Do-Now: Figuring out the fractionsThe length measures shown below were used in ancient Mesopotamia for thousands of years:
Based on that picture, fill in the following sentences with words:
Now, write the same facts using math sentences:
- A reed is a of a rod.
- A pace is a of a reed.
- A cubit is a of a pace.
|1 reed = rod||1 pace = reed||1 cubit = pace|
Unit fractions of a rodNext, we will use the facts above to figure out what fraction of a rod a pace or cubit is.
Now, write those same facts using math sentences:
- 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.
|1 reed = rod||1 pace = rod||1 cubit = rod|
Writing fractional amountsFractions 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 amountsAn 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 HomeworkFor 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?