# Unit Fractions

**Friday 11/7/08**

### Do-Now: Figuring out the fractions

The length measures shown below were used in ancient Mesopotamia for thousands of years:

Based on that picture, fill in the following sentences with words:

- A reed is a
__ __ of a rod.

- A pace is a
__ __ of a reed.

- A cubit is a
__ __ of a pace.

Now, write the same facts using math sentences:1 reed = __ __ rod | 1 pace = __ __ reed | 1 cubit = __ __ pace |
---|

### Unit fractions of a rod

Next, we will use the facts above to figure out what fraction of a rod a pace or cubit is.

- Since a pace is a
__ __ of a reed, which is a __ __ of a rod, a pace would be a __ __ of a rod.

- Since a cubit is a
__ __ of a pace, which we just discovered is a __ __ of a rod, a cubit would be a __ __ of a rod.

Now, write those same facts using math sentences:1 reed = __ __ rod | 1 pace = __ __ rod | 1 cubit = __ __ rod |
---|

### Writing fractional amounts

Fractions like the ones you have been using so far are called **unit fractions** because they act like units: they tell you the size of thing you are working with, whereas the **numerator** of the fraction will then tell you the number of those units that you have. So, a sixth of a rod is a particular size of thing; if I write 5/6 rod, I mean that I have five of them.

For each of the following, refer to the unit fractions you know from above to write the measurement as a fraction of a rod. Then, write out in words how you would read that fraction.- Seven reeds

- Eleven paces

- Five cubits

### Writing mixed number amounts

An amount with both a whole number of rods and another set of units as well can be written as a mixed number of rods. So, for example:

2 rods + 4 paces = 2 rods + 4/6 rod = 2 4/6 rod

I read this measurement as "Two and four sixths of a rod," and I picture it as two whole rods, plus two parts taken from a rod that has been broken into six pieces.

For each of the measurements below, write it as a mixed number of rods. Then, write out in words how you would read that.- Three rods and five cubits

- A rod and a reed

- Four rods and two paces

- Two rods, a reed, and a pace

*Hint: convert the reed into paces*

- Three rods, two paces, and a cubit

*Hint: convert the paces into cubits*

- Four rods, a reed, two paces, and a cubit

# Unit Fractions Homework

For each problem, write out your answer using math, but then **also write it out in words**.- If there are seven blorbs in a krebf, what fraction of a krebf are three blorbs?

- If a nitfol is a fourth of a gnusto, and a cleesh is a third of a nitfol, what fraction of a gnusto is a cleesh?

- How would I write three pints as a fraction of a gallons?

- How would I write a gallon and nine cups as a mixed number of gallons?

- How would I write three cups, two pints, a quart, and two gallons as a mixed number of gallons?