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Sagot :
Certainly! Let's go through each question step-by-step:
6. Find the square of 32:
To square the number 32, you multiply 32 by itself.
[tex]\[ 32 \times 32 = 1024 \][/tex]
Therefore, the square of 32 is 1024.
7. Represent [tex]\(\frac{2}{7}\)[/tex] on the number line:
To represent the fraction [tex]\(\frac{2}{7}\)[/tex] on the number line, we first understand that this fraction is between 0 and 1. Divide the interval from 0 to 1 into 7 equal parts. Each part corresponds to a [tex]\(\frac{1}{7}\)[/tex]. The fraction [tex]\(\frac{2}{7}\)[/tex] would be located at the second mark after 0 on this interval.
Numerically, [tex]\(\frac{2}{7} \approx 0.2857142857142857\)[/tex], which helps us pinpoint the location on the number line.
8. Write Multiplicative inverse of 0:
The multiplicative inverse of a number [tex]\(a\)[/tex] is a number [tex]\(b\)[/tex] such that [tex]\(a \times b = 1\)[/tex]. However, for zero, there is no number [tex]\(b\)[/tex] such that [tex]\(0 \times b = 1\)[/tex]. Therefore, the multiplicative inverse of 0 does not exist.
9. The product of a number and its reciprocal:
The reciprocal of a number [tex]\(a\)[/tex] (assuming [tex]\(a \neq 0\)[/tex]) is [tex]\(\frac{1}{a}\)[/tex]. The product of [tex]\(a\)[/tex] and its reciprocal is:
[tex]\[ a \times \frac{1}{a} = 1 \][/tex]
So, the product of a number and its reciprocal is always 1.
10. Write in ascending and descending order:
We are given the fractions [tex]\(\frac{4}{5}, \frac{3}{7}, \frac{-1}{5}, \frac{2}{3}, \frac{5}{7}\)[/tex].
Let's first convert these to their decimal equivalents:
[tex]\[ \frac{4}{5} = 0.8, \quad \frac{3}{7} \approx 0.42857142857142855, \quad \frac{-1}{5} = -0.2, \quad \frac{2}{3} \approx 0.6666666666666666, \quad \frac{5}{7} \approx 0.7142857142857143 \][/tex]
Now we can sort these decimals in ascending order:
[tex]\[ -0.2, 0.42857142857142855, 0.6666666666666666, 0.7142857142857143, 0.8 \][/tex]
And in descending order:
[tex]\[ 0.8, 0.7142857142857143, 0.6666666666666666, 0.42857142857142855, -0.2 \][/tex]
Thus, the fractions in ascending order are:
[tex]\[ \frac{-1}{5}, \frac{3}{7}, \frac{2}{3}, \frac{5}{7}, \frac{4}{5} \][/tex]
And the fractions in descending order are:
[tex]\[ \frac{4}{5}, \frac{5}{7}, \frac{2}{3}, \frac{3}{7}, \frac{-1}{5} \][/tex]
Hope this helps! Let me know if you have any questions.
6. Find the square of 32:
To square the number 32, you multiply 32 by itself.
[tex]\[ 32 \times 32 = 1024 \][/tex]
Therefore, the square of 32 is 1024.
7. Represent [tex]\(\frac{2}{7}\)[/tex] on the number line:
To represent the fraction [tex]\(\frac{2}{7}\)[/tex] on the number line, we first understand that this fraction is between 0 and 1. Divide the interval from 0 to 1 into 7 equal parts. Each part corresponds to a [tex]\(\frac{1}{7}\)[/tex]. The fraction [tex]\(\frac{2}{7}\)[/tex] would be located at the second mark after 0 on this interval.
Numerically, [tex]\(\frac{2}{7} \approx 0.2857142857142857\)[/tex], which helps us pinpoint the location on the number line.
8. Write Multiplicative inverse of 0:
The multiplicative inverse of a number [tex]\(a\)[/tex] is a number [tex]\(b\)[/tex] such that [tex]\(a \times b = 1\)[/tex]. However, for zero, there is no number [tex]\(b\)[/tex] such that [tex]\(0 \times b = 1\)[/tex]. Therefore, the multiplicative inverse of 0 does not exist.
9. The product of a number and its reciprocal:
The reciprocal of a number [tex]\(a\)[/tex] (assuming [tex]\(a \neq 0\)[/tex]) is [tex]\(\frac{1}{a}\)[/tex]. The product of [tex]\(a\)[/tex] and its reciprocal is:
[tex]\[ a \times \frac{1}{a} = 1 \][/tex]
So, the product of a number and its reciprocal is always 1.
10. Write in ascending and descending order:
We are given the fractions [tex]\(\frac{4}{5}, \frac{3}{7}, \frac{-1}{5}, \frac{2}{3}, \frac{5}{7}\)[/tex].
Let's first convert these to their decimal equivalents:
[tex]\[ \frac{4}{5} = 0.8, \quad \frac{3}{7} \approx 0.42857142857142855, \quad \frac{-1}{5} = -0.2, \quad \frac{2}{3} \approx 0.6666666666666666, \quad \frac{5}{7} \approx 0.7142857142857143 \][/tex]
Now we can sort these decimals in ascending order:
[tex]\[ -0.2, 0.42857142857142855, 0.6666666666666666, 0.7142857142857143, 0.8 \][/tex]
And in descending order:
[tex]\[ 0.8, 0.7142857142857143, 0.6666666666666666, 0.42857142857142855, -0.2 \][/tex]
Thus, the fractions in ascending order are:
[tex]\[ \frac{-1}{5}, \frac{3}{7}, \frac{2}{3}, \frac{5}{7}, \frac{4}{5} \][/tex]
And the fractions in descending order are:
[tex]\[ \frac{4}{5}, \frac{5}{7}, \frac{2}{3}, \frac{3}{7}, \frac{-1}{5} \][/tex]
Hope this helps! Let me know if you have any questions.
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