Ratios and Rates
Give an example of a ratio comparing two quantities with the same attribute and write it three ways
What is "3:2", 3223, "3 to 2"?
Convert 3 meters to centimeters
3 m = 300 cm
Write 0.45 as a percent and as a fraction in simplest form
0.45 = 45% =45/100 = 9/20
Convert the fraction 3/4 to a decimal and to a percent.
3/4 = 0.75 = 75%
7+(−3)
7 + (-3) = 4
If a recipe uses 3 cups of flour for every 2 cups of sugar, how many cups of flour are needed for 8 cups of sugar? Show a proportion or unit rate method.
Setup: 32=x8⇒x=1223=8x⇒x=12 cups flour.
Convert 5,000 milliliters to liters
5000 mL = 5 L
Find 25% of 240. Show work using a fraction and a decimal method
25% of 240 = 0.25 x 240 = 60
Convert 0.125 to a fraction in simplest form and to a percent.
−12−(−5)
-12 - (-5) = -12 + 5 = -7
A car travels 210 miles in 3 hours. What is the unit rate in miles per hour? Then write the rate as a ratio.
Unit rate: 210/3=70 mph; ratio 210:3 or 70:1
A ribbon is 2.75 meters long. Convert its length to centimeters.
2.75 m = 275 cm
A jacket is $80 with a 15% discount. What is the sale price? Show both finding the discount amount and the final price.
Discount: 0.15 x 80 = 12; sale price 80 - 12 = 68
A donation form shows 18% highlighted. Write this as a fraction and as a decimal.
18% = 0.18 = 18/100 = 9/50
Multiply: −8×6
-8 x 6 = -48
A classroom has 18 girls and 12 boys. Express the ratio of girls to boys in simplest form and then find how many girls there would be if the total students were scaled to 150 while keeping the same ratio.
Simplest ratio girls:boys = 18/12=3/2. For total 150, parts = 3+2=5; girls = 150×3/5=90.
Convert 4.5 kilograms to grams
4.5 kg=4500 g
A student earned 42 out of 50 points on a test. What percent did the student earn? Show the work and round to the nearest tenth if needed.
42/50 = 0.84 = 84%
Convert 7/20 to a percent and explain one real-world situation where that percent could be used.
7/20 = 0.35 = 35% Example: 35% of students prefer pizza.
-42/7
-42/7 = -6
A map scale shows 1 inch represents 15 miles. If two towns are 8.4 inches apart on the map, how far apart are they in miles? Show work using a unit rate or proportion
Unit rate: 15 miles per inch → 8.4×15=126 miles.
A recipe needs 2 1/3 cups but you only have a measuring cup marked in tablespoons. Convert the amount to tablespoons (1 cup = 16 tablespoons).
213 cups = 7/3; 7/3×16 = 112/3 ≈ 37 1/3 tablespoons (or 37.33 tbsp)
The population of a town increased from 12,000 to 13,560. What is the percent increase? Show work and round to the nearest tenth of a percent.
increase amount 13,560 - 12,000 = 1,560; 1560/12000 = 0.13 = 13%
A store advertises "Save 1/6 off the original price." Convert this discount to a percent and a decimal, then find the sale price of an item originally priced at $84.
1/6 = 0.166 = 16.66%
Discount = $70
A submarine is at −120 meters. It rises 35 meters, then descends 50 meters. What is its final depth? Show each step using integer addition/subtraction
Start at −120.
Rise 35: −120+35 = −85.
Descend 50: −85−50=−135.
Final depth: −135 meters