# Tag Archives: fractions

## Split a length into 5 equal pieces – fractions

The parallel equally spaced lines

and the  desired  length HI, of ribbon, wood, anything non-elastic.

DONE !

Filed under fractions, Uncategorized

## 1/5 is one fifth of the length of a line segment of one unit – but how?

### ….but how do you do it ?????

The mystery is solved…….

Here is the line, with 0 and 1 marked. /You chose it already !

Here is a numbered line, any size, equally spaced, at intervals of one unit.

It only has to start from zero.

Now construct the line from point 5 to the “fraction” line at point 1, and a parallel line from point 1 on the numbered line.

The point of intersection of the parallel line and the “fraction” line is then 1/5 of the distance from 0 to 1 on the “fraction” line.

1/5, 2/5, 3/5, 4/5 and 1 are equally spaced on the fraction line.

L cannot be moved in the static picture.

Filed under fractions, geometry, math, Uncategorized

Who needs LCM ?

First, three views of LCM with no comments :

### 3: The GCF and LCM are the underlying concepts for finding equivalent fractions and adding and subtracting fractions, which students will do later.

Now we can do fraction addition without LCM. It just needs the use of the distributive law, and the result shows the way in which the divisors combine.

And now using 3/4

But the best one is via multiplication ……

Now for multiplication and division.

Filed under algebra, arithmetic, fractions, Uncategorized

## Egyptian fractions

I found this on Quora. What would the standard algorithm be, I wonder.
……………………………………………………………………………………………………
David Joyce, Professor of Mathematics at Clark Uni… (more)

Suppose you have five loaves of bread and you want to divide them evenly among seven people.  You could cut the five loaves in thirds, then you’d have 15 thirds.  Give two of them to each of the seven people.  You’ll have one third of a loaf left.  Cut it into seven equal slices and give one to each person.

There may be other solutions.   a = b = 3, c = 21.   (Egyptian Fractions)

……………………………………………………………………………………………………

Filed under arithmetic, fractions, math, operations

## Fractional doggerel – verse problem

Mary’s mother brought a pizza
For her little kiddies, two.
“Johnny, you can have threequarters.
Mary, just a half will do.”.

Then the kiddies started eating.
Soon Mary grabbed her final piece.
“That’s mine” screamed Johnny, then the fighting
Broke the tranquil mealtime peace.

How much pizza then was eaten?
How much pizza on the floor?
Mother swore and left the building.
“I should have ordered just one more”.

1 Comment

Filed under arithmetic, fractions, humor, language in math, verse

## Fractions, at home and away

In the morning Johnny’s mom
Said “Here’s six candies for your break.
“Give your sister half of them”.
Now Johnny’s brain is on the make.
He gives her one, and then another.
Little sister stamps her feet!
“And the last one!” says his mother.
“Damn” thinks Johnny, “I can’t cheat!”.

Later that day

“Johnny, what is half of six?”.
“I dunno”.
“Well, go get out six lego bricks
“And make a row.
“Now break the row right in the middle.
“That’s half the row.
“Just split the half and count the bricks”.
“I got three”.
“So now you see, three’s half of six”.
But does he know?

Filed under arithmetic, fractions, humor, language in math, teaching, verse

## Pythagoras converse, proof from scratch

There is a website with 100 proofs of the famous theorem of Pythagoras, but when I trawled the net looking for a proof of the converse, they all assume the basic theorem.

Here’s how to do it from scratch, which is considerably more satisfying, and also a simple application of similar triangles and basic algebra:

July 2, 2014 · 7:21 pm

## Q: Who needs polynomial division? A: In high school, NOBODY !

Polynomial division is a completely unnecessary procedure. It is not needed for partial fractions. It is not needed for finding factors, etcetera…

The same result can be obtained in a more logical and meaningful way, by considering the structure of polynomial and rational expressions.

Check this out :

Filed under algebra

## Fractions are parts of the same whole, part 3

When is a whole not a whole? (again)

When it’s two wholes (or more) :-

John eats 1/2 of his pizza, Mary eats 3/4 of her pizza. So between them they ate 1/2 + 3/4 of a pizza, or 5/4 of a pizza.

So which whole are we referring to ? John’s pizza ……. No.   Mary’s pizza ……. No.    Both pizzas …….. No.    John’s pizza and  Mary’s pizza and  both pizzas …….. No.

Conclusion: What we are referring to as “the same whole” is an abstract unit of one pizza, and the fractions are measurements using this unit. Wouldn’t it be a good idea to start off like this, with fractions as measurements, and avoid years of misunderstanding, stress and confusion.

Is this so different from adding whole(adjective!) numbers , as when  adding two numbers they have to be counts of the same thing (or whole(!) before it is chopped up).?

Fun arithmetic:        3 apples + 4 bananas = 7 applanas

Desperately fun arithmetic :  1/2 of my money + 1/2 of your money = 1/2 of our money

Filed under arithmetic, fractions

## Fractions are parts of the same whole, part 2

When is a whole not a whole ?

When it’s a hole.

(which half of the hole shall we fill first, the top half or the bottom half?)

Besides, I thought whole was an adjective.