Ray's New Higher Arithmetic · Arts. 223–224 · Unit 11: Compound Denominate Numbers
56. Multiplying and dividing compound numbers
Goal: Your student multiplies and divides compound numbers, carrying and reducing remainders 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
Multiplication of compound numbers (definition, the example 9 hr. 14 min. 8.17 sec. × 10, the rule, 14 examples) and division (two cases, the example of sugar shared among 4 men, the rule, and 12 examples). Answers are printed.
The lesson, step by step
Warm-up
Mental: 3 × (2 ft. 8 in.); half of 5 lb. 4 oz.
Multiplying
Read:
the process of multiplying a Compound Number by an Abstract Number.
Work the book's example: 9 hr. 14 min. 8.17 sec. × 10. Seconds: 81.7 = 1 min. 21.7 sec. Minutes: 140 + 1 = 141 = 2 hr. 21 min. Hours: 90 + 2 = 92 hr. = 3 da. 20 hr. Answer 3 da. 20 hr. 21 min. 21.7 sec.
Guided practice
Together:
Multiply 26 bu. 2 pk. 7 qt. .37 pt. by 10.
(267 bu. 7 qt. 1.7 pt.)
Dividing
Read:
Division of Compound Numbers is the process of dividing when the dividend is a Compound Number.
If a remainder occur after any division, reduce it to the next lower denomination
Work the book's sugar example: 5 cwt. 3 qr. 24 lb. 14¾ oz. among 4 men gives each 1 cwt. 1 qr. 24 lb. 15 11/16 oz.
Second case
Read:
Problems under the second case are solved by reducing both Compound Numbers to the same denomination.
Try: How many 2 ft. 6 in. pieces can be cut from 20 ft.? (240 in. ÷ 30 in. = 8.)
Independent practice
Your student works a selection, including:
Divide 16 mi. 109 rd. by 7.
(2 mi. 107 rd.)
Wrap-up
Ask: Can you multiply a compound number by a compound number, say 3 ft. × 2 ft.? (Not in this chapter: the multiplier must be abstract. Areas come later.)