Showing posts with label Mathematic vocabulary. Show all posts
Showing posts with label Mathematic vocabulary. Show all posts

Saturday, 10 July 2010

Numbers:How to say- Fractions, Decimals, zero, Spoken calculations...

1 Fractions

We say fractions like this:

  • 1/8 one eighth

  • 3/7 three sevenths

  • 2/5 two fifths

  • 1/16  eleven sixteenths


We normally use a singular verb after fractions below 1.

  • Three quarters of a ton is too much.


We use a plural noun with fractions and decimals over 1.

  • one and a half hours (NOT one and a half hour)

  • 1 -3 millimetres (NOT 1 3 millimetre)


2 Decimals

We say decimal fractions like this: 0-125  nought point one two five (NOT 0,125—nought comma one two five)

3-7  three point seven

3 nought, zero, nil etc

The figure 0 is usually called nought in British English, and zero in American English.
When we say numbers one figure at a time, 0 is often called oh (like the letter 0).

  • My account number is four one three oh six.


In measurements of temperature, 0 is called zero.

  • Zero degrees Centigrade is thirty-two degrees Fahrenheit.


Zero scores in team games are called nil (American zero).
Zero in tennis and similar games is called love.

4 Telephone numbers

We say each figure separately.
When the same figure comes twice, we usually say double (British English only).

  • 307 4922    three oh seven four nine double two.


5 Kings and Queens

We say the numbers like this:

  • Henry VIII

  • Henry the Eighth (NOT Henry Eight)

  • Louis XIV

  • Louis the Fourteenth


6 Floors

The ground floor of a British house is the first floor of an American house;
the British first floor is the American second floor, etc.

7 and

In British English, we use and between the hundreds and the tens in a number.

  • 310    three hundred and ten (US three hundred ten)

  • 5,642    five thousand, six hundred and forty-two


Note that in writing we use commas (,) to separate thousands.

8 a and one

We can say a hundred or one hundred, a thousand or one thousand. One is more formal.

  • I want to live for a hundred years.(NOT . . . for hundred years.)

  • Pay Mr J Baron one thousand pounds, (on a cheque)


We only use a at the beginning of a number. Compare:

  • a hundred

  • three thousand one hundred


We can use a with other measurement words.

  • a pint

  • a foot

  • a mile


9   Plurals without -s

After a number or determiner, hundred, thousand, million and dozen have no final -s. Compare:

  • five hundred pounds

  • hundreds of pounds

  • several thousand times

  • It cost thousands


Other number expressions have no -s when they are used as adjectives

  • a five-pound note

  • a three-mile walk


10 Measurements

We use be in measurements.

  • She's five feet eight (inches tall).

  • I'm sixty-eight kilos.

  • What shoe size are you?


In an informal style, we often use foot instead of feet when we talk about people's heights.

  • My father's six foot two.


11 Money

  • 1p    one penny or a penny

  • 5p    five pence

  • £3.75    three pounds seventy-five


When we use sums of money as adjectives, we use singular forms.

  • a five pound note (NOT a five-pounds note)


12 Adjectives

When expressions of measurement, amount and quantity are used as adjectives, they are normally singular.

  • a ten-mile walk (NOT a ten-miles walk)

  • six two-hour lessons

  • a three-month-old baby


We can use possessives in expressions of time.

  • a week's holiday

  • four days' journey


13 there are . ..

When we count the number of people in a group, we often use the structure there are + number + of+ pronoun.

  • There are only seven of us here today.

  • There were twelve of us in my family.
    (NOT We were twelve . . .)


14   Spoken calculations

Common ways of calculating are:

  • 2 + 2=4
    two and two is/are four
    (informal)
    two plus two equals four
    (formal)

  • 7-4=3
    four from seven is three (informal)
    seven minus four equals three
    (formal)

  • 3x4 = 12
    three fours are twelve
    (informal)
    three multiplied by four equals twelve
    (formal)

  • 9 / 3=3
    nine divided by three equals three

Tuesday, 29 June 2010

Cardinal Numbers, Ordinal numbers, dates, Fractions, decimals, Percentages, Arithmetic, Saying '0'

Cardinal numbers



  • 379 = three hundred and seventy nine

  • 2,860 = two thousand eight hundred and sixty

  • 5,084 = five thousand and eighty-four

  • 470,000 = four hundred and seventy thousand

  • 2,550,000 = two million, five hundred and fifty thousand

  • 3,000,000,000 = three billion


Note: There is no plural's' after hundred, thousand, million and billion when they are part of a number.

On their own, they can be plural, e.g. thousands of people; millions of insects.

Ordinal numbers and dates


One of the problems with dates is that we write them and say them in a different way:

  • We write 4 January (or 4th January), but say the fourth of January or January the fourth.

  • We write 21 May (or 21st May), but say the twenty-first of May or May the twenty-first.

  • 1997 = nineteen ninety seven

  • 1905 = nineteen hundred and five or nineteen oh five


Fractions and decimals



  • 1 1/4 = one and a quarter

  • 1 1/2 = one and a half

  • 1 3/4 = one and three quarters

  • 1 1/3 = one and a third

  • 1.25 = one point two five

  • 1.5 = one point five



  • 1.75 = one point seven five

  • 1.33 = one point three three


Percentages



  • 26% = twenty-six per cent

  • More than 50% is the majority; less than 50% is the minority.


Arithmetic

There are four basic processes for working out (= calculating) a problem:

+ = addition e.g. 6 + 4 = 10 (six plus/and four equals/is ten)

- = subtraction e.g. 6-4 = 2 (six minus four equals/is two)

X = multiplication e.g. 6 X 4= 24 (six times / multiplied by four equals/is twenty-four)

/ = division e.g. 4/2 = 2 (four divided by two equals/is two)

Saying '0'


This can be spoken in different ways in different contexts.

  • telephone number: 603 724 = six oh three, seven two four (AmEng = six zero three)

  • mathematics: 0.7 = nought point seven, 6.02 = six point oh two

  • temperature: -10 degrees = ten degrees below zero / minus ten degrees

  • football: 2-0 = two nil

  • tennis: 40-0 = forty love

Saturday, 26 June 2010

Distance, dimension, Size in people and things

Distance


The most common way of asking about distance is probably:

  • How far is it? Is it a long way? Is it a long way? Is it very far? Is it very far?

  • No, just round the corner. / a couple of minutes' walk (= very near).

  • No, not far. / No, about five or ten minutes' walk (= quite near).

  • Yeah quite a long way. / Yeah, over a mile.

  • Yes it's a long way. / Yes it's miles. / Yes it's too far to walk.




Note:

  • We can use far in a question or negative but not in a positive statement on its own

  • We don't say 'it's far', we say 'it's a long way'. But we can say 'it's too far to walk'.


Size and dimension







We can describe size using the nouns above or the adjectives formed from them, like this:

  • What's the length/width/height/depth/size of ...?

  • How long/wide/high/tall/deep/big is ...?


Note:

• We generally use tall to describe people, trees and buildings; and high to describe mountains. We also say high-rise buildings.

• Notice also that in the answer to these questions, an adjective follows the measurement: The garden is about ten metres wide. (= The width is about ten metres.)

Size in people and things


We use different words to describe the size of people and things:

  • a tall girl     (not a short girl)

  • a fat person    (not a thin person)

  • a long book (= many pages)    (not a short book)

  • a deep lake (= many metres)   (not a shallow lake)

  • a thick book (not a thin book)



  • a wide road    (not a narrow road)


Note:

  • We can use big or large to describe size in English, but not great.

  • For English speaking people, great (infml) = fantastic.

  • But we can use great before big to say that something is very big, e.g. I saw a great big dog in the park.

  • If you want to ask about size in clothes, you say: What size are you? or What size (shoes) do you take? If you don't know, then you need someone to measure you.

Monday, 31 May 2010

Measurements, Geometric shapes, Area and Volume Formulas

MEASUREMENTS AND GEOMETRIC SHAPES


A. Measurements



1. height
2. width
3. depth

4. length
5. inch
6. foot-feet
7. yard
8. centimeter
9. meter

10. distance
11. mile
12. kilometer

B. Lines



13. straight line
14. parallel lines
15. perpendicular lines

C. Geometric Shapes



16. square a. side
17. rectangle
a. length
b. width
c. diagonal
18. right triangle
a. apex
b. right angle
c. base
d. hypotenuse
19. isosceles triangle
a. acute angle
b. obtuse angle
20. circle
a. center
b. radius
c. diameter
d. circumference
21. ellipse/oval

D. Solid Figures


22. cube
23. cylinder
24. sphere
25. cone
26. pyramid
1 inch(1") = 2.54 centimeters (cm)
1 foot (1') = 0.305 meters (m)
1 yard (1yd.) = 0.914 meters (m)
1 mile (mi.) = 1.6 kilometers (km)

Rectangle


Area   A = l *w

Perimeter   P=   2l + 2w

Square


Area A= s*s

Perimeter P= 4s


Triangle


Area A= b*h* 1/2


Parallelogram


Area A= b*h

Trapezoid


A= (b1+b2)*h * 1/2

Circle


Area A= ∏*r*r

Circumference C= ∏*d = 2*∏*r

Prism


Surface Area S = 2*B + P*h

Volume V = B*h

Cylinder


Surface Area S = 2*B + C*h = 2*∏*r*r + 2*∏*r*h

Volume V = B*h = ∏ *r*r*h

Pyramid


Surface Area

S= B + P*l*1/2

Volume V = B*h*1/3

Cone


Surface Area

S= B + ∏*r*l = ∏*r*r + ∏*r*l

Volume V = B*h*1/3 = ∏*r*r*h

Sunday, 30 May 2010

Table of Measures

TIME


60 seconds (sec) = 1 minute (min)

60 minutes = 1 hour (hr)

24 hours = 1 day

7 days = 1 week

4 weeks (approx.) = 1 month

365 days = 52 weeks (approx.) = 12 months = 1 year

10 years = 1 decade

100 years = 1 century

Length


10 millimeters (mm) = 1 centimeter (cm)

100 cm = 1000 mm = 1 meter (m)

1000 m = 1 kilometer (km)

Area


100 square millimeters (mm2) = 1 square centimeter (cm2)

10,000 cm2 = 1 square meter (m2)

10,000 m2 = 1 hectare (ha)

Volume


1000 cubic millimeters (mm3) = 1 cubic centimeter (cm3)

1,000,000 cm3 = 1 cubic meter (m3)

Liquid Capacity


1000 milliliters (mL) = 1 liter (L)

1000 L = 1 kiloliter (kL)

Mass


1000 milligrams (mg) = 1 gram (g)

1000 g = 1 kilogram (kg)

1000 kg = 1 metric ton (t)

Temperature

Degrees Celsius (°C)

0°C = freezing point of water

37°C = normal body temperature

100°C = boiling point of water

Wednesday, 12 May 2010

EXPONENTS AND RADICALS




1. Multiplying and Dividing Powers

To multiply powers with the same base, add the exponents and keep the same base:

3                 4          3+4               7

b     X     b =    b         =   b

To divide powers with the same base, subtract the exponents and keep the same base:

12          8             12-8               4

b   /     b   =     b        =     b

2. Raising Powers to Powers

To raise a power to a power, multiply the exponents:

3    5         3x5              15

(x   )  =   x      =     x

3. Negative Powers

A number raised to a negative exponent is simply the reciprocal of that number raised to the corresponding positive exponent.

-3

2   = 1 =  1

3       8

2

4. Simplifying Square Roots ________

V

To simplify a square root, factor out the perfect squares under the radical, unsquare them and put the result in front:

__       ____     __         __           ___

V12 = V 4X3 = V 4   X  V 3    = 2 V 3

5. Adding and Subtracting Roots

You can add or subtract radical expressions when the part under the radicals is the same:

__        __       ___

2 V7 + 3 V7 = 5 V7

Don't try to add or subtract when the radicals are different.  You cannot simplify expressions like:          ___             __

2  V 3     +  3  V 5

6. Multiplying and Dividing Roots

The product of square roots is equal to the square root of the product:

__          __       ______       ___

V 2    x  V 3  =  V 2 X  3  =  V 6

The quotient of square roots is equal to the square root of the quotient:

__            ___         ____        ___

V 8    /     V  2     =  V 8/4   =  V 2

AVERAGE, MEDIAN, AND MODE




1. Average or Arithmetic Mean

To find the average of a set of numbers, add them up and divide by the number of numbers.

Sum of the terms

Average                        =         Number of terms

To find the average of the five numbers 12, 15, 23, 40, and 40, first add them:

12 + 15 + 23 + 40 + 40 = 130. Then divide the sum by 5: 130 / 5 = 26.

2. Using the Average to Find the Sum

Sum = (Average) X (Number of terms)

If the average of ten numbers is 60, then they add up to 10 X 60, or 600.

3. Finding a Missing Number

To find a missing number when you're given the average, use the sum.   If the average of four numbers is 7, then the sum of those four numbers is 4  X  7, or 28.   Suppose that three of the numbers are 3, 5, and 8. These three numbers add up to 16 of that 28, which leaves 12 for the fourth number.

4. Median

The median of a set of numbers is the value that falls in the middle of the set. If you have five test scores, and they are 88, 86, 57, 94, and 73, you must first list the scores in increasing or  decreasing order: 57,73, 86, 88, 94.

The median is the middle number, or 86. If there is an even number of values in a set (six test scores, for instance), simply take the average of the two middle numbers.

5. Mode

The mode of a set of numbers is the value that appears most often.   If your test scores were 88, 57, 68, 85,99, 93, 93, 84, and 81, the mode of the scores would be 93 because it appears more often than any other score.  If there is a tie for the most common value in a set, the set has more than one mode.

6. Standard Deviation

Standard Deviation is a complex statistical measure, but for the test you mainly need to know that the it is the measure of how spread out a group of numbers are.  For example, the numbers {0, 10, 20} have a Standard Deviation of about 8.17 while the numbers {9, 10, 11} have a Standard Deviation of about 0.82.   Both have an average of 10, but because the first group was more "spread out" it had a higher Standard Deviation.

RATIOS, PROPORTIONS, AND RATES




1. Setting up a Ratio

To find a ratio, put the number associated with the word of in the nominator and the quantity associated with the word to in the denominator. Then reduce.   The ratio of  15 cakes to 12 candys is 15/12,  which reduces to 5/4.

2. Part-to-Part Ratios and Part-to-Whole Ratios

If the parts add up to the whole, a part-to-part ratio can be turned into two part-to-whole ratios by putting each number in the original ratio over the sum of the numbers.

Example:  If the ratio of cats to dogs is 1 to 5, then the cat-to-whole ratio is 1 / (1 + 5) = 1/6

and the dog-to-whole ratio is 5 / (1 + 5) = 5/6.  In other words, 5/6 of the animals are dogs.

3. Using Ratios to Solve Rate Problems

Example: If snow is falling at the rate of one foot every four hours, how many inches of snow will fall in seven hours?

Setup:

1 foot =       x inches

4 hours                         7 hours

Make the units the same:

12 inches =    x inches

4 hours             7 hours

Solve:

4x= 12 X 7

x= 21

4. Average Rate

Average rate is NOT simply the average of the rates.

Total A

Average A per B =         Total B

Total distance

Average Speed =          Total time

To find the average speed for 120 miles at 40 mph and 120 miles at 60 mph, don't just average the two speeds.   First figure out the total distance and the total time. The total distance is 120 + 120 = 240 miles. The times are two hours for the first leg and three hours for the second leg, or five hours total. The average speed, then, is 240/5 = 48 miles per hour.

5)   Common Formulas for Word Problems:

a)  Distance = Rate x Time

Example:  Two cars leave Miami at the same time traveling in opposite directions.  One car travels at 60 mph and the other travels at 50 mph.  In how many hours will they be 880 miles apart?

Let R1 be the rate of the first car;  let R2 be the rate of the second car

Let T1 be the time of the first car;  let T2 be the time of the second car

The distance the first car travels is R1 x T1 and the distance the second car travels is R2 x T2

R1 T1 + R2 T2 = 880.  We also know that T1 = T2.  Our new equation is:

60T + 50T = 880

T = 8

It will take 8 hours for the cars to be 880 miles apart.

b)  Work = Rate x Time

Example:  If Jasmine can sew a dress alone in 6 days and Amy can sew the same dress in 8 days, how long will it take them to sew the dress if they both work on it?

Let x be the number of hours if they work together.

Jasmine                        Amy                 Together

Hours to sew                             6                                  8                      x

Part done in one day                 1                                  1                      1

1/6  +  1/8  =  1/x

Solving for x, we get 3  3/7 days

c)  Interest = Principal Amount x Rate x Time

Example:  If Michelle has $6,700 in a bank that pays 4% simple interest for three years, how much interest will she earn in three years?  (Assume no compounding).

Interest = Principal Amount x Rate x Time

Interest = (6700)(0.04)(3) = $804

PERCENTS




1. Percent Formula

Part = Percent X Whole

Example: What is 32% of 25?                            Setup: Part = .32  X  25

Example: 15 is 12% of what number?                  Setup: 15 = .12  X  Whole

Example: 25 is what percent of 7?                      Setup: 25 = Percent  X   7

2. Percent Increase and Decrease

To increase a number by a percent, add the percent to 100 percent, convert to a decimal, and

multiply.   To increase 60 by 25 percent, add 25 percent to 100 percent, convert 125 percent to 1.25, and multiply by 60.      1.25 X 60 = 75.

3. Finding the Original Whole

To find the original whole before a percent increase or decrease, set up an equation. Think of

the result of a 17 percent increase over x as 1.17x.

Example: After a 75 percent increase, the population was 5,879. What was the population before the increase.  Setup: 1.07x = 5,879

4. Combined Percent Increase and Decrease

To determine the combined effect of multiple percent increases and/or decreases, start with 100 and then combine.

Example: A price went up 12 percent one year, and the new price went up 24 percent the next year. What was the combined percent increase?

Setup: First year: 100 + (12 percent of 100) =112.

Second year:   112 + (24 percent of 112) = 139.

That's a combined 39 percent increase.

NUMBER PROPERTIES

1. Integers

Integers are whole numbers.. .-4,-3,-2,-1,0, 1,2,3,4,5.......

Positive integers are the numbers 1,2,3,4,5....

Zero is neither positive nor negative.

Negative integers are the numbers -1,-2,-3,-4,-5,-6,-7

Consecutive integers are writeen as x, x+1, x+2,....

Consecutive even or odd integers are written as x, x+2, x+4, x+6,.....

2. Nonintegers

Nonintegers are numbers which have a fractional part.

Examples of nonintegers are t, 3.75, -1/2, 5/6 and pi.

3. Adding/Subtracting Signed Numbers

To add a positive and a negative, first ignore the signs and find the positive difference between the number parts. Then attach the sign of the original number with the larger number part.

For example, to add 41 and -28, first we ignore the minus sign and find the positive difference between 41 and 28,which is 13. Then we attach the sign of the number with the larger number part.  In this case it's the plus sign from the 41.   So, 41 + (-28) = 13.

Make subtractions simpler by turning them into addition. For example, think of

-18 -(-26) as -18 + (+26).

To add or subtract a string of positives and negatives, first turn everything into addition. Then

combine the positives and negatives so that the string is reduced to the sum of a single positive

number and a single negative number.

4. Multiplying/Dividing Signed Numbers

To multiply and/or divide positives and negatives, treat the numbes as usual and attach a minus sign if there were originally an odd number of negatives.

For example, to multiply -2, -4, and -6, first multiply the number parts:

2 X 4 X 6 = 30.   Then go back and note that there were three negatives (an odd number), so the

product is negative: (-2) X (-4) X (-6) = -48.

5. Order of Operations

Perform multiple operations in the following order:

a)  Parentheses

b)  Exponents

c)  Multiplication and Division (left to right)

d)  Addition and Subtraction (left to right)

In the expression 9 -3 X (6 -3) + 6/3 , begin with the parentheses: (6 -3) = 3. Then do the exponent: (3)(3) = 9.   Now the expression is: 9 -3 X 9 + 6/3.   Next do the multiplication and division to get: 9 - 21 + 2, which equals -10.

6. Counting Consecutive Integers

To count consecutive integers, subtract the smallest from the largest and add 1. To count the

integers from 18 through 56, subtract: 56 -18 = 38.   Then add 1: 38 + 1 = 39.

7. Absolute Value

The absolute value of any number is its distance from zero on the number line. The absolute value of a positive number is simply that number. To find the absolute value of a negative number, just drop the negative sign. Absolute value is represented by putting two vertical lines around the number. So the absolute value of 8 = /8/ = 8. The absolute value of -43 = /-43/ = 43. The absolute value of any nonzero number is always positive. The absolute value of 0 is 0.

Basic Mathematic United States Customary Vocabulary

Length


12 inches (in.) = 1 foot (ft)

36 in. = 3 ft= 1 yard (yd)

5280 ft = 1760 yd = 1 mile (mi)

Area


144 square inches (in.2) = 1 square foot (ft2)

9 ft2 = 1 square yard (yd2)= 43,560 ft2

4840 yd2 = 1 acre (A)

Volume


1728 cubic inches (in.3) = 1 cubic foot (ft3)

27 ft3 = 1 cubic yard (yd3)

Liquid Capacity


8 fluid ounces (fl oz) = 1 cup (c)

2 c = 1 pint (pt)

2 pt = 1 quart (qt)

4 qt = 1 gallon (gal)

Weight


16 ounces (oz) = 1 pound (lb)

2000 lb = 1 ton (t)

Temperature


Degrees Fahrenheit (°F)

32°F = freezing point of water

98.6°F = normal body temperature

212°F = boiling point of water

MORE:


1 foot = 12 inches

1 yard = 3 feet

1 quart = 2 pints

1 gallon = 4 quarts

1 pound = 16 ounces

1 inch = 2.54 centimeters

1 liter = 1.06 quarts

1 kilogram = 2.2 pounds






































































Fluid Ounces29.57grams
Ounces (dry)28.35grams
Grams0.0353ounces
Grams0.0022pounds
Kilograms2.21pounds
Pounds453.6grams
Pounds0.4536kilograms
Quarts0.946liters
Quarts (dry)67.2cubic inches
Quarts (liquid)57.7cubic inches
Liters1.0567quarts
Gallons3,785cubic centimeters
Gallons3.785liters

Measuring Liquids



















































1 dash6 drops
24 drops1/4 tsp
3 tsp1 tbsp
1 tbsp1/2 fluid ounce
2 tbsp1 fluid ounce
2 cups16 fluid ounces (1 pint)
3 tbsp1.5 fluid ounces (1 jigger)
1/2 cup4 fluid ounces
16 tbsp1 cup
1 cup8 fluid ounces (1/2 pint)
2 pints1 quart
4 quarts1 gallon