Question

given a real - world context, write ratios to show the relative sizes of two quantities using appropriate notation: (\frac{a}{b}), (a) to (b), or (a:b) where (b
eq0); writing part - to - whole ratios where quantities have the same units (l3) ar.3.1
21
an animal shelter is caring for 250 animals. 95 of them are dogs, the rest are cats. write a ratio comparing the number of cats to the total number of animals.
write 3 more possible ways to write this ratio. (think about simplest form)
a semi truck is transporting 350 crates of fruit. 150 of the crates are apples, the rest are plums. write a ratio of the number of crates of plums to the total crates of fruit being transported.
write 3 more possible ways to write this ratio. (think about simplest form)

Explanation:

Step1: Solve for Animal Shelter Problem

First, find the number of cats. Total animals = 250, dogs = 95. So cats = 250 - 95 = 155.
Ratio of cats to total animals: $\frac{155}{250}$. Simplify by dividing numerator and denominator by 5: $\frac{31}{50}$.
Other equivalent ratios: Multiply numerator and denominator by 2: $\frac{62}{100}$; by 3: $\frac{93}{150}$; by 4: $\frac{124}{200}$.

Step2: Solve for Semi Truck Problem

Total crates = 350, apples = 150. So plums = 350 - 150 = 200.
Ratio of plums to total crates: $\frac{200}{350}$. Simplify by dividing by 50: $\frac{4}{7}$.
Other equivalent ratios: Multiply numerator and denominator by 2: $\frac{8}{14}$; by 3: $\frac{12}{21}$; by 4: $\frac{16}{28}$.

Answer:

Animal Shelter (Cats to Total Animals):

• Simplest ratio: $\frac{31}{50}$ (or 31:50, 31 to 50)
• Additional ratios: $\frac{62}{100}$, $\frac{93}{150}$, $\frac{124}{200}$ (or 62:100, 93:150, 124:200; or 62 to 100, 93 to 150, 124 to 200)

Semi Truck (Plums to Total Crates):

• Simplest ratio: $\frac{4}{7}$ (or 4:7, 4 to 7)
• Additional ratios: $\frac{8}{14}$, $\frac{12}{21}$, $\frac{16}{28}$ (or 8:14, 12:21, 16:28; or 8 to 14, 12 to 21, 16 to 28)