Here is what her ruler says:

What size hinge should she be looking for?

In this concept, you will learn how to measure lengths to a fraction of an inch.

### Measuring Lengths Using Fractions

Think about using a ruler, sometimes you will have something that measures evenly, meaning that the item measures in whole inches. More often, you will have an item that does not measure evenly. When this happens, you will need to measure the item to a **fraction** of an inch.

Each whole inch has sixteen lines. This is because one inch is \begin{align*}\frac{8}{16}\end{align*} or (one half) of an inch. Count to the twelfth line is or (three fourths) of an inch.

of an inch long. Count four lines, you are at or (a quarter) of an inch. Count to the eighth line, you are atLook at this ruler.

The arrow is above a line that does not indicate one whole inch. Use fractions to write this fraction of an inch. Count the lines. The arrow is above the eighth line. Write the measurement as a fraction of an inch.

Measurements are often written as a fraction in simplest form. \begin{align*}\frac{8}{16}\end{align*} in simplest form is equal to . The measurement is or inch.

Here is an example of a whole number measurement with a fraction of another inch.

This measurement is 1 inch and a fraction of another inch. The arrow is above \begin{align*}\frac{12}{16}\end{align*} in simplest form is . This measurement is or inches.

.Notice that a ruler has lines with four different lengths. The longest line on the ruler indicates a whole inch. The second longest line indicates a half

inch. The line shorter than the half inch line marks a quarter inch. Some rulers have marks for an eighth of an inch, like the image below.### Examples

#### Example 1

Earlier, you were given a problem about Meg’s door hinge.

Find the measurement of her door hinge to a fraction of an inch.

Here is what her ruler says:

The measurement is between 3 and 4 inches. The arrow is pointing to the quarter inch mark.

Meg’s is looking for a door hinge that is

inch long.#### Example 2

What is the measurement of the crayon?

First, look at the measurement of the crayon. It is between 3 and 4 inches long. Count the number of lines after the 3 inch mark. It is

of an inch beyond the 3 inch mark.Then, simplify \begin{align*}\frac{10}{16}\end{align*}.

The crayon is

inches.#### Example 3

What is the second quarter inch between 3 and 4?

The second quarter inch is also

.

The second quarter inch between 3 and 4 is

inch.#### Example 4

Locate

inches on a ruler. Check your answer with a friend.Look on the ruler. The line should be exactly half - way between 2 and 3.

#### Example 5

How many parts is an inch divided into on a ruler?

An inch is divided into 16 parts.

### Review

Work with a partner and follow the directions. You will need a ruler.

- Find 15 items of all different sizes.
- Next, make a list of the names of the items that you have selected.
- Measure each item and write down the measurements. Do this independently.
- Compare measurements with your partner.
- Discuss any discrepancies and make adjustments as needed.

### Review (Answers)

To see the Review answers, open this PDF file and look for section 5.13.