Math Lesson 1.4 A Tale of Two Numbers: Ratios and Proportions

A production company spent 52 1/2 days filming its first movie. The company’s second movie was filmed in 9 3/4 weeks. Find the ratio of the first movie’s filming time to the second movie’s filming time. Compare in weeks. The Ratio is…… Step 1: The units are different, they must be the same. Convert days to weeks. So rewrite fraction as a decimal. (numerator/denominator). Keep whole number as is. Do this to the other fraction as well. Ex; 52.5 days times 1 week over 7 days = 7.5 weeks•Now you have the ratio 7.5 weeks over 9.75 weeks. Step 2: This should be in who numbers. So eliminate the decimals by multiplying both numerator and denominator by 100.7.5= (7.5)(100)=7509.75= (9.75)(100)=975Step 3: Reduce 750 over 975 into lowest terms. (Find Greatest Common Denominator) 750/975 = 10/13Answer: 10 over 13
Write the rate as a fraction in lowest terms. 8 people for 20 dresses Step 1: First write the ratio as a fraction, with 1st part being the numerator and 2nd part being denominator. (8/20)Step 2: Put the fraction into lowest terms. (Do this by dividing the numerator and the denominator by heir greatest common factor) 8/4=2 and 20/4=5Answer: The rate is 2 people over 5 dresses
A long distance phone call between two cities costs $2.97 for 9 minutes. What is the rate in cents per minute. The Rate is…. Step 1: Convert dollars to cents. (just take out the decimal point)Step 2: To finding a rate is to write the ratio in faction form and include the measures. (the 1st number is always the numerator) Step 3: Divide the numerator and the denominator. (remember that a ratio is a quotient of two quantities) Ex. 2500 km over 50 hr = 50km/hrAnswer: The rate is 33 cents/minute
When a ratio is used to compare two different kinds of measure its called what? Rate
To water a lawn adequately, it takes 617 gal of water for every 1000 sq. ft. What is the rate in gallons per square foot. The rate is…. Step 1: Take 617 Gal and divide that by 1000 sq. ft. that gives you 0.617 gal/sq ft.Answer: The rate is 0.617 gal/ sq. ft.
Determine if the quantities in the following rates are proportional. 72 miles in 8 hours and 85.5 miles in 9.5 hours. Step 1: Write each rate as a quotient and divide to determine that the quantities are proportional. If the rates are equal, then the quantities are proportional. Ex; 72 miles over 8 hours do division. That equals 9 mph. Step 2: Now write 85.5 miles in 9.5 hours as a quotient. Ex: 85.5 miles over 9.5 hours and divide that and you get 9 mphAnswer: The quantities are proportional because both rates have the same value, 9mph
Are the quantities in the following rate proportional? Decide by converting each rate to a decimal rounded to the nearest tenth. 257 miles in 4 hours and 395 miles in 6 hours. Step 1: 257 divided by 4 = 64.25 now round that. Look at the 5 and that rounds the 2 to a 3. So its 64.3 mphStep 2: 395 miles divided by 6 hours = 65.83So the 8 is in the tenths place look at the 3 and since that is smaller than 5, we keep the 8 as is. So its 65.8 mphAnswer: The quantities are not proportional because the rates are not equal.

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