Grade 8: The Learning Equation Math

11.03 Three-Term Ratios

Refresher pp 6-7

The student will:

express three-term ratios in equivalent forms.

Concept	Explanation	Example(s)	Unit Rate/Ratio
Rate	A comparison of 2 measurements with different units.c; To simplify (find the unit rate) use greatest common factor (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 use greatest common factor (GCF). There are three ways to write ratios: Match the Equivalent Ratio	3:9 120 to 20	1:3 6 to 1
Three-term ratios	You can use the dimensions of a rectangle to make a three-term ratio.	You can write the measurements of the length, width, and height of the rectangle in a ratio: 25 : 5 : 5	This can be reduced to simplest terms by dividing all 3 terms by 5. 5 : 1 : 1

Similar Triangles

Click and drag on vertex A or B. The proportion of the corresponding sides remains constant until you change the position of the slider. The two triangles are similar triangles. The sides of each similar triangle form a three-term ratio.

a:b:c d:e:f

The ratio of three sides and a perimeter of a triangle are in a given. How do you find the length of the three sides.

http://www.webmath.com/Wordp/ratio5.html

Three Term Ratio Problem

The numbers of dogs, goats and hens on a farm are in the ratio 2:3:10 respectively. If there are 60
hens then how many dogs are there?

source: GMAT - Exponents, Ratios & Percents - Page 4

Review:

http://www.webmath.com/Wordp/ratio3.html

http://www.webmath.com/Wordp/ratio5.html

http://www.webmath.com/Wordp/ratio6.html

http://www.webmath.com/Wordp/ratio7.html

Enrichment:

Pythagorean Triple

To get an equivalent three-term ratio, multiply each side of a Pythagorean Triple by the same number!! For the example below, some of the equivalent three-term ratios are:

{3, 4, 5}
{6, 8, 10}
{9, 12, 15}

Enter two positive integers (smallest first):
s: < t:

A Pythagorean Triple:

Enter your own values for s and t to discover other Pythagorean triples.

Pythagorean triples are integer length sides of right triangles. Here's a trick for finding them.

You pick s and t from the positive integers, but s must be smaller than t.

To compute (x, y, z):

(t² - s², 2st, t² + s²)

Example, if s=1 and t=2 you get:

( 2² - 1², 2(1)(2), 2² + 1²)

(3,4,5)

Source: Pythagorean Triple Calculator in JavaScript

Key Terms:

ratio, term, equivalent ratio, greatest common factor

Wordsearch 1101-1105

Prerequisite Skills:

Recognize, model, identify, find, and describe common multiples and least common multiple using numbers 1 to 100.

Conversion of Fractions: Grade 7 Lesson 11.05

Recognize, model, identify, find, and describe common factors and greatest common factor using numbers 1 to 100.

Adding Fractions with Unlike Denominators: Grade 8: Lesson 12.02

Recognize, model prime factorization, using numbers 1 to 100.

Prime Factorization Machine

This page runs a script that will return the prime factorization of a positive integer. Of course the bigger the number, the longer it will take. Just to be safe I decided to limit it to numbers less than 1,000,000 (see below). Even with this limit, some numbers (those with very large prime factors) may take a few minutes to factor if your computer has a slow processor, so be patient if nothing happens after you click the button.

Enter a positive integer in the left box and press the button

Override limit*

Source: Prime Factorization Machine

Demonstrate and explain the meaning of ratios concretely, pictorially, and symbolically.

Rate and Ratio: Grade 7 Lession 12.08

Distinguish between rate and ratio and use them to solve problems.

Rate and Ratio: Grade 7: Lesson 12.08

Explain, demonstrate, and use proportion in solving problems.

Proportions: Grade 7: Lesson 12.09

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