For more information, please see full course syllabus of Basic Math
For more information, please see full course syllabus of Basic Math
Discussion
Study Guides
Practice Questions
Download Lecture Slides
Table of Contents
Transcription
Related Books
Solving Proportions
Related Links
- Portion: An equality of two ratios
Solving Proportions
[3/5]
- [(3 ×2)/(5 ×2)] = [6/10]
- [(6 ×2)/(10 ×2)] = [12/20]
[11/44]
- [(11 ÷11)/(44 ÷11)] = [1/4]
- [(1 ×2)/(4 ×2)] = [2/8]
[3/5] = [x/10]
- [(3 ·2)/(5 ·2)] = [x/10]
[1/8] = [x/24]
- [(1 ·3)/(8 ·3)] = [x/24]
[3/z] = [12/16]
- [(3 ·4)/(z ·4)] = [12/16]
[4/40],[8/80]
- [(4 ×2)/(40 ×2)] = [8/40]
[12/24],[24/47]
- [(12 ×2)/(24 ×2)] = [24/48]
[13/26],[25/52]
- [(13 ×2)/(26 ×2)] = [26/52]
- [26/52] ≠ [25/52]
[5/x] = [2/20]
- 2x = 5 ·20
- 2x = 100
- [2x/2] = [100/2]
- x = [100/2]
[2/4] = [y/16]
- 4y = 2 ·16
- 4y = 32
- [4y/4] = [32/4]
- y = [32/4]
*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.
Answer
Solving Proportions
Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.
- Intro 0:00
- Proportions 0:05
- An Equality of Two Ratios
- Cross Products
- Extra Example 1: Find Two Equivalent Ratios for Each 3:21
- Extra Example 2: Use Mental Math to Solve the Proportion 5:52
- Extra Example 3: Tell Whether the Two Ratios Form a Proportion 8:21
- Extra Example 4: Solve the Proportion 13:26
Basic Math Online Course
Transcription: Solving Proportions
Welcome back to Educator.com.0000
For the next lesson, we are going to be solving proportions.0002
A proportion is when we have two equal ratios.0008
A ratio is a comparison between two parts, A and B.0014
Here this is a ratio comparing A and B together.0022
You read it as A to B.0028
You can also write ratios A to B like that.0030
But when you are taking two ratios and you are comparing them0036
to each other and you are saying that they are equal,0039
the ratio of A to B is equal to the ratio of C to D, then you have a proportion.0042
You are actually going to have to write it A to B like a fraction.0049
Proportion is when you have ratio equaling another ratio.0056
To solve proportions, let's say you are missing one of these.0062
You are missing A; or you are missing B; one of these.0065
To solve a proportion, you are going to use what is called cross products.0069
Cross products is when you multiply across.0075
You are going to go A times D equal to B times C.0078
You have the proportion A over B equal to C over D.0089
Then you are going to find the products AD.0096
Cross products, that is A times D.0100
When you write two variables next to each other like that, that means multiply.0103
A times D equal to B times C.0107
Be careful, this is not the same thing as cross cancelling.0113
Cross cancelling is when you are multiplying fractions0117
and you can cancel out numbers if they have common factors.0120
But this is cross products; this is for proportions.0126
This is only when they are equal to each other.0129
Then you can multiply across and make it equal to this across.0132
AD, A times D is equal to B times C.0140
Let's do an example; if I have let's say 1/2 equal to X/ 4.0145
This one is easy; we know we can do this in our head.0156
One half, 1/2, is the same thing as 2/4.0158
I know that X has to be 2.0163
But to solve it, just to use cross products, it will be 2 times X.0167
2 times X is 2X; same thing as 2 times X.0174
It is equal to 1 times 4 which is 4.0178
Then to solve this out, we are going to... remember one-step equation.0183
This is 2 times X or 2 times what equals 4?0188
2 times 2 equals 4; X equals 2.0193
Let's do a few examples; the first example, find two equivalent ratios for each.0200
We know that proportions are when we have two equal ratios.0207
Let's find two other ratios that are equal to this.0214
3/4, I can say that if I multiply this by 2, then this is 6/8.0218
This ratio is equal to this ratio.0228
To find another one, how about if I multiply it by 3?0232
3 times 3 is 9; 4 times 3 is 12.0235
Here are my two equivalent ratios.0241
Here I can also divide.0248
If I divide by 10, divide this by 10, because I know 10 goes into both, this becomes 1/2.0250
That is one equivalent ratio.0261
I can multiply this by 2; multiplied by 2; multiplied by 2.0266
This can be 2/4.0272
This and this, they don't look like they are equivalent.0276
But they actually are because if you simplify this, this is 1/2.0279
If you simplify this, this is 1/2; it is the same; it is equivalent ratios.0284
This one, you can multiply it by 2; you can divide.0294
I know that 11 and 33 have factors of 11.0301
11 divided by 11 is 1 over... 33 divided by 11 is 3.0308
Again you can just base it on this for the next one.0315
Multiply it by 2; it will be 2.0318
Multiply this by 2; it will be 6.0321
There are actually many, many different ratios or fractions that you can write out to make them equivalent.0327
There is going to be many, many; these are not the only answers.0336
These are not the only fractions that are equal to this fraction.0339
If you want, you can multiply this by 10, multiply it by 20.0344
As long as you do it to both numbers, you are going to have equivalent ratios.0347
Let's solve these proportions; but we are going to use mental math.0354
Meaning we are going to try to solve these out in our head.0358
For the first one, I want to solve for X; 3/4 equals X/12.0362
If this fraction is going to have to equal this fraction, 4 times what is 12?0371
4 times 3 is 12; that means I have to multiply the top number by 3.0376
X has to be 9; X equals 9.0382
Same thing here; this is 1 times 5 which gave me 5.0388
Then I have to multiply 5 to this; A is going to be 25.0394
Same thing here.0404
If you look at the bottom numbers, this is 6 times 1 equals 6.0406
Something times 1 is going to equal 4; isn't this 4 times 1?0414
This is going to be the same fraction; 4/6 has to equal 4/6.0418
D is going to be 4.0424
The next one, this one is a little bit different0428
because I can't divide and multiply a number 15 to give me 12.0433
What I can do is I can just simplify this ratio because I have both the top and bottom number.0441
I want to simplify this ratio to help me solve for this ratio.0449
If I simplify this, I know that 4 goes into both numbers.0454
Divide this by 4; this is 3/2; this ratio is equivalent to that ratio.0459
I just have to base this one on this then.0473
3 times 5 is 15; to go from here to here, it is times 5.0480
To go from here to here then, it will be times 5.0489
Z has to be 10.0493
Tell whether the two ratios form a proportion.0503
That just means that they have to be equal.0508
It is just a yes or no.0511
Are they equal or are they not equal?--because proportions have to be two equal ratios.0512
Is this ratio equal to this ratio?0519
2/3, multiply this by 10 to get 20; multiply this to 10 to get 30.0525
Is it equal?--yes, this one is equal.0533
The next one, are these equal ratios?0539
This one, you had to multiply this by 7 to get 35.0543
How about this one?0548
If you multiply this by 7, you have to multiply it by the same number.0549
Does it give you that?--this one is yes.0552
This one here, again I can't multiply or divide this number to get this number.0560
I can find another equivalent ratio to base both of these on.0566
I know that 5 goes into both of these.0572
5 goes into 25 five times; I am dividing by 5.0577
70 divided by 5 is going to be...0584
Again if you want to just divide it out, it is going to be 70 divided by 5.0589
Otherwise it is going to be 14.0594
I know that because... I will just solve it out.0598
Let's do it right here; 70 divided by 5.0602
1 is going to give you 5; subtract it; 2; 5 times 4 is 20.0608
That means to get from 5 to 35, I have to multiply this by 7.0617
What is 14 times 5?--it is 70; I know it is not 70.0626
This has to be 70; so I am going to say no.0636
The next one, here 42/21, this also is going to be equivalent fraction.0651
This will be 2/1 because 42/21... 21 is half of 42.0666
Again I can just divide this by 21 to get 2; and then 21 to get 1.0680
To get from here to here... or see if this one equals the same thing.0687
This one, divide this by common factor; is this 12?0693
This becomes 2; this becomes 1.0703
See how this was equal to this?--and then this also equal to this?0707
That means these are the same; so this one is yes.0712
You can do the same thing for this one.0716
I know that this simplified to get that.0720
Here 35 divided by 5 because a common factor between this one and this one is 5.0724
This one is 7 over... 75 divided by 5.0740
75 divided by 5 is going to be 15.0751
That will just be 5, 2; bring down the 5; this is 15.0757
Automatically because these are different, I know that it is a no.0765
Again if you want to figure out if two ratios are equal, you can either multiply, see if it is the same factor.0772
Or can just simplify each one of them and see if those simplified fractions are the same.0783
Like the bottom one right here, this last one, you simplify this; it became 2/1.0791
You simplify this; it became 2/1.0796
Since they simplify to become the same fraction, you know that these are the same.0798
So that is yes.0804
For the next example, we are going to solve the proportion using cross products.0807
Just practice using these cross products.0814
You are going to multiply these across.0816
You are going to make it equal to those two multiplied.0822
This becomes 2 times X; I am just going to write that as 2X.0828
Remember whenever you multiply a number with a variable, you can write it together like that.0832
Then equals 5 times 10 which is 50.0838
Again be careful, cross products is not the same thing as cross cancel.0843
You are not cancelling anything out.0849
This 5 and this 10, they have a common factor of 5.0850
But you are not cross cancelling out.0856
You only cross cancel when you are multiplying the fractions.0858
But here you are solving proportions where it is an equal, not a multiplication.0863
You are going to multiply them together and you are going to make it this side.0867
From here, I have to find out what X is; 2 times something equals 50.0874
2 times 25 equals 50; think of 50 cents.0880
2 times 2 quarters... that is 25 cents... equals 50 cents.0888
Or you can also just divide this 2; X is going to equal 25.0895
If you want, you can just use division like this.0906
2 goes into 5 two times; 4; subtract it; you bring down the 1.0910
Bring down the 0; 2 times 10 is 6; X is 25.0917
Same thing here; let's cross multiply; cross products.0927
3 times M would be 3M; just write them together like that.0939
Make sure you don't do it with numbers.0945
If it was 3 times 4, then you can't put 34 because it looks like the number 34.0946
This means 3 times M; then 4 times 21; 4 times 21 is 84.0952
21 times 4; 1 times 4 is 4; 4 times 2 is 8.0968
From here, 3 times something equals 84.0976
That means I have to divide this 3.0979
I need to divide the 3 to get my answer; 84 divided by 3.0984
How many times does 3 go into 8?--two times; that becomes 6.0993
I am going to subtract and get 2; bring down the 4.0998
3 times 8 equals 24; 24, 0; my M is 28.1002
Make sure you write what the variable is; the variable equals 28.1018
Don't forget, when you are solving proportions, if you can do it mentally, then go ahead and do that using mental math.1023
Otherwise you are going to just multiply this.1030
These two across equal these two across; then solve for your variable.1032
That is it for this lesson; thank you for watching Educator.com.1038
2 answers
Last reply by: Ana Chu
Sun Feb 1, 2015 11:21 AM
Post by mohamed bulhan on July 3, 2014
PROPORTIONS are confusing to me. what is the easiest way to solve proportions?