Understanding Ratios and Proportions
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Questions and Answers

What is a ratio?

A comparison of 2 numbers that have the same units.

How many ways are there to write a ratio?

3

Simplify the ratio 5/10 and write in two other ways.

1/2, 1 to 2, 1:2

What is a rate?

<p>A ratio that compares 2 numbers with different units.</p> Signup and view all the answers

Examples of rates are...

<p>miles per hour, miles per gallon, words per minute, meters per second</p> Signup and view all the answers

What is a UNIT rate?

<p>A rate that has a denominator of 1.</p> Signup and view all the answers

What is the difference between a rate and a unit rate?

<p>A unit rate always has a denominator of 1.</p> Signup and view all the answers

We calculate the unit rate using which operation?

<p>Division</p> Signup and view all the answers

Calculate the unit rate for 24 miles/3 gallons.

<p>8 miles/1 gallon</p> Signup and view all the answers

Calculate the unit rate for making cookies if it takes 1/3 a cup of sugar to make 1/2 a batch of cookies.

<p>2/3 a cup per 1 batch of cookies</p> Signup and view all the answers

When finding the unit rate of a graph or table, do you use y/x or x/y?

<p>y/x</p> Signup and view all the answers

Find the rate of the graph.

<p>0.5 cups / 1 recipe</p> Signup and view all the answers

Find the unit rate of the table.

<p>40 miles/1 hour</p> Signup and view all the answers

What is a proportion?

<p>A comparison of 2 ratios.</p> Signup and view all the answers

2 ratios are considered proportional if they are...

<p>Equal</p> Signup and view all the answers

How do you check to see if 2 ratios are proportional?

<p>Cross-multiply (butterfly)</p> Signup and view all the answers

1/3 = 2/6 is proportional?

<p>True</p> Signup and view all the answers

3/12 = 1/4 is proportional?

<p>True</p> Signup and view all the answers

3/4 = 8/10 is proportional?

<p>False</p> Signup and view all the answers

Solve for a missing number in proportions by...

<p>Cross-multiplying and then dividing by the leftover number.</p> Signup and view all the answers

3/21 = c/35, what is c?

<p>5</p> Signup and view all the answers

9/105 = 15/y, what is y?

<p>175</p> Signup and view all the answers

26/p = 13/0.4, what is p?

<p>0.8</p> Signup and view all the answers

To see if a table is proportional, you must...

<p>Cross-multiply</p> Signup and view all the answers

Is this table proportional?

<p>True</p> Signup and view all the answers

Is this table proportional?

<p>True</p> Signup and view all the answers

Is this table proportional?

<p>False</p> Signup and view all the answers

What is the constant of proportionality?

<p>Unit rate of the graph.</p> Signup and view all the answers

What is the CoP of the graph?

<p>0.4 miles/1 minute</p> Signup and view all the answers

What is the CoP of the graph?

<p>$20/1 foot$</p> Signup and view all the answers

How do you know if a graph is proportional?

<p>1.) Line goes directly through the origin; (0,0). 2.) 2 ordered pairs from the graph form a proportion (proof!).</p> Signup and view all the answers

Is this graph proportional? Prove in 2 ways.

<p>True</p> Signup and view all the answers

Is this graph proportional? Prove in 2 ways.

<p>False</p> Signup and view all the answers

You can buy six cans of root beer for $2.50. How many cans of root beer can you buy for $10?

<p>24 cans</p> Signup and view all the answers

David paints 3 rooms in 7 hours. At the same pace, how long would it take him to paint 15 rooms?

<p>35 hours</p> Signup and view all the answers

LHMS has 750 girls. The ratio of boys to girls is 3:5, how many boys are at LHMS?

<p>450 boys</p> Signup and view all the answers

Study Notes

Ratios

  • A ratio compares two numbers with the same units.
  • Ratios can be expressed in multiple formats: as "a to b" (2:3), decimal (2/3), or word form (2 to 3).

Rates

  • A rate compares two numbers with different units, e.g., miles per hour or words per minute.
  • A unit rate is a specific type of rate with a denominator of 1.

Unit Rates

  • To find the unit rate, divide the numerator by the denominator.
  • Example: From 24 miles and 3 gallons, the unit rate is 8 miles per gallon.

Proportions

  • A proportion compares two ratios and is evident when two ratios are equal.
  • Cross-multiplication can be used to determine if two ratios are proportional.

Checking Proportionality

  • Example of proportional ratios: 1/3 = 2/6 (yes), 3/12 = 1/4 (yes).
  • Example of non-proportional ratios: 3/4 = 8/10 (no).

Solving Proportions

  • When solving for a missing number in proportions, cross-multiply and then divide by the remaining number.

Constant of Proportionality

  • This reflects the unit rate in a graph, defined as Y/X.
  • Graphs can be considered proportional if they pass through the origin.

Recognizing Proportional Graphs

  • A graph is considered proportional if the line passes through (0,0) and two points from it form a proportion.
  • Example: If a graph shows a line through the origin and maintains consistent ratios, it is proportional.

Word Problems Involving Ratios and Proportions

  • Example: To find how many root beer cans can be bought with $10 when 6 cans cost $2.50, set up the equation $2.50/6 = $10/x and solve to find 24 cans.
  • Example: David painting rooms involves setting up their rates; if 3 rooms take 7 hours, then 15 rooms would take 35 hours.

Application of Ratios in Real Contexts

  • In the context of a school with 750 girls and a boy-to-girl ratio of 3:5, solve for the number of boys by using the equation (x/750 = 3/5) to find 450 boys.

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Description

This quiz focuses on the fundamental concepts of ratios, rates, unit rates, and proportions. Test your knowledge on how to express, compare, and solve problems involving these mathematical concepts. Dive deep into understanding proportionality and the constant of proportionality.

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