i do not understand why he give me a question about:q/q+5=12/27.and suddenly next stop just became:27q=12q+60.what the hell is that number 60 coming form? (⊙⊙?)

When you cross multiply, you have to make sure to distribute if a numerator/denominator has multiple terms in it. Here's how the equation looks directly after you cross-multiply: (27) q = (q + 5) 12 The 12 distributes to both the q and the 5, creating: 27q = 12q + 60 15q = 60 q = 4

Does anyone know practical applications of similarity concepts in common engineering fields? I'm interested in the practical applications of these otherwise abstract concepts, and was wondering if anyone had any interesting insights. Thanks!

Say an engineer makes a prototype of a design. A company likes it but wants to adjust the size a bit. The engineer must use similarity to 'scale up' or 'scale down' the prototype by a certain amount.

why did you put 60 over 8?

8/10 = 6/x you cross multiply 8 * x = 8x 6 * 10 = 60 then you dive 60 over 8 which equals 7.5

why is it 10m and how does that get rid of the ten when its not negative

You multiply the 10 by 1/10 so you have 10/10 which simplifies into 1

For the last problem, I solved it by looking at the percentage of 12/27 and then realized that 4/9 has the same rate. Is there a more efficient way of doing this?

Reduce the fraction, solve for q; in this case, solving for q becomes unnecessary once you've reduced, because most people will quickly recognize that q must be four. This actually brings up a good general principle in math: do what you know you can do, then look at the problem again, and see if it has gotten easier. Simplifying, expanding, factoring, substituting equivalent expressions, are all good things to try if you get stuck. Of course, you'll want a pretty good idea of how to do these already when you need them, say on a test, so do a variety of exercises to expose yourself to different types of problems.

Main content

High school geometry

Course: High school geometry > Unit 4

Lesson 1: Definitions of similarity

Getting ready for similarity

Google Classroom

Practicing identifying proportional relationships and solving equations with proportions helps us get ready to learn about similarity.

Let’s refresh some concepts that will come in handy as you start the similarity unit of the high school geometry course. You’ll see a summary of each concept, along with a sample item, links for more practice, and some info about why you will need the concept for the unit ahead.

This article only includes concepts from earlier courses. There are also concepts within this high school geometry course that are important to understanding similarity. If you have not yet mastered the Congruent triangles lesson or the Dilations preserved properties lesson, it may be helpful for you to review those before going farther into the unit ahead.

Identifying proportional relationships

What is this, and why do we need it?

A relationship between two quantities is proportional if the ratio between those quantities is always equivalent. We will look at side length ratios to find out whether triangles are similar or not.

Practice

Problem 1

Triangle A has a height of 2, point, 5, start text, space, c, m, end text and a base of 1, point, 6, start text, space, c, m, end text. The height and base of triangle B are proportional to the height and base of triangle A.

Which of the following could be the height and base of triangle B?

(Choice A)
Height: 2, point, 75, start text, space, c, m, end text
Base: 1, point, 76, start text, space, c, m, end text
(Choice B)
Height: 9, point, 25, start text, space, c, m, end text
Base: 9, point, 16, start text, space, c, m, end text
(Choice C)
Height: 3, point, 2, start text, space, c, m, end text
Base: 5, start text, space, c, m, end text
(Choice D)
Height: 1, point, 25, start text, space, c, m, end text
Base: 0, point, 8, start text, space, c, m, end text
(Choice E)
Height: 2, start text, space, c, m, end text
Base: 1, point, 28, start text, space, c, m, end text

For more practice, go to Proportional relationships.

Where will we use this?

Here are a few of the exercises where reviewing proportional relationships might be helpful:

Solve equations with proportions

What is this, and why do we need it?

When two ratios are equal, we create a proportion equation. If we multiply the equation by both denominators, we can solve the resulting equation just like a linear (or quadratic, but not in this unit) equation. We will set up equations with proportions to find lengths in similar figures.

Practice

Problem 2.1

Current

Solve for m.
Do not round. If needed, write your answer as a fraction.

start fraction, 8, divided by, 10, end fraction, equals, start fraction, 6, divided by, m, end fraction

m, equals

For more practice, go to Solving proportions 2.

Where will we use this?

Here are a few exercises where reviewing proportions equations might be helpful.

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Anais Lee
Posted 3 years ago. Direct link to Anais Lee's post “i do not understand why h...”
i do not understand why he give me a question about:q/q+5=12/27.and suddenly next stop just became:27q=12q+60.what the hell is that number 60 coming form?
(⊙⊙?)
Button navigates to signup pageButton navigates to signup page
(15 votes)
Answer
- Hecretary Bird
  Posted 3 years ago. Direct link to Hecretary Bird's post “When you cross multiply, ...”
  When you cross multiply, you have to make sure to distribute if a numerator/denominator has multiple terms in it. Here's how the equation looks directly after you cross-multiply:
  (27) q = (q + 5) 12
  The 12 distributes to both the q and the 5, creating:
  27q = 12q + 60
  15q = 60
  q = 4
  Button navigates to signup page
  (29 votes)
Nathaly Flores
Posted 5 months ago. Direct link to Nathaly Flores's post “how do you math?”
how do you math?
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(12 votes)
Answer
1+1=6
Posted a year ago. Direct link to 1+1=6's post “... the q/q+5=12/27 is 4....”
... the q/q+5=12/27 is 4. It's not that hard tbh
Button navigates to signup pageComment on 1+1=6's post “... the q/q+5=12/27 is 4....”
(3 votes)
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- sebastian.gamon
  Posted 7 months ago. Direct link to sebastian.gamon's post “bro no ones cares lmao”
  bro no ones cares lmao
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  (12 votes)
student4
Posted 6 months ago. Direct link to student4's post “Does anyone know practica...”
Does anyone know practical applications of similarity concepts in common engineering fields? I'm interested in the practical applications of these otherwise abstract concepts, and was wondering if anyone had any interesting insights. Thanks!
Button navigates to signup pageComment on student4's post “Does anyone know practica...”
(5 votes)
Answer
- Cedar
  Posted 6 months ago. Direct link to Cedar's post “Say an engineer makes a p...”
  Say an engineer makes a prototype of a design. A company likes it but wants to adjust the size a bit. The engineer must use similarity to 'scale up' or 'scale down' the prototype by a certain amount.
  Button navigates to signup page
  (7 votes)
az10920
Posted 5 months ago. Direct link to az10920's post “why did you put 60 over 8...”
why did you put 60 over 8?
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(3 votes)
Answer
- chowdd
  Posted 5 months ago. Direct link to chowdd's post “8/10 = 6/x you cross mult...”
  8/10 = 6/x
  you cross multiply
  8 * x = 8x
  6 * 10 = 60
  then you dive 60 over 8
  which equals 7.5
  Button navigates to signup page
  (10 votes)
Daniel531
Posted 3 years ago. Direct link to Daniel531's post “why is it 10m and how doe...”
why is it 10m and how does that get rid of the ten when its not negative
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(5 votes)
Answer
- Shreshta
  Posted a year ago. Direct link to Shreshta's post “It is a fraction...”
  It is a fraction...
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  (0 votes)
Gabriel Alonso
Posted 5 months ago. Direct link to Gabriel Alonso's post “why is it 10m and how doe...”
why is it 10m and how does that get rid of the ten when its not negative
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(2 votes)
Answer
- E
  Posted 5 months ago. Direct link to E's post “You multiply the 10 by 1/...”
  You multiply the 10 by 1/10 so you have 10/10 which simplifies into 1
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  (3 votes)
Sophie
Posted 6 days ago. Direct link to Sophie's post “why is this important in ...”
why is this important in life.
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(1 vote)
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- lex
  Posted 4 days ago. Direct link to lex's post “its not tbh”
  its not tbh
  Comment on lex's post “its not tbh”
  (2 votes)
denzel.chukwu
Posted 2 months ago. Direct link to denzel.chukwu's post “For the last problem, I s...”
For the last problem, I solved it by looking at the percentage of 12/27 and then realized that 4/9 has the same rate. Is there a more efficient way of doing this?
Button navigates to signup pageComment on denzel.chukwu's post “For the last problem, I s...”
(1 vote)
Answer
- Jermaine Race
  Posted 25 days ago. Direct link to Jermaine Race's post “Reduce the fraction, solv...”
  Reduce the fraction, solve for q; in this case, solving for q becomes unnecessary once you've reduced, because most people will quickly recognize that q must be four.
  
  This actually brings up a good general principle in math: do what you know you can do, then look at the problem again, and see if it has gotten easier. Simplifying, expanding, factoring, substituting equivalent expressions, are all good things to try if you get stuck. Of course, you'll want a pretty good idea of how to do these already when you need them, say on a test, so do a variety of exercises to expose yourself to different types of problems.
  Button navigates to signup page
  (2 votes)