Ray's New Higher Arithmetic · General Problems; Miscellaneous Exercises · Unit 6: Division
23. General problems and miscellaneous exercises
Goal: Your student says in words how to find any missing number among sum, difference, product, dividend, divisor and quotient, and solves mixed problems.
You'll need
- The book
- A slate, small whiteboard or scrap paper
- A notebook and pencil
What's in the book
Fourteen general questions (for example, when the product of two numbers and one of them are given, how is the other found?), then about 25 miscellaneous word problems on pages 56 to 58 with printed answers. The scan of page 58 was not checked for this guide.
The lesson, step by step
Warm-up
Mental: A number times 7 is 84. What is the number?
General problems
Read and answer aloud, one by one:
When the sum of two numbers, and one of them, are given, how is the other found?
If the dividend and quotient are given, how do you find the divisor?
Your student answers all 14 in full sentences. These have no printed answers; they are below.
Guided practice
Together:
A grocer gave 153 barrels of flour, worth $6 a barrel, for 54 barrels of sugar: what did the sugar cost per barrel?
When the divisor is 35, quotient 217, and remainder 25, what is the dividend?
($17; 7620.)
Independent practice
Your student works the miscellaneous exercises from 3 onward. For each, first write which operation(s) it needs, then solve.
Check
The book prints the answers.
Wrap-up
Your student writes one word problem for each of the four operations for you to solve.
Afterwards
The miscellaneous exercises make good review for two or three days.
Answers to the book's problems
General problems (in words): 1) add the separate costs; 2) subtract the given number from the sum; 3) add the difference to the less; 4) subtract the difference from the greater; 5) multiply the cost of one by the number; 6) divide the total cost by the number of articles; 7) multiply the divisor by the quotient; 8) divide the number by the size of each part; 9) divide the number by the number of parts; 10) divide the product by the given factor; 11) divide the dividend by the quotient; 12) divide the product by the product of the two given numbers; 13) multiply divisor by quotient and add the remainder; 14) subtract the remainder from the dividend and divide by the quotient.
Worked out for this site from the scan. If a number in your copy differs, trust the book.