7. How many metric tons are there in each of the f lowing: 678 Kg.; 437 Kg.; 308 Kg.; 8,503 Dg.; 30,456 K 8. What is the cost of 5 Dm. 7 m. 8 dm. cloth at $2. per meter?

9. What is the value of 6.473 Hl. milk at 12 ¢ per lite 10. How long will it take to ride 9,834.7 Dm. at the ra of 31 Km. per hour?

97. Equivalents of Metric Units in English Units.

State without the use of pencil and paper about wh amount must be bought in metric weights or measures get each of the following:

1.

6 lb.; 12 lb.; 25 lb.; 100 lb.; 36 lb.; 16 lb. 2. 5 T.; 8 T.; 32 T.; 56 T.; 100 T.

3.

6 yd.; 12 yd.; 5 yd.; 40 yd.; 8 yd.

4. 2 qt.; 6 qt.; 3 gal.; 8 gal.; 2 gal.; 3 qt.

5.

The sum of the metric tons in Ex. 7, above, is equal about how many of our tons?

6. Mary's father gave her 5 yd. of cloth for a dres About how many meters was this?

7. Coal sold last year for $4.50 per ton. About wh would this be per ton after the metric system has bee adopted?

8. What will be the cost per meter of cloth selling f 35¢ per yard? for 60 ¢ per yard? for $1.25 per yard?

VI

LITERAL NUMBERS

98. Arithmetical Equation.-Mathematicians use of shorthand in making statements. These statemen sist of mathematical symbols and letters. The letters the places of words are usually the first of the word. the place of

Minuend minus subtrahend equals remain

is written M

S

=

Ꭱ

Similarly,

total price equals number of articles times price of o

P

=

n

X

Ρ

Each expression, as (1) and (2), is called an equati states that two numbers, or sets of numbers, are that is, they have the same value. The parts on ea of the equals sign are called the members of the eq Every letter in the equation represents some number

An equation shows at a glance the relation betwe numbers it contains. Equations will be used to si the solution of problems. Hence, learn thoroughly 1 make and to use these shorthand statements.

To express that Henry is 15 yr. older than George,

The small H and G tell whose age is meant. Small or numerals placed at the lower right-hand corner are

Write each of the following statements in full. Then write them in this shorthand mathematics.

and the left hand members of each equation.

1.

State the ri

Minuend equals remainder plus subtrahend.

2. Dividend equals divisor times quotient plus remaind (Use D and d for dividend and divisor.)

3. Dividend minus divisor times quotient equals mainder.

4. The larger of two numbers equals the smaller p six. (Use N and n.)

5. The larger of two numbers is four times the small 6. The larger of two numbers less the smaller equals f times the smaller number.

Express each of the following as an equation:

7. The larger of two numbers exceeds twice the sma by 13.

8. Profits equal total sales less total expenses.

9.

Total sales less profits equal total expenses. 10. Total sales less profits less expenses equal nothing 11. Total profits equal total sales times rate of gain. 12. Loss equals total expenses less total sales. 13. Give the equations for losses corresponding to statements 9, 10, and 11 for profits.

14. Mary is twice as old as Jane.

15. Henry is 5 yr. older than William.

16.

Elizabeth is 6 yr. more than twice as old as May 17. James weighs twice as much as Harry.

John weighs 6 lb. less than twice as much as Ha
William weighs as much as Henry and John togeth

The numerator of a fraction is 2 more than 5 tir

values in an equation is called evaluation or subs Thus, if in

D= d X q + r
զ

(1)

the quotient is 4, divisor 7, and remainder 3, the divi found by replacing the letters in the equation by numerical values when

1. Find the dividend when the quotient is 8, di and remainder 4; quotient 17, divisor 9, and remain 2. In division we also have

r = D-dXq.

Find r when D =

532, d = 25, and q = 21.

If N and n are two numbers, what is the equivale

lish expression of the equations:

3. N = n + 12.

4. N = 3 x n.

7.

Find N for each equation when n = 6;

8. What would the letters M, S, and R stand for traction? Fill in the right-hand members of the fo equations using these meanings of the letters:

12. Play a number game, using equations and su

tions

100. Solution of Equations.-If an equation contain only one literal number, its numerical value can be foun Finding this value is called solving the equation. Th numerical value of the literal number found is called th root of the equation.

The equation stating that five times a number equals 30

Hereafter 5 X n, 7 × n, etc., will be written 5n, 7n, et 5n, 7n, etc., mean that there are 5 n's, 7 n's, etc.

Solutions of equations depend upon the following: Both members of an equation may be multiplied or divided b the same number and still leave a true equation. 2. The sam number may be added to, or subtracted from, both members an equation and still leave a true equation.

The left-hand member is 5n. If this be divided by 5 th quotient will be n. Why? This will equal the right-han member also divided by 5. Hence,

EXERCISES

1. How much is 30 times any number divided by 3 divided by 2? divided by 5? divided by 10? divide by 30?

2. How much is 30n3? 30n ÷ 2? 30n 10 30n5? 30n ÷ 30?

3. By what would you divide 12n to get 3n? to g 4n? to get 6n? to get 2n? to get n?

Solve the following equations: