Question

How many bows can you make from `3 2/3` meters of ribbon if `1/4` of a meter of ribbon makes one bow?

Answer 1

You can make 14 bows. with some ribbon left over

Explanation:

There are two ways that students can TEACH THEMSELVES how to go about solving confusing problems like this.

`color(white)(mmmmmmmm)`Self-teaching Method One

`"Drastically simplify the problem"`

1) Simplify the problem so that it is obvious `"how to"` solve it.
2) Then use the exact same method to solve the hard problem

Here is a `"Drastically simplified"` re-write of this problem:

You have ONE yard of fabric
It takes 1/2 a yard to make a bow
How many bows can you make?

You obviously know that you can make `2` bows.

Here is how you automatically solved it in your head:
You thought "One yard divided into half-yard pieces"

`1 -: "1/2" = 2`   (To divide fractions, you multiply by the reciprocal of the divisor)

This easy problem SELF-TAUGHT you the correct procedure:
`"Divide the total length by the length of each bow"`

`3 (2)/(3) -: (1)/(4)`  Now multiply by the reciprocal of the divisor

`(11)/(3) xx (4)/(1)`

You can make 14 bows. with some ribbon left over `larr` Answer

`color(white)(mmmmmmmm)`――――――――――――

`color(white)(mmmmmmmm)`Self-Teaching Method Two

`"Change the problem to money"`

People have good intuition when it comes to money, so re-writing a word problem as a money problem can let you see how to solve it.

`"You have $3.66. How many times can you spend 25ȼ?"`
This re-write is exactly the same as
"You have 3 2/3 yards. How many times can you use 1/4 yard?"

Probably you solved the money problem by thinking:
"I can get four quarters out of each of the three dollars.
Then I can get two more quarters out of the 66ȼ.

So I can make 4 bows from each of the 3 yards, and two more bows from the 2/3 of a yard

That comes to (4)(3) + 2

You can make 14 bows, with some ribbon left over `larr` Same answer