MO MAP Grade 6 Ratios and Proportional Relationships. Practice it free.

Two gallons of water is $32$ cups. With a $4$ to $32$ ratio, $\dfrac{4}{32} = \dfrac{x}{32}$, so $x = 4$ cups of dye concentrate.

Multiply by the reciprocal: $\dfrac{5}{6} \times \dfrac{5}{3} = \dfrac{25}{18} = \dfrac{25}{18}$.

Use a conversion factor with quarts in the numerator so gallons cancel: $3 \text{ gal} \times \dfrac{4 \text{ qt}}{1 \text{ gal}} = 12 \text{ qt}$.

$0.2 = \dfrac{1}{5}$.

Convert $40\%$ to a decimal and multiply: $0.40 \times 320 = 128$ spaces.

Convert kilometers to meters, then meters to centimeters: $6 \text{ km} \times \dfrac{1{,}000 \text{ m}}{1 \text{ km}} \times \dfrac{100 \text{ cm}}{1 \text{ m}} = 600{,}000 \text{ cm}$.

Four gallons of water is $4 \times 16 = 64$ cups. With an $8$ to $64$ ratio, $\dfrac{8}{64} = \dfrac{x}{64}$, so $x = 8$ cups of antifreeze concentrate.

Multiply across: $\dfrac{3 \times 5}{6 \times 8} = \dfrac{15}{48} = \dfrac{5}{16}$.