Ray's New Higher Arithmetic · Arts. 221–222 · Unit 11: Compound Denominate Numbers
55. Adding and subtracting compound numbers
Goal: Your student adds and subtracts quantities written in several denominations, carrying and borrowing by the right scale.
You'll need
- The book
- A slate, small whiteboard or scrap paper
- A notebook and pencil
What's in the book
Compound numbers can be added, subtracted, multiplied and divided like simple numbers, but with varying scales. Addition: definition, worked examples, the rule and 25 examples. Subtraction: the rule, worked examples (9 yd. 1 ft. 6½ in. − 1 yd. 2.45 ft.), and 26 examples, including angles and dates. Answers are printed.
The lesson, step by step
Warm-up
Mental: 40 minutes + 35 minutes as hours and minutes. 1 ft. − 5 in.
The idea
Read:
Compound Numbers may be added, subtracted, multiplied, and divided.
The only difference from simple numbers: you carry and borrow by 12, 16, 60 or whatever the table says, not always by 10.
Adding
Read:
Addition of Compound Numbers is the process of finding the sum of two or more similar Compound Numbers.
Write the remainder under the column added, and carry the quotient to the next column.
Work: 5 hr. 40 min. + 3 hr. 35 min. = 8 hr. 75 min. = 9 hr. 15 min.
Subtracting
Read:
Place the subtrahend under the minuend, so that numbers of the same denomination stand in the same column.
Work the book's example: From 9 yd. 1 ft. 6½ in. take 1 yd. 2.45 ft. The answer is 7 yd. 2 ft. 1.1 in. Follow the book's working to see how it borrows.
Guided practice
Together:
Subtract 43° 18' 57.18" from a quadrant.
Subtract 161° 34' 11.8" from 180°.
(46° 41' 2.82"; 18° 25' 48.2".)
Independent practice
Your student works a selection of the addition and subtraction examples.
Check
Answers are printed; the scan of the addition answers is faint, so add the numbers back in a different order to check. Read the book's remark:
The proof of each fundamental operation in Compound Numbers is the same as in Simple Numbers.
Wrap-up
Ask: When you borrow from the feet column to the inches column, how many do you add? (12.)
Afterwards
Two sittings: addition one day, subtraction the next.