What is the fraction of a fraction called? [The word "of" between its several parts]. A Compound Fraction. Give an instance. of of of, &c., = 1304 = 4 If a whole number be prefixed to a fraction, what is it called? Turn the mixed number 83 into an Improper Fraction. 8939 = 8 × 7+3 = 5,9. Express the method or rule that you here use. Multiply the whole number by the denominator, add the numerator to the product, and under this put the denominator. ii. Decimal Fractions. What is the difference between a Vulgar and a Decimal Fraction? In a Vulgar Fraction, the Integer may be broken into any number of parts: that is, the Denominator may be any sum whatever. In a Decimal Fraction, the Denominator is ten, or some power of ten. What do you mean by a power of ten? Ten multiplied into itself any number of times. 10 x 10 = 100; 100 × 10 = 1000; 1000 × 10 = 10000; and so on. Is the Denominator written down in full? No: a dot or point is put before the numerator. What are .2, .35, .672, .8964, when written in full? How do we at once see the value of a decimal fraction? If we put unity, or 1, in the place of the dot, and Zero, or 0, for each digit or figure, the resulting number is the denominator. How do you turn a vulgar fraction into a decimal ? What are the fractions, 4, 2? Vulgar fractions. Turn them into decimal fractions. = .5; = .25; 2 = .75. Write these decimals in full. What is the Square of any number? The Product of any number when multiplied into itself. The square of 12 is 144: 12 x 12 = 144. The = 400. of 20 is 400: 20 × 20 square What is the square root of any number or sum? That number which when multiplied by itself produces the given number. Give instances. The square root of 81 is 9; for 9 × 9 = 81. The square root of 900 is 30; for 30 x 30 = 900. What is the Cube of any number? The square of a number multiplied by the number itself. Give instances. 7 x7 = 49, the square of 7: and 49 × 7 = 343, the cube of 7. 9 × 9 = 81; 81 × 9 = 729, the cube of 9. 12 × 12 = 144; 144 × 12 = = 1728, the cube of 12. What do square numbers give us? The Areas or Surfaces of things. What do cube numbers give us? In what are Duodecimals used? In some parts of Mensuration. What is the peculiarity of this sort of fractions? II. MENSURATION. What does Mensuration teach us? How to measure bodies. Explain your meaning. It teaches us how to measure Surfaces and Solidities; also What do you mean by measuring a surface? Finding its extent (as the number of square feet contained in it) from its dimensions. What do you mean by measuring a solidity? Finding the content of a body from its dimensions. What do you call the measure of Surfaces. Square Measure; as square miles, square yards, &c. What does Cubic Measure teach us? How The solidity, bulk, content of bodies: as cubic yards, cubic feet, &c. many Dimensions has a Surface? Two; length and breadth. How many Dimensions has a Solid? Three length, breadth, and depth. Where should we begin the study of mensuration? With its first elements. What is essential to the sound knowledge of any subject? What is a Point? 1. Point, Line, Angle. That which has neither length nor breadth. What is a Line? What has length, but is without breadth. How many sorts of lines are there? Two; straight lines and curves. What line do you call a Curve? One that bends, winds about, waves. What line do you call Straight? One that does not bend, wind about, or wave. How many straight lines inclose an Area? Not less than three. What do you mean by an Angle? It is formed by the meeting of two said to be the opening between B- What does this diagram give you? The angle B, or ABC. How many kinds of angles are there? Three: Right, Acute, Obtuse. 1. What is a Right Angle? A An angle formed by two lines perpendicular to each other. When is one line said to be perpendicular to another? The line AB is perpendicular to the line DBC, when the angle ABD What are these angles called? Adjacent angles. 2. What is an Acute Angle? An angle less than a right angle. 3. What is an Obtuse Angle? An angle greater than a right angle. How are angles measured? By dividing them into degrees. B A What is a Degree? The 90th part of a right angle. Thus a right angle contains 90 degrees; an acute angle less, and an obtuse angle more, than 90 degrees. A figure formed by 3 straight lines meeting each other at the ends. To what are the 3 angles of a triangle together equal? To two right angles, or 180 degrees, (180°.) [Euc. i. 32.] How many sorts of triangles are there? Six. How are they classed? Three by their sides, and three by there angles. A 1. What is an Equilateral Triangle? Its three sides are equal to one another. What must each of its angles be? Acute; equal... 60°. 2. What is an Isoscles Triangle? A triangle which has two of its sides equal. What must its angles be? The angles opposite the equal sides are A B angle according to the dimensions of the sides. 3. What is a Scalene Triangle? A triangle whose three sides are un equal. What must its angles be? A One of them right or obtuse, and the B |