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

1 Answer
Mar 6, 2018

Answer:

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