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

Mar 6, 2018

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.

$\textcolor{w h i t e}{m m m m m m m m}$Self-teaching Method One

$\text{Drastically simplify the problem}$

1) Simplify the problem so that it is obvious $\text{how to}$ solve it.
2) Then use the exact same method to solve the hard problem

Here is a $\text{Drastically simplified}$ 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.

You thought "One yard divided into half-yard pieces"

$1 \div \text{1/2} = 2$   (To divide fractions, you multiply by the reciprocal of the divisor)

This easy problem SELF-TAUGHT you the correct procedure:
$\text{Divide the total length by the length of each bow}$

$3 \frac{2}{3} \div \frac{1}{4}$  Now multiply by the reciprocal of the divisor

$\frac{11}{3} \times \frac{4}{1}$

You can make 14 bows. with some ribbon left over $\leftarrow$ Answer

$\textcolor{w h i t e}{m m m m m m m m}$――――――――――――

$\textcolor{w h i t e}{m m m m m m m m}$Self-Teaching Method Two

$\text{Change the problem to money}$

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.

$\text{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 $\leftarrow\$ Same answer