MATH

  1. three cannot be substituted for x in the expression two divided by three subtracted from x because the denominator of any fraction cannot be equal to zero because numbers cannot be divided into zero equal parts and remain real
  2. the conditions for any mathematical expression that can be written as a fraction always include that the denominator cannot be equal to zero no matter the values of the variables in the first expression of number two the conditions on the variable x would include that it would not equal zero. On the second expression under the heading number two on the worksheet x could not equal four. On the third expression x could not equal zero once more. On the fourth expression x could not equal negative one. On the fifth expression of heading two on the written work worksheet x could not equal three and five tenths
  3. negative one thousand could be written as negative one thousand over one and its reciprocal could be written as negative one over one thousand. Nine tenths could be written as the fraction nine over ten and its reciprocal could be written as the mixed number one and one ninth or the fraction ten ninths. Three hundredths could be written as a fraction by writing three over one hundred and its reciprocal could be written as the fraction one hundred over three or the mixed number thirty three and one hundredth. Two hundred thirty seven thousandths can be expressed as the fraction two hundred thirty seven over one thousand its reciprocal could be expressed as the fraction one thousand over two hundred and thirty seven or as the mixed number

 

 

four times seven is twenty eight four times thirty is one hundred and twenty four times two hundred equals eight hundred  so that equals nine hundred and forty eight

 

on book six page 18 second section the book asks me to factor polynomials in expressions and then write my own answers here are the first few

first polynomial consists of 3y over 3y+6 equals 3*? Over 3(?) that would be y over y+2 then I would cancel the three times “Y”s to get one half. In the next polynomial I am asked to factor x squared plus two x over five x plus ten this would equal x times the quantity x plus two over five times the quantity x plus two I would then cancel out the quantities x plus two giving m three fifths. The next polynomial down gives me x squared plus five x over six x plus thirty. I would factor out the x on top to get x times the quantity x plus five then on the bottom I would factor out the six to get six times the quantity x plus five. I would then cancel out the quantities of x plus five and get x over six. The next polynomial is x squared minus nine x over x squared plus xy. I would factor out the x and get x times the quantity x minus nine and then on the bottom I would factor out the x again to get x times the quantity x  plus y . I would then cancel out the x s to get x minus nine over x plus y. on the next page I am asked to simplify fractions the first one is a squared plus three times a over three times a plus nine I would pull a out of the top and get a times the quantity a plus three over three times the quantity a plus three I would have the quantities cancel out to have a thirds

There's an anecdote about how the philosopher- mathematician Pythagoras overcame a student's natural dislike of geometry. The student was poor, so Pythagoras offered to pay him an obol for each theorem he learned. Eager for the money, the student agreed and applied himself. Soon, however, he became so intrigued, he begged Pythagoras to go faster, and even offered to pay his teacher. In the end, Pythagoras recouped his losses.

Etymology provides a safety net of de-mystification. When all the words you hear are new and confusing, or when those around you put old words to strange purposes, a grounding in etymology may help. Take the word line. You put ruler to paper and draw a line against the straight edge. If you're an actor, you learn your lines -- line after line of text in a script. Clear. Obvious. Simple. But then you hit Geometry. Suddenly your common sense is challenged by technical definitions, and "line," which comes from the Latin word linea (a linen thread), loses all practical meaning, becoming, instead, an intangible, dimension-less concept that goes off at both ends to eternity. You hear about parallel lines that by definition never meet each other -- except they do in some warped reality dreamt up by Albert Einstein. The concept you have always known as line has been renamed "line segment."

After a few days, it comes as something of a relief to run into an intuitively obvious circle, whose definition as a set of points equidistant from a central point still fits your previous experience. That circle (coming either from a Greek verb meaning to hoop around or from the circular Roman circus) is marked with what you would have, in pre-geometry days, called a line across part of it. This "line" is called a chord. The word chord comes from the Greek word (chordê) for a piece of animal gut used as a string in a lyre. They still use cat gut for violin strings.

After circles, you'll probably study equiangular or equilateral triangles. Knowing the etymology, you can break those words up into component parts: equi (equal), angular, angle, lateral (of a side/sided), and tri (3). A three-sided object with all sides equal. It is possible that you'll see triangle referred to as trigon. Again, tri means 3, and gon derives from the Greek word for corner or angle, gônia. However, you're far more likely to see the word trigonometry -- trigon + the Greek word for measure. Geo-metry is the measure of Gaia (Geo), the Earth.

If you're studying geometry, you probably already know you must memorize theorems, axioms, and definitions corresponding with names for such shapes as: cylinder dodecagon heptagon hexagon octagon parallelogram polygon prism pyramid quadrilateral rectangle sphere square and trapezoid.

 

While the theorems and axioms are pretty much geometry-specific, the names of shapes and their properties have further applications in science and life. Beehives and snowflakes are both dependent on the hexagon. If you hang a picture, you want to make sure its top is parallel to the ceiling.

 

Shapes in geometry are usually based on the angles involved, so the two root words (gon and angle [from the Latin angulus which means the same thing as the Greek gônia]) are combined with words that refer to number (like triangle, above) and equality (like equiangular, above). Although there are apparent exceptions to the rule, generally, the numbers used in combination with angle (from the Latin) and gon (from the Greek) are in the same language. Since hexa is Greek for six, you're unlikely to see hexangle. You're far more likely to see the combined form hexa + gon, or hexagon.

Another Greek word used in combination with the numbers or with the prefix poly- (many) is hedron, which means a foundation, base, or sitting place. A polyhedron is a many sided three-dimensional figure. Construct one from cardboard or straws, if you like, and demonstrate its etymology, by making it sit on each of its many bases.

Even if it doesn't help to know that a tangent, the line (or is that line segment?) that touches at only one point, comes from the Latin tangere (to touch) or the oddly shaped quadrilateral known as a trapezoid got its name from looking like a table, and even if it doesn't save a lot of time to memorize the Greek and Latin numbers, instead of just the names of shapes -- if and when you run into them, the etymologies will come back to add color to your world, and to help you with trivia, aptitude tests and word puzzles. And if you ever do run into the terms on a geometry exam, even if panic sets in, you'll be able to count through in your head to figure out whether it's a regular pentagon or heptagon that you would inscribe with a traditional five-pointed star.

Latin Numbers | Greek Numbers | Latin and Greek Geometry Terms

Pythagoras | Greek Mathematics

For other math words, please see these extensive, overlapping glossaries: Origins of some Math terms and Math Words, and Some Other Words, of Interest. While useful for explaining the meanings of terms in geometry, some of the etymologies are off. Slupan, if it is the root of the word "slope," does not come from Latin.

Next page > Latin Numbers > Page 1, 2, 3, 4

 

 

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