Question: What are the values for $A$ and $B$?
top-left: a peach hexagon labeled $24$ above a lavender triangle labeled $2$; the math relation is $24 = 2 \times 12$.
top-center-left: a pink hexagon labeled $48$ above a green triangle labeled $4$; the math relation is $48 = 4 \times 12$.
top-center-right: a yellow-green hexagon labeled $84$ above a blue triangle labeled $A$; the math relation is $84 = A \times 12$.
top-right: a red hexagon labeled $72$ above a light-green triangle labeled $B$; the math relation is $72 = B \times 12$.
1. **State the problem:** We need to find the values of $A$ and $B$ given the equations:
$$ 84 = A \times 12 $$
$$ 72 = B \times 12 $$
2. **Formula used:** To find $A$ or $B$, divide both sides of the equation by $12$:
$$ A = \frac{84}{12} $$
$$ B = \frac{72}{12} $$
3. **Important rule:** When dividing both sides of an equation by the same nonzero number, the equality remains true.
4. **Calculate $A$:**
$$ A = \frac{84}{12} $$
Simplify by canceling common factors:
$$ A = \frac{\cancel{12} \times 7}{\cancel{12}} = 7 $$
5. **Calculate $B$:**
$$ B = \frac{72}{12} $$
Simplify by canceling common factors:
$$ B = \frac{\cancel{12} \times 6}{\cancel{12}} = 6 $$
6. **Final answer:**
$A = 7$
$B = 6$