QUESTIONS.

OF CALIFORNIA

41

6. What name is given to the first period at the right of the decimal point? The second? The third ?

7. What is addition? What kind of numbers can be added?

8. Define subtraction, minuend, subtrahend, remainder. What is a proof of subtraction? What is the sign of subtraction, and where placed?

9. What is a parenthesis? A vinculum? For what are they used ?

10. What is multiplication? The multiplier? The mul tiplicand? The product?

11. The multiplier and the multiplicand are what of the product?

12. What is the sign of multiplication and how is it used? Define division, divisor, dividend, quotient, remainder.

13. What is the sign of division, and how is it used? 14. Express the division of 12 by 8 in as many ways as you can.

15. To what terms in multiplication do the divisor, quotient, and dividend correspond?

16. How do you find the dividend when the divisor, quotient, and remainder are given?

17. When is the quotient an abstract number ?

18. When the quotient and dividend are like numbers, what kind of a number is the divisor?

19. How can we divide when the divisor is 10? 100 ? 1000? When the divisor is 20? 50? 300?

20. Multiplying both dividend and divisor by the same number affects the quotient how?

21. Dividing both divisor and dividend by the same number affects the quotient how?

22. Multiplying the dividend affects the quotient how? The divisor? Dividing the dividend? The divisor?

23. Define exact divisor, factor, prime factor, factoring. 24. How can you find the prime factors of a number? 25. Define divisor. Common divisor. The greatest common divisor. Give rule to find greatest common divisor.

26. Define multiple, common multiple, least common multiple. Give rule for finding the least common multiple.

120. Define fraction, fractional unit, unit of a fraction, denominator, numerator, terms of a fraction, common fraction, integer, proper fraction, improper fraction, mixed number, simple fraction, compound fraction, complex fraction. What is the value of a fraction? State the principles of fractions. What is it to reduce a fraction?

How are fractions reduced to lowest terms? To highest terms?

How can an improper fraction be reduced to a whole or a mixed number? A whole or a mixed number to an improper fraction ?

What are like fractions? Unlike fractions?

How can fractions be reduced to others having a common denominator? A least common denominator?

How can two or more fractions be added?

How can the sum of fractions be found? bers?

Mixed num

How can the difference of fractions be found? Mixed numbers?

How can a fraction be multiplied by a fraction? A fraction by an integer?

How can an integer be multiplied by a fraction? By a mixed number?

How can a fraction be divided by a fraction?

How do you reduce a complex fraction to a simple fraction?

COMPOUND NUMBERS.

121. A number composed of only one kind of unit is a Simple Number; as, 5 pk., 4 apples, 6.

122. A Denomination is a name given to a unit of measure or of weight.

123. A number composed of different kinds of units is a Compound Number; as, 3 bu. 2 pk. 1 qt.

A number having one or more denominations is also called a Denominate Number.

124. Reduction is the process of changing a number from one denomination to another without changing its value.

125. Changing to a lower denomination is called Reduction Descending; as, 2 bu. 3 pk. 88 qt.

=

126. Changing to a higher denomination is called Reduction Ascending; 88 qt. 2 bu. 3 pk.

=

127. Linear Measure is used in measuring lines or distances.

128. Surveyors' Measure is used in measuring land.

NOTE.

A surveyors' chain is 4 rods long, and contains 100 links. A chain, or steel measuring tape, 100 feet long, is sometimes used

130. A square mile of land is called a Section.

A square rod is sometimes called a perch (P.). A rood (R.) is 40 sq. rods.

NOTE.1 acre 43560 sq. ft. There are 10 square chains in

an acre.

Roofing, paving, etc., are often estimated by the Square, which is 100 square feet.

131. Cubic Measure is used in measuring volumes or solids.

A gallon contains 231 cubic inches.

The standard barrel is 31 gal., and the hogshead 63 gal 129. Apothecaries' Fluid Measure is used in mixing medi cines in liquid form.

133. Dry Measure is used in measuring roots grain, vegetables, etc.

TABLE.

The bushel contains 2150.42 cubic inches.

134. Avoirdupois Weight is used in weighing all common articles; as, coal, groceries, hay, etc.

The Long Ton of 2240 pounds is used at the U. S. Cus

tom-House and in weighing coal at the mines.