Mathematics Tasks?l Know the best brains would answer this questions .Many thanks?

Question

Question 1 .The standard procedure for dividing by a fraction is to turn upside down and multiply.how would you justify this rule to a child?What higher level of mathematics informs your understanding of the procedure?

Question 2.Tiles in the shape of regular hexagons can be used to cover any plane surface,but those in the form of regular pentagons cannot ,by themselves,be used to tiling an area.How might a teacher use this activity to enable children to deduce some facts about angles in polygons?How might examples from art or architecture be included to enhance study of the topic

Answer 1

1) You could describe how this works with fractions like 1/2, 1/3, 1/4, etc. When you divide a set of objects into halves, you have twice as many pieces as you did before. When you divide a set of objects into thirds, you have three times as many as you did before, etc.

As for a "higher level math" justification, we can prove that dividing a fraction by c/d is the same as multiplying it by d/c:

(a/b) / (c/d) =
[ (a/b) / (c/d) ] * 1 =
[ (a/b) / (c/d) ] * (d/d) =
(a/b)d / (c/d)d =
(ad / b) / c =
[(ad / b) / c ] * (c/c) =
[(ad / b)c / c ] * (1/c) =
[(ad / b) / 1 ] * (1/c) =
[ad / b] * (1/c) =
[ad / bc] =
(a/b) * (d/c)

2) Give the students pentagon-shaped tiles and ask if they can connect them to make a flat surface with no holes. Look at honey comb patterns, bathroom tile patterns, etc..

Answer 2

Yes, we tell our pupils to divide fractions this way, and they never question it, do they ? Now, it`s going to be hard to show you because I can`t show fractions properly on here, so you`ll have to follow it as best you can. I`m going to take an example:

3/4 divided by 7/8, which we can write as:

3/4
___ I`m now going to multiply top and bottom of this by 8/7:
7/8

= 3/4 x 8/7
________
7/8 x 8/7

8/7 over 8/7 is 1, so I haven`t changed the number value of the fraction, just changed the way it`s written. The bottom line, 7/8 x 8/7 becomes 1, so because we`re dividing, we can ignore it. So, the sum now becomes:
3/4 x 8/7

and that`s why we tell them to turn the second one upside down and multiply.

I hope you find this clear, and useful, Twiggy.

Answer 3

Fractions are a numerical convention. The number above the line is divided by the number below the line.
When you multiply a number by a fraction, you first multiply by what's above the line (the multiplicand) and then divide by what's under the line (the divisor). To divide a number by a fraction, you multiply it by the divisor and divide it by the multiplicand - in other words turn the fraction upside down and multiply it. There's no mystery in this. It's what fractions mean.

To cover an area with regular polygons, the angles at a node (where the corners meet up) have to add up to 360 degrees. That's only true with equilateral triangles, squares and regular hexagons.

Answer 4

For question a million an understanding of section could help of course. you will desire to to start with the part of an straightforward sq.. possibly use the lecture room or their desks as an occasion and function them degree the distances. i think of having the ability to *see* something enables with the assumption of section. question 2 - properly, there are 4 letters, maximum suitable? each and each letter represents a diverse term. possibly have money characterize each and each term. A penny is A, a nickel is B, a dime is C, and 1 / 4 is D. you do no longer could use the decimals unavoidably, you may in simple terms use a million, 5, 10, and 25. those are straightforward ones to learn the two aspects of the equation to. babies have the main subject with algebra (in my adventure) in simple terms in accepting that the letter represents a variety. I teach some bigger point math and usually could revert back to person-friendly algebraic equations to make factors. i understand that doesn't answer your total question, yet i'm hoping it enables a minimum of.

Answer 5

1) Because multiplication is the opposite of division. Division is the opposite of multiplication. If you are dividing fractions and turn one upside down then you have the opposite fraction and then can multiply.