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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

Have you ever had to measure something, and it wasn't an even inch? Here is a situation just like that one.

Margaret and Sarah are working in the art room. They are making mosaics. To make a mosaic, you have to cut a piece of cardboard or wood, then you glue different colored tiles onto the wood or cardboard to make a picture.

Sarah has measured her wood, and has measured her tiles. She is trying to figure out how many tiles to put horizontally on the piece of wood. This is tricky because the tiles aren't an even measure. Sarah has chosen a really beautiful tile, but she has this dilemma.

Here is what her ruler says:

Do you know what the side length of the tile is?

This Concept is all about measuring lengths to a fraction of an inch. When finished, you will know how to help Sarah.

### Guidance

One of the places that we often see fractions in real life is when we measure different things. 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 1216\begin{align*}\frac{12}{16}\end{align*} or 34\begin{align*}\frac{3}{4}\end{align*} (three fourths) of an inch.

If you look at this ruler, you will see that the arrow is above a line that does not indicate one whole inch. We need to use our fractions to write this fraction of an inch. If we were to count the lines, we would see that the arrow is above the eighth line. Here is our measurement to a fraction of an inch.

Our answer is 816\begin{align*}\frac{8}{16}\end{align*} or 12\begin{align*}\frac{1}{2}\end{align*}.

We can also have an example where we have a whole number measurement and then a fraction of another inch.

To measure this measurement, we can see that we have 1 and a fraction of an inch. If you look you can see that the arrow is above 11216\begin{align*}1 \frac{12}{16}\end{align*} or 134\begin{align*}1 \frac{3}{4}\end{align*}.

Our answer is 134\begin{align*}1 \frac{3}{4}\end{align*}.

Now it is time for you to try a few on your own. Simplify the fraction too.

#### Example A

What is the second quarter inch between 3 and 4?

Solution: 312\begin{align*}3 \frac{1}{2}\end{align*} inches

#### Example B

Locate 212\begin{align*}2 \frac{1}{2}\end{align*} inches on a ruler. Check your answer with a friend.

Solution: The line should be exactly half - way between 2 and 3.

#### Example C

How many parts is a ruler divided into?

Solution: 16 parts

Now back to the original dilemma about tile.

Margaret and Sarah are working in the art room. They are making mosaics. To make a mosaic, you have to cut a piece of cardboard or wood, then you glue different colored tiles onto the wood or cardboard to make a picture.

Sarah has measured her wood, and has measured her tiles. She is trying to figure out how many tiles to put horizontally on the piece of wood. This is tricky because the tiles aren't an even measure. Sarah has chosen a really beautiful tile, but she has this dilemma.

Here is what her ruler says:

Do you know what the side length of the tile is?

If you look at this measurement, you will see that it is between 3 and 4 inches. The first longer line has been indicated by the arrow. This is the first quarter inch.

Sarah's tile is 314\begin{align*}3 \frac{1}{4}\end{align*} inches long.

### Vocabulary

Measurement
using different units to figure out the weight, height, length or size of different things.
Length
how long an item is
Customary units of length
units of measurement such as inches, feet, yards and miles
Inches
the smallest customary units of measurement, measured best by a ruler
Foot
a customary unit of measurement, there are 12 inches in 1 foot
Yard
a customary unit of measurement, there are 3 feet in 1 yard
Mile
a customary unit for measuring distances, there are 5280 feet in 1 mile

### Guided Practice

Here is one for you to try on your own.

What is the measure of the crayon?

The crayon is 334\begin{align*}3 \frac{3}{4}\end{align*} inches.

### Practice

Directions: The best way to learn how to measure lengths to a fraction of an inch is to practice. For this practice set, you will be working with a partner. You will each need a ruler. Now follow these directions.

1. Find 15 items of all different sizes.

2. Next, you should each 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.

### Vocabulary Language: English

Customary units of length

Customary units of length

Customary units of length include: inches, feet, yards and miles.
Foot

Foot

A foot is a customary unit of measurement. There are 12 inches in 1 foot.
Inches

Inches

An inch is a customary unit of measurement, measured best by a ruler.
Length

Length

Length is a measurement of how long something is. Examples of customary units of length are inches, feet, yards and miles.
Measurement

Measurement

A measurement is the weight, height, length or size of something.
Mile

Mile

A mile is a customary unit for measuring distance. There are 5280 feet in 1 mile.
Yard

Yard

A yard is a customary unit of measurement. There are 3 feet in 1 yard.