tex]\( 0.5476 \)[/tex]:
[tex]\[ \text{new midpoint} = \frac{\frac{3}{7} + 0.5476}{2} \approx 0.4881 \][/tex]
- Another point between [tex]\( 0.5476 \)[/tex] and [tex]\( \frac{2}{3} \)[/tex]:
[tex]\[ \text{new midpoint} = \frac{0.5476 + \frac{2}{3}}{2} \approx 0.6071 \][/tex]
- The three rational numbers between [tex]\( \frac{3}{7} \)[/tex] and [tex]\( \frac{2}{3} \)[/tex] are:
[tex]\[ 0.5476, 0.4881, 0.6071 \][/tex]
(ii) Find [tex]\( \frac{3}{7} + (-\frac{6}{11}) + (-\frac{8}{21}) + (\frac{5}{22}) \)[/tex]:
- Sum of the fractions:
[tex]\[ \frac{3}{7} + (-\frac{6}{11}) + (-\frac{8}{21}) + \frac{5}{22} \approx -0.2706 \][/tex]
### Section-13
Question 6: Multiply the negative of [tex]\( \frac{2}{3} \)[/tex] by the inverse of [tex]\( \frac{9}{7} \)[/tex]:
- Take the negative of [tex]\( \frac{2}{3} \)[/tex], which is [tex]\( -\frac{2}{3} \)[/tex].
- The inverse of [tex]\( \frac{9}{7} \)[/tex] is [tex]\( \frac{7}{9} \)[/tex].
- Multiplying these two together, we get:
[tex]\[ -\frac{2}{3} \times \frac{7}{9} \approx -0.5185 \][/tex]
Question 7: Write [tex]\( \frac{2}{3}, -\frac{4}{9}, -\frac{8}{11} \)[/tex] in ascending order:
- Convert the fractions to decimals for easier comparison:
- [tex]\( \frac{2}{3} \approx 0.6667 \)[/tex]
- [tex]\( -\frac{4}{9} \approx -0.4444 \)[/tex]
- [tex]\( -\frac{8}{11} \approx -0.7273 \)[/tex]
- Arranging them in ascending order:
[tex]\[ -\frac{8}{11}, -\frac{4}{9}, \frac{2}{3} \][/tex]
Or in decimal form: [tex]\(-0.7273, -0.4444, 0.6667\)[/tex]
### Section-C
Question 8: Write:
(i) A rational number which has no reciprocal:
- The rational number which has no reciprocal is [tex]\( 0 \)[/tex].
(ii) A rational number whose product with a given rational number:
- If we consider the given rational number as [tex]\( 5 \)[/tex], a rational number which gives the same number when multiplied is [tex]\( 1 \)[/tex].
(iii) A rational number which is equal to its reciprocal:
- A rational number that is equal to its reciprocal is [tex]\( 1 \)[/tex].
### Section-D
Question 9:
(i) Find three rational numbers between [tex]\( \frac{3}{7} \)[/tex] and [tex]\( \frac{2}{3} \)[/tex]:
- The midpoint between [tex]\( \frac{3}{7} \)[/tex] and [tex]\( \frac{2}{3} \)[/tex]:
[tex]\[ \text{midpoint} = \frac{\frac{3}{7} + \frac{2}{3}}{2} \approx 0.5476 \][/tex]
- Another point between [tex]\( \frac{3}{7} \)[/tex] and [tex]\( 0.5476 \)[/tex]:
[tex]\[ \text{new midpoint} = \frac{\frac{3}{7} + 0.5476}{2} \approx 0.4881 \][/tex]
- Another point between [tex]\( 0.5476 \)[/tex] and [tex]\( \frac{2}{3} \)[/tex]:
[tex]\[ \text{new midpoint} = \frac{0.5476 + \frac{2}{3}}{2} \approx 0.6071 \][/tex]
- The three rational numbers between [tex]\( \frac{3}{7} \)[/tex] and [tex]\( \frac{2}{3} \)[/tex] are:
[tex]\[ 0.5476, 0.4881, 0.6071 \][/tex]
(ii) Find [tex]\( \frac{3}{7} + (-\frac{6}{11}) + (-\frac{8}{21}) + (\frac{5}{22}) \)[/tex]:
- Sum of the fractions:
[tex]\[ \frac{3}{7} + (-\frac{6}{11}) + (-\frac{8}{21}) + \frac{5}{22} \approx -0.2706 \][/tex]
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