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

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Mar 7, 2018


You can make 14 bows. with some ribbon left over


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)#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

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