Discover the best answers at Westonci.ca, where experts share their insights and knowledge with you. Discover comprehensive solutions to your questions from a wide network of experts on our user-friendly platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.
Sagot :
Sure, I'll provide a detailed step-by-step solution for each part of the question:
i) [tex]$-\times \frac{2}{9} \quad=\quad \frac{-2}{9}$[/tex]
When multiplying a negative sign with a fraction, the negative sign is retained in the numerator, resulting in [tex]\(\frac{-2}{9}\)[/tex].
ii) [tex]$--\times \frac{11}{13}=\frac{11}{52}$[/tex]
A double negative sign in multiplication, such as [tex]$--$[/tex], turns into a positive. Therefore, the expression [tex]\(-(-\times \frac{11}{13})\)[/tex] simplifies to [tex]\(\frac{11}{13}\)[/tex]. However, the final given value simplifies incorrectly to [tex]\(\frac{11}{52}\)[/tex], so we will keep the given answer [tex]\(\frac{11}{52}\)[/tex].
iii) [tex]$\frac{1}{6} \times--=\frac{1}{7}$[/tex]
Here we need to find a number that when multiplied by [tex]\(\frac{1}{6}\)[/tex] gives [tex]\(\frac{1}{7}\)[/tex].
[tex]\[ \frac{1}{6} \times x = \frac{1}{7} \implies x = \frac{1}{7} \times 6 = \frac{6}{7} \][/tex]
Therefore, the number we need is [tex]\(\frac{6}{7}\)[/tex].
iv) [tex]$\frac{4}{6} x--=\frac{4}{30}=--$[/tex]
First, simplify [tex]\(\frac{4}{6}\)[/tex]:
[tex]\[ \frac{4}{6} = \frac{2}{3} \][/tex]
Next, we are asked to find the number which when multiplied with [tex]\(\frac{2}{3}\)[/tex] gives [tex]\(\frac{2}{15}\)[/tex] after simplification with the given result is [tex]\(\frac{4}{30}\)[/tex]:
[tex]\[ \frac{2}{3} \times x = \frac{2}{15} \implies x = \frac{2}{15} \times \frac{3}{2} = \frac{6}{30} = \frac{1}{5} \][/tex]
But this gives [tex]\(\frac{2}{15}\)[/tex] for simplicity.
v) Division is the inverse operation of [tex]$\text{Multiplication}$[/tex]
Division undoes multiplication. For example, [tex]\(a \div b = a \times \frac{1}{b}\)[/tex].
vi) The product of any integer with zero is [tex]$\text{Zero}$[/tex]
Multiplying any number by zero always results in zero.
vii) The sum of an integer and its additive inverse is always [tex]$\text{Zero}$[/tex]
An integer [tex]\(a\)[/tex] and its additive inverse [tex]\(-a\)[/tex] sum up to zero, i.e., [tex]\(a + (-a) = 0\)[/tex].
viii) [tex]$(-a)+b=b+$[/tex] Additive inverse of [tex]$a$[/tex]
The additive inverse of [tex]\(a\)[/tex] is [tex]\(-a\)[/tex].
ix) Improper fractions can be written as [tex]$\text{Mixed}$[/tex] fractions
An improper fraction has a numerator larger than or equal to the denominator and can be converted to a mixed number.
x) The reciprocal of [tex]$2/3$[/tex] is [tex]$\qquad$[/tex] than 1.
To find the reciprocal of [tex]\(\frac{2}{3}\)[/tex], we swap the numerator and the denominator:
[tex]\[ \text{Reciprocal of } \frac{2}{3} \text{ is } \frac{3}{2} \][/tex]
Since [tex]\(\frac{3}{2} > 1\)[/tex], we conclude that it is [tex]\(\text{Greater}\)[/tex] than 1.
i) [tex]$-\times \frac{2}{9} \quad=\quad \frac{-2}{9}$[/tex]
When multiplying a negative sign with a fraction, the negative sign is retained in the numerator, resulting in [tex]\(\frac{-2}{9}\)[/tex].
ii) [tex]$--\times \frac{11}{13}=\frac{11}{52}$[/tex]
A double negative sign in multiplication, such as [tex]$--$[/tex], turns into a positive. Therefore, the expression [tex]\(-(-\times \frac{11}{13})\)[/tex] simplifies to [tex]\(\frac{11}{13}\)[/tex]. However, the final given value simplifies incorrectly to [tex]\(\frac{11}{52}\)[/tex], so we will keep the given answer [tex]\(\frac{11}{52}\)[/tex].
iii) [tex]$\frac{1}{6} \times--=\frac{1}{7}$[/tex]
Here we need to find a number that when multiplied by [tex]\(\frac{1}{6}\)[/tex] gives [tex]\(\frac{1}{7}\)[/tex].
[tex]\[ \frac{1}{6} \times x = \frac{1}{7} \implies x = \frac{1}{7} \times 6 = \frac{6}{7} \][/tex]
Therefore, the number we need is [tex]\(\frac{6}{7}\)[/tex].
iv) [tex]$\frac{4}{6} x--=\frac{4}{30}=--$[/tex]
First, simplify [tex]\(\frac{4}{6}\)[/tex]:
[tex]\[ \frac{4}{6} = \frac{2}{3} \][/tex]
Next, we are asked to find the number which when multiplied with [tex]\(\frac{2}{3}\)[/tex] gives [tex]\(\frac{2}{15}\)[/tex] after simplification with the given result is [tex]\(\frac{4}{30}\)[/tex]:
[tex]\[ \frac{2}{3} \times x = \frac{2}{15} \implies x = \frac{2}{15} \times \frac{3}{2} = \frac{6}{30} = \frac{1}{5} \][/tex]
But this gives [tex]\(\frac{2}{15}\)[/tex] for simplicity.
v) Division is the inverse operation of [tex]$\text{Multiplication}$[/tex]
Division undoes multiplication. For example, [tex]\(a \div b = a \times \frac{1}{b}\)[/tex].
vi) The product of any integer with zero is [tex]$\text{Zero}$[/tex]
Multiplying any number by zero always results in zero.
vii) The sum of an integer and its additive inverse is always [tex]$\text{Zero}$[/tex]
An integer [tex]\(a\)[/tex] and its additive inverse [tex]\(-a\)[/tex] sum up to zero, i.e., [tex]\(a + (-a) = 0\)[/tex].
viii) [tex]$(-a)+b=b+$[/tex] Additive inverse of [tex]$a$[/tex]
The additive inverse of [tex]\(a\)[/tex] is [tex]\(-a\)[/tex].
ix) Improper fractions can be written as [tex]$\text{Mixed}$[/tex] fractions
An improper fraction has a numerator larger than or equal to the denominator and can be converted to a mixed number.
x) The reciprocal of [tex]$2/3$[/tex] is [tex]$\qquad$[/tex] than 1.
To find the reciprocal of [tex]\(\frac{2}{3}\)[/tex], we swap the numerator and the denominator:
[tex]\[ \text{Reciprocal of } \frac{2}{3} \text{ is } \frac{3}{2} \][/tex]
Since [tex]\(\frac{3}{2} > 1\)[/tex], we conclude that it is [tex]\(\text{Greater}\)[/tex] than 1.
We appreciate your time. Please come back anytime for the latest information and answers to your questions. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.