Let's solve each of the equations step-by-step.
### a. [tex]\( 7 \cdot 5 = 35 \)[/tex]
This is a given multiplication sentence. Confirming the operation:
[tex]\[ 7 \cdot 5 = 35 \][/tex]
[tex]\[
35 = 35
\][/tex]
This confirms the equality.
### b. [tex]\( (-3) \cdot \square = -24 \)[/tex]
We need to solve for the unknown value:
[tex]\[ (-3) \cdot x = -24 \][/tex]
To find [tex]\( x \)[/tex], divide both sides of the equation by [tex]\(-3\)[/tex]:
[tex]\[
x = \frac{-24}{-3} = 8
\][/tex]
### c. [tex]\( 9 \cdot \square = -540 \)[/tex]
We need to solve for the unknown value:
[tex]\[ 9 \cdot x = -540 \][/tex]
To find [tex]\( x \)[/tex], divide both sides of the equation by 9:
[tex]\[
x = \frac{-540}{9} = -60
\][/tex]
### d. [tex]\( \square \cdot (-15) = 0 \)[/tex]
We need to solve for the unknown value:
[tex]\[ x \cdot (-15) = 0 \][/tex]
To find [tex]\( x \)[/tex], divide both sides of the equation by [tex]\(-15\)[/tex]:
[tex]\[
x = \frac{0}{-15} = 0
\][/tex]
### e. [tex]\( \square \cdot 25 = -100 \)[/tex]
We need to solve for the unknown value:
[tex]\[ x \cdot 25 = -100 \][/tex]
To find [tex]\( x \)[/tex], divide both sides of the equation by 25:
[tex]\[
x = \frac{-100}{25} = -4
\][/tex]
### f. [tex]\( \square \cdot 200 = -400 \)[/tex]
We need to solve for the unknown value:
[tex]\[ x \cdot 200 = -400 \][/tex]
To find [tex]\( x \)[/tex], divide both sides of the equation by 200:
[tex]\[
x = \frac{-400}{200} = -2
\][/tex]
### g. [tex]\( 12 \cdot \square = 12 \)[/tex]
We need to solve for the unknown value:
[tex]\[ 12 \cdot x = 12 \][/tex]
To find [tex]\( x \)[/tex], divide both sides of the equation by 12:
[tex]\[
x = \frac{12}{12} = 1
\][/tex]
### i. [tex]\( 9 \cdot \square = -72 \)[/tex]
We need to solve for the unknown value:
[tex]\[ 9 \cdot x = -72 \][/tex]
To find [tex]\( x \)[/tex], divide both sides of the equation by 9:
[tex]\[
x = \frac{-72}{9} = -8
\][/tex]
### h. [tex]\( (-17) \cdot \square = -51 \)[/tex]
We need to solve for the unknown value:
[tex]\[ (-17) \cdot x = -51 \][/tex]
To find [tex]\( x \)[/tex], divide both sides of the equation by [tex]\(-17\)[/tex]:
[tex]\[
x = \frac{-51}{-17} = 3
\][/tex]
### j. [tex]\( \square \cdot (-35) = 140 \)[/tex]
We need to solve for the unknown value:
[tex]\[ x \cdot (-35) = 140 \][/tex]
To find [tex]\( x \)[/tex], divide both sides of the equation by [tex]\(-35\)[/tex]:
[tex]\[
x = \frac{140}{-35} = -4
\][/tex]
Here are the results in a summarized form:
- b: [tex]\( x = 8 \)[/tex]
- c: [tex]\( x = -60 \)[/tex]
- d: [tex]\( x = 0 \)[/tex]
- e: [tex]\( x = -4 \)[/tex]
- f: [tex]\( x = -2 \)[/tex]
- g: [tex]\( x = 1 \)[/tex]
- i: [tex]\( x = -8 \)[/tex]
- h: [tex]\( x = 3 \)[/tex]
- j: [tex]\( x = -4 \)[/tex]
