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Grade 7:  The Learning Equation Math

12.09 Proportions

Number Operations

Refresher pp 40-1
Learning Objectives:

The student will:

Concept

Explanation

Example

Unit Rate/Ratio

Rate

 A comparison of 2 measurements with different units.   To simplify (find the unit rate) use GCF.

10 km per 2 h

$6 per 3 h

 5 km per h

<$2/h
Ratio
 A comparison of numbers with the same units so units are not required.  To simplify (find the unit ratio) use GCF.  There are three ways to write ratios:

Match the Equivalent Ratio

3:9

4/12

5 to 20

 1:3

<1/3

1 to 4

 

Unit Ratio Calculator

Enter a ratio on the right hand side.  Click Calculate to find the unit ratio.   The first example has been entered for you for each type of ratio.  Explore unit ratios further.  Click Reset and enter your own numbers.
---------

=

---------
     1
:

=

: 1
to

=

to 1
 

 

Proportion

 Used to compare two ratios or make equivalent fractions.  To solve one can:
  • use equivalent fractions.
  • cross multiply.

1/2 = 3/4

1 x 4 = 2 x 3

Note:  The product of the outside (first and last) numbers equals the product of the two middle numbers.

Proportion Calculator

1/2 = x/6

1/2 = 3/x

x/2 = 3/6

1/x = 3/6

Algebra.help -- Proportion Calculator - excellent resource

Equivalent Fractions using Cuisenaire Rods

Integer Bars (Cusienaire Rods): Learning Fractions

Pattern Blocks: Exploring Fractions with Shapes

 

Review:

Algebra.help -- Basics of the Proportion (means and extremes are not part of this course)

Ratios and Proportion

Scientific Calculator

 

Enrichment:

 
Key Terms: A-E F-J K-O P-R S-Z

proportion, denominator, numerator, equivalent ratios, simplest terms, decimal equivalent, product, percent, ratio, rate

 
Prerequisite Skills:

Rate and Ratio:  Grade 7 Lesson 12.08

Rate and Ratio:  Grade 7 Lesson 12.08

Linear Equations 1:  Grade 7 Lesson 22.02

Linear Equations 2:  Grade 7 Lesson 22.03

Factor Calculator

Quia! Matching - Factors

Greatest Common Factor Calculator

 

Least Common Multiple (LCM) Calculator

Greatest Common Divisor (GCD) corresponds to Greatest Common Factor (GCF)

 

source:  common.java

 

Least Common Multiple

 

 

 

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Comments to:  Jim Reed

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