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

Math = numbers + operations operations = surgery numbers = random shapes math = random shaped surgery

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

Course: Integrated math 2 > Unit 8

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

2.5 cm

and a base of

1.6 cm

. 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?

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

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

\frac{8}{10} = \frac{6}{m}

m =

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 4 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 pageComment on Anais Lee's post “i do not understand why h...”
(21 votes)
Answer
- Hecretary Bird
  Posted 4 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
  Comment on Hecretary Bird's post “When you cross multiply, ...”
  (42 votes)
Nathaly Flores
Posted a year ago. Direct link to Nathaly Flores's post “how do you math?”
how do you math?
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(17 votes)
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- Elaine
  Posted 6 months ago. Direct link to Elaine's post “Math = numbers + operatio...”
  Math = numbers + operations
  
  operations = surgery
  numbers = random shapes
  
  math = random shaped surgery
  Button navigates to signup page
  (15 votes)
1+1=6
Posted 2 years 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
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- sebastian.gamon
  Posted a year ago. Direct link to sebastian.gamon's post “bro no ones cares lmao”
  bro no ones cares lmao
  Comment on sebastian.gamon's post “bro no ones cares lmao”
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az10920
Posted a year 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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(4 votes)
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- chowdd
  Posted a year 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
  (13 votes)
student4
Posted a year 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...”
(6 votes)
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- Cedar
  Posted a year 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)
Sophie
Posted 7 months ago. Direct link to Sophie's post “why is this important in ...”
why is this important in life.
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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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- Shreshta
  Posted 2 years ago. Direct link to Shreshta's post “It is a fraction...”
  It is a fraction...
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Gabriel Alonso
Posted a year 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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- E
  Posted a year 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)
denzel.chukwu
Posted 9 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 8 months 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
  (3 votes)
elilavoie
Posted 21 days ago. Direct link to elilavoie's post “This does not give the fu...”
This does not give the fundamentals but gives advanced problems. If I could rate this it would not be a pretty review.
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