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# Length Measurements to a Fraction of an Inch

## Measuring using 16ths

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Practice Length Measurements to a Fraction of an Inch

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Length Measurements to a Fraction of an Inch
Meg is looking to replace a door hinge that broke. She’s shopping online for the hinge, but the measurements are all listed in fractions of inches. She measured the size of the hinge on a ruler.

Here is what her ruler says:

License: CC BY-NC 3.0

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 1616\begin{align*}\frac{16}{16}\end{align*} of an inch long. Count four lines, you are at 416\begin{align*}\frac{4}{16}\end{align*} or 14\begin{align*}\frac{1}{4}\end{align*} (a quarter) of an inch. Count to the eighth line, you are at 816\begin{align*}\frac{8}{16}\end{align*} or 12\begin{align*}\frac{1}{2}\end{align*} (one half) of an inch. Count to the twelfth line is 1210\begin{align*}\frac{12}{10}\end{align*} or 34\begin{align*}\frac{3}{4}\end{align*} (three fourths) of an inch.

Look at this ruler.

License: CC BY-NC 3.0

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.

816\begin{align*}\frac{8}{16}\end{align*}

Measurements are often written as a fraction in simplest form. 816\begin{align*}\frac{8}{16}\end{align*} in simplest form is equal to 12\begin{align*}\frac{1}{2}\end{align*}. The measurement is 816\begin{align*}\frac{8}{16}\end{align*} or 12\begin{align*}\frac{1}{2}\end{align*} inch.

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

License: CC BY-NC 3.0

This measurement is 1 inch and a fraction of another inch. The arrow is above 11216\begin{align*}1\frac{12}{16}\end{align*}. 1216\begin{align*}\frac{12}{16}\end{align*} in simplest form is 34\begin{align*}\frac{3}{4}\end{align*}. This measurement is 11216\begin{align*}1\frac{12}{16}\end{align*} or 134\begin{align*}1\frac{3}{4}\end{align*} 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 (12)\begin{align*}\left ( \frac{1}{2} \right )\end{align*} inch. The line shorter than the half inch line marks a quarter (14)\begin{align*}\left ( \frac{1}{4} \right )\end{align*} inch. Some rulers have marks for an eighth (18)\begin{align*}\left ( \frac{1}{8} \right )\end{align*} 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:

License: CC BY-NC 3.0

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 314\begin{align*}3\frac{1}{4}\end{align*} inch long.

#### Example 2

What is the measurement of the crayon?

License: CC BY-NC 3.0

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 1016\begin{align*}\frac{10}{16}\end{align*} of an inch beyond the 3 inch mark.

Then, simplify 1016\begin{align*}\frac{10}{16}\end{align*}.

1016=58\begin{align*}\frac{10}{16} = \frac{5}{8}\end{align*}

The crayon is 358\begin{align*}\frac{35}{8}\end{align*} inches.

#### Example 3

What is the second quarter inch between 3 and 4?

The second quarter inch is also 24\begin{align*}\frac{2}{4}\end{align*}.

24=12\begin{align*}\frac{2}{4} = \frac{1}{2}\end{align*}

The second quarter inch between 3 and 4 is 312\begin{align*}3\frac{1}{2}\end{align*} inch.

#### Example 4

Locate 212\begin{align*}2 \frac{1}{2}\end{align*} 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.

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

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

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### Vocabulary Language: English

TermDefinition
Customary units of length Customary units of length include: inches, feet, yards and miles.
Foot A foot is a customary unit of measurement. There are 12 inches in 1 foot.
Inches An inch is a customary unit of measurement, measured best by a ruler.
Length Length is a measurement of how long something is. Examples of customary units of length are inches, feet, yards and miles.
Measurement A measurement is the weight, height, length or size of something.
Mile A mile is a customary unit for measuring distance. There are 5280 feet in 1 mile.
Yard A yard is a customary unit of measurement. There are 3 feet in 1 yard.