Charlie tried to do the same with 1/8 can you finish Charlie calculations to see which one work?
1/8=1/9=?
1/8=1/10=?
1/8=1/11=?
Can all unit fractions be made in more then one way like this?
Choose different unit fractions of your own to test out your theories
What you typed makes no sense, but I think you are probably looking
at a topic called "Egyptian Fractions"
In that topic, each proper fraction is written as a sum of unit fractions.
e.g. 7/8 = 1/2 + 1/3 + 1/24 or 1/2 + 1/4 + 1/8
showing that such a presentation is not unique.
The question becomes: Is this possible for any given proper fraction
e.g. 17/23
take out the largest unit fraction, which is 1/2
17/23 = 1/2 + 11/46 , the next largest fraction would be 1/2, but 11/46 < 1/3, so is 11/46 < 1/4
so we go all the way to 1/5
= 1/2 + 1/5 + 9/230
= 1/2 + 1/5 + 1/26 + 1/1495
you can check this with a calculator using the "a b/c" fraction calculator key
Here is a online Egyptian fraction calculator:
http://www.calcul.com/show/calculator/egyptian-fraction?n=17&d=23
It gave me the same result.
I wrote it how they asked it
That literally how they wrote the question on my worksheet
Unit fractions (fractions which have numerators of 1) can be written as the sum of two different unit fractions.
For example
12=13+16
Charlie thought he'd spotted a rule and made up some more examples.
12=110+120
13=14+112
13=17+121
14=15+120
Are all his examples correct?
What do you notice about the sums that are correct?
Find some other correct examples..
How would you explain to Charlie how to generate lots of correct examples?
Alison started playing around with 16 and was surprised to find that there wasn't just one way of doing this.
She found:
16=17+142
16=18+124
16=19+118
16=110+115
16=112+112 (BUT she realised this one didn't count because they were not different.)
Charlie tried to do the same with 18. Can you finish Charlie's calculations to see which ones work?
18=19+?
18=110+?
18=111+?
..........
Can all unit fractions be made in more than one way like this?
Choose different unit fractions of your own to test out your theories.
Thank you so much for answering my question
So you would say it’s no for the unit fractions can be made more then one way
So the example you use I can pretty much use that to showcase how the theories doesn’t work and not all unit fractions can be made in more then one way
To complete Charlie's calculations, we need to find the values of the variables on the right-hand side of each equation. Let's solve each equation one by one:
1/8 = 1/9
To find the value of the variable on the right-hand side, we can use the concept of cross-multiplication. Cross-multiplication involves multiplying the numerator of one fraction by the denominator of the other fraction. So, in this case, we have:
1 * 9 = 8 * x
9 = 8x
To isolate the variable, we divide both sides of the equation by 8:
9/8 = x
So, 1/8 is equivalent to 9/72.
1/8 = 1/10
Again, we can use cross-multiplication to solve for the variable:
1 * 10 = 8 * x
10 = 8x
Dividing both sides of the equation by 8, we get:
10/8 = x
Simplifying the fraction, we have:
5/4 = x
So, 1/8 is equivalent to 5/20.
1/8 = 1/11
Using cross-multiplication:
1 * 11 = 8 * x
11 = 8x
Dividing both sides of the equation by 8, we get:
11/8 = x
Hence, 1/8 is equivalent to 11/88.
Now, let's address your second question. Not all unit fractions can be expressed in more than one way. Unit fractions, by definition, have a numerator of 1. Since the numerator is fixed, there is only one way to express a unit fraction using different denominators. For example, 1/2, 1/3, and 1/4 can all be considered unit fractions, but they cannot be expressed in any other way. The numerator will always be 1, while the denominator may change.
To test this, you can choose any rational number greater than 1 and less than 10 as a numerator and pair it with various denominators. For instance, you can try:
2/9 = 2/10
3/4 = 3/5
5/7 = 5/8
In each case, the fractions cannot be simplified further, and no other equivalent fractions can be obtained.