QUESTIONS FOR REVIEW.

331. NOTATION AND NUMERATION. - Define a unit; a number; notation. In what two ways may numbers be represented? Define numeration; Arabic notation. What characters are employed in the Arabic notation? How are numbers grouped in the Arabic notation?

When two figures are written side by side, what do they represent? Three figures? Four figures? Five figures? Six figures? Seven figures? How are numbers expressed by two figures read? By three figures? By four figures? By five figures? By six figures? By seven figures? How are the figures of a number often grouped for convenience in reading the number? Name five periods in succession, beginning at the right. Give a rule for pointing off numbers for reading. Which period may contain less than three figures?

How many cents are there in one dime? In one dollar? What places do cents occupy in the notation of United States money? What is used to separate dollars from cents? If the number of cents is less than 10, what figure is written in the first place to the right of the decimal point? What is the sign of dollars? Where is it written? What is a mill? In business, what is the rule about mills?

What is the Roman notation? What letters are employed in the Roman notation? Give the principles governing the Roman notation and illustrate each one.

ADDITION.

- Define addition; sum, or amount. Describe the sign of addition; the sign of equality. How is + read?

=

How is read? How are numbers to be added arranged? Can they be added under any other arrangement? Why are units written under units, tens under tens, etc.? What is the most convenient way of adding several numbers?

When the units are added and the sum is greater than 9, what is done with the tens' figure?

SUBTRACTION. - Define subtraction; minuend; subtrahend; remainder. Which is the greater, the minuend or the subtrahend? How can the minuend be obtained from the subtrahend and the remainder? How can we find out whether the answer is correct? What is the sign of subtraction called? How is 10-4 read? What is the meaning of 104?

How are the minuend and subtrahend arranged for subtraction? Could the subtraction be performed if the subtrahend were written above the minuend? How is 8 subtracted from 24? 81 from 245? How is 25 subtracted from 100? What is done when some figure of the subtrahend expresses more than the corresponding figure of the minuend?

MULTIPLICATION. - Define multiplication; multiplicand; multiplier; product; factors of the product. Describe the sign of multiplication and its use. How can 3 x 4 be found by addition? Describe how 122 is multiplied by 3; 125 by 3; 142 by 3. Is it necessary to begin at the right to multiply? How is a number multiplied by 10? By 100? By 1000? By 1 with any number of ciphers annexed? By any number with ciphers annexed?

How is 136 multiplied by 67? How is a number multiplied by a number expressed by more than one significant figure? Give an explanation of the process. What are numbers called that are added to obtain the product? When there are ciphers between significant figures of the multiplier, how is the multiplication performed?

DIVISION.-Define division; dividend; divisor; quotient; remainder. Describe the sign of division. State how division may be indicated. How do we know that 4 is contained 5 times in 20? Solve an example in short division and explain the process. What divisors are usually employed in short division? Why are not longer divisors used?

How is a number most conveniently divided by 10, 100, 1000, etc.?

How does long division differ from short division? Give a rule for long division. How is the correctness of the result proved?

What is the use of the parenthesis, the vinculum, and the brackets? Illustrate their use. Give a rule for finding the

value of such expressions.

FACTORING. - Define integer; factors of a number; exact divisor; prime number; composite number; prime factor; even number; odd number; factoring. How can we tell, without actually dividing, whether a number is divisible by 2? By 5? By 10? By 3? By 9? Describe the process of separating a number into its prime factors. Why may equal factors be canceled from the dividend and divisor? Why is cancellation useful? Make an example and solve it by cancellation.

FRACTIONS. What is a fraction? Express 3 of the 5 equal parts of a unit. What are the terms of a fraction? What does each indicate? What is the difference between proper and improper fractions? Define and illustrate mixed number. What besides 3 of the 5 equal parts of 1 may the fraction express? Write in words the equivalent of § in three ways.

Define reduction of fractions. Illustrate. How is a mixed number reduced to a fraction? What kind of a fraction results from this reduction? Why? What kind of fractions can be reduced to integers or mixed numbers? Why?

Illustrate. How is the reduction performed?

How is a fraction reduced to lower terms? Illustrate. Give the reason for the process. When is a fraction in its lowest terms? How may a fraction be reduced to higher terms? What are similar fractions? Dissimilar fractions? Why are and called similar fractions? If several fractions have the same denominator, what is this denominator called? How are dissimilar fractions reduced to similar fractions having the least common denominator?

Give a rule for adding fractions so that the sum will be in as simple a form as possible. Give a rule for subtraction when one or both of the numbers are fractions. In what two ways may a fraction be multiplied by an integer? Illustrate each. How is an integer multiplied by a fraction? An integer by a mixed number? Multiply by and explain the process. Give the rule for multiplying a fraction by a fraction. How does the rule apply to 2 × ? To 5 ×? Multiply by . What reduction of the result is avoided by cancellation? What is a compound fraction? How is a fraction divided by an integer? An integer by a fraction? An integer by a mixed number? Divide 2 by the process. Explain how is divided by . for dividing a fraction by a fraction. Show that this rule has a general application in division, whether the dividend or divisor is a fraction, an integer, or a mixed number. What is a complex fraction?

and explain Give a rule

How is the relation of one number to another found? What is an aliquot part of a number? Give some of the aliquot parts of a dollar. Find a number of which 25 is and explain how the whole of any number is found when a given part of it is known.

What is a decimal fraction? What is the meaning of the word decimal? What kind of a notation is the Arabic notation? How is the Arabic notation for integers extended

to express decimals? How is expressed as a decimal? Too? 1000? Give the rule for expressing such fractions in the decimal form. Name the first six orders of decimals. How many decimal places are required to express tenths? Hundredths? Thousandths? Ten-thousandths? Write as a decimal 16 tenths; 16 hundredths; 16 thousandths.

If ciphers are annexed to a decimal, how is the value of the decimal affected? How, if decimal ciphers are prefixed to a decimal? How does the number of places in a decimal compare with the number of ciphers in the denominator of the equivalent common fraction? Why? Explain that .63.630 = .6300. How are dissimilar decimals reduced to similar decimals? How is a decimal reduced to a common fraction? Illustrate. How is written as a decimal? Explain fully how is reduced to the decimal form. Give a rule for reducing a common fraction to a decimal.

Give a rule for adding decimals. Illustrate. Give a rule for subtracting one decimal from another. Illustrate. Show how this rule is applied when a decimal is subtracted from an integer. How does the number of decimal places in the product of two or more numbers compare with the number of decimal places in the factors? Illustrate. How is a decimal multiplied by 10? By 100? By 1000? Explain that .5 x .03.015 and give a rule for multiplication of decimals. If the product does not contain a sufficient number of decimal places, what is done? How does the number of decimal places in the quotient compare with the number of decimal places in the dividend and divisor? Why? Give a rule for division of decimals. If the quotient does not contain a sufficient number of decimal places, what must be done? What may be done when the dividend contains fewer decimal places than the divisor? Illustrate. When the division is not exact, what is commonly done in business? How is a decimal divided by 10, 100, 1000, etc.?