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

**Our answer** is \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: \begin{align*}3 \frac{1}{2}\end{align*} inches**

#### Example B

Locate \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 \begin{align*}3 \frac{1}{4}\end{align*} inches long.

**This is our answer.**

### 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?

**Answer**

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

### Video Review

MathLessons: How to Convert Inches Into a Fraction

### 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.