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Answer :
- Fill in the blanks.
(i) The additive inverse of [tex]0[/tex] is [tex]0[/tex].
The additive inverse of a number is what you add to it to get zero. Since [tex]0 + 0 = 0[/tex], the additive inverse of [tex]0[/tex] is [tex]0[/tex] itself.
(ii) The reciprocal of [tex]\frac{8}{19}[/tex] is [tex]\frac{19}{8}[/tex].
The reciprocal of a fraction is obtained by swapping the numerator and the denominator. So, the reciprocal of [tex]\frac{8}{19}[/tex] is [tex]\frac{19}{8}[/tex].
(iii) [tex]0 - \frac{48}{29} = -\frac{48}{29}[/tex].
Subtracting a positive number from zero will result in the negative of that number.
(iv) [tex]\frac{1}{3} \times \frac{1}{4} \times \frac{1}{5} = \frac{1}{60}[/tex].
To multiply fractions, multiply the numerators together and the denominators together. The numerators will be [tex]1 \times 1 \times 1 = 1[/tex] and the denominators will be [tex]3 \times 4 \times 5 = 60[/tex], so the result is [tex]\frac{1}{60}[/tex].
(v) Among [tex]\frac{6}{11}, -\frac{6}{13}[/tex] and [tex]-\frac{6}{7}[/tex], the greatest rational number is [tex]\frac{6}{11}[/tex].
To find the greatest rational number, compare their values. Positive fractions are always greater than negative fractions, so [tex]\frac{6}{11}[/tex] is the greatest.
- Answer True (T) or False (F).
(i) [tex]-\frac{8}{0}[/tex] is a negative rational number. False.
Division by zero is undefined, so [tex]-\frac{8}{0}[/tex] is not a rational number.
(ii) The operation of subtraction is not closed for rational numbers. False.
The set of rational numbers is closed under subtraction, meaning if you subtract any two rational numbers, the result is also a rational number.
(iii) [tex]\frac{1}{16}[/tex] is a rational number between [tex]-\frac{1}{4}[/tex] and [tex]\frac{1}{8}[/tex]. False.
[tex]\frac{1}{16}[/tex] is smaller than [tex]\frac{1}{8}[/tex] but greater than 0, while [tex]-\frac{1}{4}[/tex] is negative, so [tex]\frac{1}{16}[/tex] is not between [tex]-\frac{1}{4}[/tex] and [tex]\frac{1}{8}[/tex].
(iv) [tex]1 + \frac{1}{4} = -\frac{1}{4}[/tex]. False.
Adding [tex]1[/tex] to [tex]\frac{1}{4}[/tex] gives [tex]\frac{5}{4}[/tex], which is not equal to [tex]-\frac{1}{4}[/tex].
(v) [tex]x + (y + z) = x + y + x + z[/tex]. False.
The expression on the right should be [tex](x + y) + z[/tex] to be equivalent. The initial statement suggests adding [tex]x[/tex] twice, which is incorrect.
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