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:

  1. A reed is a              of a rod.

  2. A pace is a              of a reed.

  3. A cubit is a              of a pace.
Now, write the same facts using math sentences:
1 reed =      rod1 pace =      reed1 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.

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

  2. 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 =      rod1 pace =      rod1 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.
  1. Seven reeds



  2. Eleven paces



  3. 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.
  1. Three rods and five cubits


  2. A rod and a reed


  3. Four rods and two paces


  4. Two rods, a reed, and a pace
    Hint: convert the reed into paces


  5. Three rods, two paces, and a cubit
    Hint: convert the paces into cubits


  6. 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.
  1. If there are seven blorbs in a krebf, what fraction of a krebf are three blorbs?



  2. 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?



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



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



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