MENTAL ARITHMETIC

QUANTITY-UNIT-NUMBER

Lesson 1

1. Make a mental picture of a line 12 in. long and also of a unit of measure 3 in. long. How many times will the 3-in. unit measure the quantity 12 in.?

2. The number 4 obtained in example 1 is 4 what? 4 units of 3-in. in what?

3. This number 4 is often called the ratio of 12 in. to 3 in. What is the ratio of 12 in. to 4 in. ?

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4. What part of 12 in. is equal to 3 in.? often called the ratio of 3 in. to 12 in. What is the

ratio of 4 in. to 12 in.?

5. Find the number of 3-in. units of length in each of these quantities: 15 in.; 2 ft.; 30 in.; 1 yd.; 1 ft. 6 in.; 2 ft. 3 in. What is the ratio of each of these quantities to the unit? Of the unit to each quantity?

6. In question 5 how did you find the number of 3-in. units in each quantity?

7. How would you find the number of 2-in. units in a given quantity? Of 3-in. units? Of 4-in. units? Of units of any length?

8. Find the number of 2-in. units in each of these quantities: 14 in., 1 ft. 8 in., 24 in.; 2 ft. 6 in.; 1 yd. 4 in.; 1 yd. 1 ft.

9. In questions 10-15 name the quantity and the unit in each case. How will you find the number of units in each quantity?

10. Into how many hair ribbons, each 9 in. long, can you divide a piece 36 in. ?

11. A can contains 12 qt. of milk. How many pitchers, each containing 3 pt., can be filled with its contents?

12. A furnace burns on the average 5 T. of coal a month. In how many months will it burn 40 T.?

13. How many pounds of sugar at 6¢ a lb. will cost 48¢? How many pounds of sugar at 5¢ a lb. will cost $2?

14. How many barrels of flour at $5 a bbl. will cost $45?

15. How many pounds of raisins at 8 a lb. will cost 56?

16. In questions 10-15 the number that you found in each case was the number of what? This number is often called the ratio of the quantity to the unit.

17. How many widths of carpet 3 ft. wide are needed to carpet a room 6 yd. wide? In terms of what unit must you express both the quantity 6 yd. and the unit 3 ft. before dividing?

18. How many strips of paper 2 ft. wide are needed to cover the walls of a room whose perimeter is 20 yd.?

19. How many quarts of milk at 6 a qt. will cost $1.80?

20. In the following examples what numbers express the measurements?

21. What is the ratio of each quantity in example 20 to its own unit? What is the ratio of the unit to the quantity?

22. A man earns $15 a week and spends $11. In how many weeks will he save $136? What is the unit here?

23. Two boats travel up a river at the rate of 12 and 9 mi. per hour, respectively. If they start together, when will the faster be 36 mi. ahead?