Let's solve both parts of the question step-by-step.
a) By what integer should [tex]\((-4)\)[/tex] be multiplied to get the product [tex]\((+20)\)[/tex]?
1. We are given that we need to find an integer, say [tex]\( x \)[/tex], such that [tex]\((-4) \times x = +20\)[/tex].
2. To isolate [tex]\( x \)[/tex], we divide both sides of the equation by [tex]\(-4\)[/tex].
[tex]\[
x = \frac{20}{-4}
\][/tex]
3. Simplifying the right-hand side, we get:
[tex]\[
x = -5
\][/tex]
So, [tex]\((-4)\)[/tex] should be multiplied by [tex]\(-5\)[/tex] to get the product [tex]\(+20\)[/tex].
b) By what integer should [tex]\((+7)\)[/tex] be multiplied to get the product [tex]\((-28)\)[/tex]?
1. We are given that we need to find an integer, say [tex]\( y \)[/tex], such that [tex]\( 7 \times y = -28 \)[/tex].
2. To isolate [tex]\( y \)[/tex], we divide both sides of the equation by [tex]\( 7 \)[/tex].
[tex]\[
y = \frac{-28}{7}
\][/tex]
3. Simplifying the right-hand side, we get:
[tex]\[
y = -4
\][/tex]
So, [tex]\(+7\)[/tex] should be multiplied by [tex]\(-4\)[/tex] to get the product [tex]\(-28\)[/tex].
Thus, the answers are:
a) [tex]\((-4)\)[/tex] should be multiplied by [tex]\(-5\)[/tex] to get [tex]\(+20\)[/tex].
b) [tex]\(+7\)[/tex] should be multiplied by [tex]\(-4\)[/tex] to get [tex]\(-28\)[/tex].
