Looking for answers? Westonci.ca is your go-to Q&A platform, offering quick, trustworthy responses from a community of experts. Experience the convenience of finding accurate answers to your questions from knowledgeable professionals on our platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.
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]
Thank you for choosing our service. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.
