The parallel equally spaced lines

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

DONE !

The parallel equally spaced lines

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

DONE !

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Filed under fractions, Uncategorized

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 :

denominators. As the common denominator, choose the LCM of

the original denominators. Then the larger the numerator, the

larger the fraction.

since if denominators are same, we just need to find LCM of

numerators, hence LCM of (a/b) and (c/b) would be LCM(a,c)/b.

So we have to first make denominators of both the fractions same.

Multiply numerator and denominator of first fraction by LCM

(b,d)/b.

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

I found this on Quora. What would the standard algorithm be, I wonder.

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Filed under arithmetic, fractions, math, operations

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”.

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

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

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

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

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

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.