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This is a MUS Pre-Algebra "specific" question, but math is math!

Problem:

"20 apples are in a bag. Rachel used 2/5 of the apples for a pie. Her Mom used 1/2 of the apples for an apple crisp.

How many apples are left in the bag?"

How is this worked? The ans key uses one method of:

2/5 of 20:

20 div by 5 = 4 (I thought this would be 20/1 div by 2/5 = 20/1 x 5/2 (inverse) = after canceling, 10x5 and 1x1 = 50/1 = 50, but that is WRONG. HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!)

4 x 2 = 8 apples R used

1/2 of 20:

20 div by 2 = 10

10 x 1 = 10 apples Mom used

8 + 10 = 18 apples used

20 - 18 = 2 apples left

**************************************

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2/5 of 20:

20 div by 5 = 4 (I thought this would be 20/1 div by 2/5 = 20/1 x 5/2 (inverse) = after canceling, 10x5 and 1x1 = 50/1 = 50, but that is WRONG. HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!)

4 x 2 = 8 apples R used

Theirs is the easiest way to reason through questions like this.

Find one fifth, then multiply by 2.

One fifth is:

1/5 x 20

or

20/5

It will work every time.

If you're going to show it in a single step it would be:

2/5 X 20

Two bags of apples: 2 x 20

One bag of apples: 1 x 20

One half bag of apples 1/2 x 20 = 20/2

Same thing.

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It is 2/5 of 20. Of means times in math. so 2/5 x 20/1. ( you tried to divide instead of multiply) That gives you 40/5 which = 8. (Or, you can cancel the 5 and 20 to leave a 4 on top. 2x4=8)

1/2 of 20= 10

18 apples used means 2 are left.

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I don't know if this method would fit with how MUS has presented the topic so far, but I would do it this way:

total fraction of apples used: 2/5 + 1/2 = 4/10+5/10 = 9/10

fraction of apples not used: 1/10

1/10 * 20 = 20/10 = 2 apples not used

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Yay I got it right LOL!!!!!

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This is a MUS Pre-Algebra "specific" question, but math is math!

Problem:

"20 apples are in a bag. Rachel used 2/5 of the apples for a pie. Her Mom used 1/2 of the apples for an apple crisp.

How many apples are left in the bag?"

How is this worked? The ans key uses one method of:

2/5 of 20:

20 div by 5 = 4 (I thought this would be 20/1 div by 2/5 = 20/1 x 5/2 (inverse) = after canceling, 10x5 and 1x1 = 50/1 = 50, but that is WRONG. HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!)

4 x 2 = 8 apples R used

1/2 of 20:

20 div by 2 = 10

10 x 1 = 10 apples Mom used

8 + 10 = 18 apples used

20 - 18 = 2 apples left

**************************************

To solve the first part of the problem, you are finding 2/5 OF 20.

So you can set it up like the book said to, and split 20 into 5 equal groups. That makes each group a set of four apples. You need two sets, so that's 8 apples.

OR you can multiply fractions. Whenever you are finding a fraction or percent of a number, the "of" means to multiply. So you would set it up like this:

2/5 x 20/1

After canceling common factors, you would have 2/1 x 4/1 which equals 8

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I'd like to thanks you all. I've never had a blitz for such an easy problem. How did I forget that "of" means multiply and not divide? Well, I wanted to say thanks - I really do appreciate it.

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OK you all, good morning! I'm confused - again! My pc is acting up, so please go up to my original post. I keyboard entered the answer from the te. They are showing division. Please re-read the steps in the above b/c that is their answer in the key. I'm CONFUSED!

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OK you all, good morning! I'm confused - again! My pc is acting up, so please go up to my original post. I keyboard entered the answer from the te. They are showing division. Please re-read the steps in the above b/c that is their answer in the key. I'm CONFUSED!

I'm not sure what you mean.

Dividing 20 by 5 and then multiplying the answer, 4, by 2 to get 8 is the same as multiplying by 2/5.

Dividing by five gives you one fifth.

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2/5 of 20:

As you've already been told, OF means multiply. The very first chapter of MUS pre-algebra teaches how to find a fraction of a number such as 2/5 of 20. You can multiply 20/1 * 2/5 multiplying straight across numerators and denominators getting 40/5. Read that as 40 divided by 5 and get the answer 8.

MUS teaches the shortcut: do the division first IF the whole number is divisible by the denominator. So, since 20 can be divided by 5, do that first getting 4, then multiply by 2 getting 8. This keeps the size of the numbers smaller and easier to work with.

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I'm not sure what you mean.

Dividing 20 by 5 and then multiplying the answer, 4, by 2 to get 8 is the same as multiplying by 2/5.

Dividing by five gives you one fifth.

NM.. This is what was in the te. "OF" means to multiply, right? Why does the answer show division? Also note that I'm very black and white on this and need to know "how" they MUS worked it. I need to understand the step by step so I may understand/teach dd. The pink was my reasoning yesterday which doesn't line up with theirs. CONFUSED! The ans key uses one method of: (showing division - I don't have a division symbol on my pc I guess)....

2/5 of 20:

20 div by 5 = 4 (I thought this would be 20/1 div by 2/5 = 20/1 x 5/2 (inverse) = after canceling, 10x5 and 1x1 = 50/1 = 50, but that is WRONG. HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!)

4 x 2 = 8 apples R used

1/2 of 20:

20 div by 2 = 10

10 x 1 = 10 apples Mom used

8 + 10 = 18 apples used

20 - 18 = 2 apples left

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NM.. This is what was in the te. "OF" means to multiply, right? Why does the answer show division? Also note that I'm very black and white on this and need to know "how" they MUS worked it. I need to understand the step by step so I may understand/teach dd. The ans key uses one method of:

2/5 of 20:

20 div by 5 = 4 (I thought this would be 20/1 div by 2/5 = 20/1 x 5/2 (inverse) = after canceling, 10x5 and 1x1 = 50/1 = 50, but that is WRONG. HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!)

4 x 2 = 8 apples R used

1/2 of 20:

20 div by 2 = 10

10 x 1 = 10 apples Mom used

8 + 10 = 18 apples used

20 - 18 = 2 apples left

Multiplying by 1/5 is the same as dividing by 5.

Multiplying by 1/2 is the same as dividing by 2.

One half of 20 is 10.

20/2 is 10

(1x20)/2=20/2=10

(1x20)/5= 20/5=4

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The way I teach it is:

2/5 = x/20

Cross multiply

5x=40

x=8

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OK, I don't use MUS, but I'll give a stab at step-by-step:

One person used two fifths of the apples, the other one half.

20 - Person1 - Person2 = the number of apples left

Person 1 used 2/5 of the apples.

Instead of jumping right into multiplying by a fraction with a numerator greater than one, let's reason our way through this.

I'm presuming there's been work already on finding 1/5, 1/3, 1/2, etc.

Two fifths is 1/5 + 1/5, or (2 x 1/5).

If we know what 1/5 is, we can determine 2/5.

1/5 of 20 is indeed 1/5 x 20, and this is the same as 20/5. The backslash "/" means "divided by" in fractions, just like it does in division.

One way to look at fractions is that they are really a division question.

1/2 means "one (whole) divided by two"

1/3 means "one (whole) divided by three"

1/5 means "one (whole) divided by five"

Times 2 means "two of something"

Times 3 means "three of something"

Times 1 means "one of something"

Times 1/2 means "one half of something"

Times 1/5 means "one fifth of something"

So to find 1/5 of something we take that thing and divide by 5

But what is our "something"? In this case it's 20.

1/5 of 20 is 20/5 = 4

But we have two fifths, not one.

One fifth = 4

Two fifths = 4 x 2 = 8

Person1 used 8 apples.

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OK you all, good morning! I'm confused - again! My pc is acting up, so please go up to my original post. I keyboard entered the answer from the te. They are showing division. Please re-read the steps in the above b/c that is their answer in the key. I'm CONFUSED!

Think about what a fraction MEANS - it means parts of a whole.

The denominator (bottom number) tells you how many parts the whole is divided into. The numerator (top number) tells you how many of those parts you are working with. 1/3 means a whole is divided into 3 equal parts, and you have one of those parts.

In your apple problem, you have to find 2/5 of 20 apples. This means that the 20 apples (the whole amount) is split up into five equal groups. This is why you are dividing - you are separating them out into equal groups. Twenty split into five groups means there are four in each group, and since you are finding 2/5 then you need two of those five groups. Two groups of four apples is 8.

I hope I can say this gently: you seem to have large gaps in your math knowledge. If this isn't just a one-time brain fart, I would get a tutor or outsource math. If your dd is in pre-algebra this year, she can't afford to be slowed down by a teacher who isn't prepared to teach. If your dd was in 3rd or 4th grade, you would have time to learn this along side her, but she doesn't have time to wait. I am not saying this to be rude or mean, but just to help you.

Khan Academy has a great "game" that allows you to fill gaps and work on skills in a logical sequence. I recommend that to help you brush up.

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