Chapter 6.6, Problem 1P

Sue needs to cut a piece of wood 0.4 of an inch thick, or just a little less thick. Sue's ruler shows sixteenths of an inch. How many sixteenths of an inch thick should Sue cut her piece of wood? What type of division problem is this?

To determine

Tocalculate : number of sixteenths on an inch thick Sue cuts her piece of wood and identify the type of division problem

Answer to Problem 1P

The given word problem is a problem for $\boxed{0.4÷\frac{1}{16}}$ ; it is a how-many-groups division problem. The number of sixteenths on an inch thick Sue cuts her piece of wood is $\boxed{6\frac{2}{5}}$

Explanation of Solution

Given information : Sue needs to cut a piece of wood 0.4 of an inch thick, or just a little less thick. Sue’s ruler shows sixteenths of an inch.

Formula used :

Invert and Multiply: To divide fraction such as $\frac{A}{B}÷\frac{C}{D},$ the standard procedure is to “invert and multiply” by inverting the divisor and multiplying by it. $\frac{A}{B}÷\frac{C}{D}=\frac{A}{B}\times \frac{D}{C}$

In other words, to divide fractions, multiply the dividend by the reciprocal of the divisor.

Concept Involved :

If we say that  $a\times b$ means  $a$ groupsof $b$ units, then

• a division situation where  $b$ units and $a\times b$ units are known but  $a$ groups is unknown is called a “how many groups?” division problem
• a division situation where  $a$  group and $a\times b$ units are known but  $b$ units is unknown is called a “how-many-units-in-1-group?” division problem

Since each $\frac{1}{16}$ of an inch represent a group, and “number of $\frac{1}{16}$ an inch thick pieces of wood” represent the number of groups, the problem uses the “how many group” interpretation.

Calculation:

To find the number of one-sixteenth $\frac{1}{16}$ inch thick pieces in 0.4 of an inch thick piece of wood, solve the division problem $0.4÷\frac{1}{16}$

To rewrite the decimal 0.4 to fraction
Step 1: Write down the decimal divided by 1, like this: decimal 1.	$\frac{0.4}{1}$
Step 2: Multiply both top and bottom by 10 for every number after the decimal point. (For example, if there are two numbers after the decimal point, then use 100, if there are three then use 1000, etc.)	$\frac{0.4\times 10}{1\times 10}=\frac{4}{10}$
Step 3: Simplify (or reduce) the fraction.	$\frac{4÷2}{10÷2}=\frac{2}{5}$

To find the number of one-sixteenth $\frac{1}{16}$ inch thick pieces in 0.4 of an inch thick piece of wood, solve the division problem $0.4÷\frac{1}{16}$
Since we already know 0.4 is equivalent to 2/5, we can set up Dividing fraction	$\frac{2}{5}÷\frac{1}{16}$
When dividing fraction we need to “invert and multiply”, that is flip the second fraction and change the division problem to multiplication	$=\frac{2}{5}\times \frac{16}{1}$
When multiplying fraction multiply numerator with numerator and denominator with denominator	$=\frac{2\cdot 16}{5\cdot 1}=\frac{32}{5}$
We need to rewrite the mixed fraction to improper fraction	$=6\frac{2}{5}$