BASIC MATH VOCABULARY 1º ESO

DEPARTAMENTO DE MATEMÁTICAS. IES RIBERA DEL BULLAQUE. SECCIÓN EUROPEA MATERIAL DE MATEMÁTICAS EN INGLÉS. VOCABULARIO BÁSICO.

Definiciones extraídas de la página web: http://www.mathsisfun.com/definitions/index.html





BLOQUE ARITMÉTICA - ARITHMETIC

UNIDAD DIDÁCTICA 1: LOS NÚMEROS NATURALES. WHOLE NUMBERS

NUMBER CARDINAL ORDINAL NUMBER CARDINAL ORDINAL

1 One First 22 Twenty-two Twenty-second

2 Two Second 23 Twenty-three Twenty-third

3 Three Third 24 Twenty-four Twenty-fourth

4 Four Fourth 25 Twenty-five Twenty-fifth

5 Five fifth 26 Twenty-six Twenty-sixth

6 Six Sixth 27 Twenty-seven Twenty-seventh

7 Seven Seventh 28 Twenty-eight Twenty-eighth

8 Eight Eighth 29 Twenty-nine Twenty-ninth

9 Nine Ninth 30 Thirty Thirtieth

10 Ten Tenth 40 Fourty Fourtieth

11 Eleven Eleventh 50 Fifty Fiftieth

12 Twelve Twelfth 60 Sixty Sixtieth

13 Thirteen thirteenth 70 Seventy Seventieth

14 Fourteen fourteenth 80 Eighty Eightieth

15 Fifteen Fifteenth 90 Ninety Ninetieth

16 Sixteen Sixteenth 100 One hundred Hundredth

17 Seventeen Seventeenth 1,000 One thousand Thousandth

18 Eighteen Eighteenth 10,000 Ten thousand Ten thousandth

19 Nineteen Nineteenth 100,000 One hundred thousand Hundred

thousandth

20 Twenty Twentieth 1,000,000 One million millionth

21 Twenty-one Twenty-first



Unidades de millón

Centenas De mil

Decenas de mil

Unidades de mil

Centenas Decenas Unidades

7 5 3 0 2 1 6

7, 530,216 Seven million, five hundred and thirty thousand, two

hundred and sixteen.

SUMA ADDITION RESTA SUBTRACTION

+ Sumar La suma

Plus (Signo) To Add (Verbo) The Sum (El resultado)

- Restar La diferencia

Minus (Signo) To Subtract (Verbo) The difference (El resultado)

MULTIPLICACIÓN MULTIPLICATION DIVISIÓN DIVISION

x Multiplicar El producto

Times (Signo) To Multiply (Verbo) The Product (El resultado)

/ Dividir

Dividend Remainder

Divided by (Signo) To Divide (Verbo) Divisor Quotient

Digit -- Cifra, dígito

Even numbers – Números pares. Odd numbers – Números impares

Is smaller than – es más pequeño que The smallest – El más pequeño

Is bigger than – es más grande que The biggest -- El más grande.

Please Excuse My Dear Aunt Sally




UNIDAD DIDÁCTICA 2: DIVISIBILIDAD. DIVISIBILITY

MÚLTIPLOS - MULTIPLES The products of a number with the natural numbers: 1, 2, 3, 4, … are called the multiples of the number.

The multiples of 7 are: 7, 14, 21, …

7, 14, 21, …. Are multiples of 7.

7 is god’s number and its multiples are …

Write down the first ten multiples of … Anota los diez primeros múltiplos de …

write down the three smallest multiples of 8 which are over 50 Anota los tres múltiplos de 8 más pequeños que superen 50.

Obtain some multiples of … Obtener algunos múltiplos de …

Find three multiples of 11 between 10 and 30 Busca tres múltiplos de 11 entre 10 y 30.

Find out if 24 is a multiple of 2. Descubre si 24 es un múltiplo de 2.

DIVISORES – FACTORS (divisors) A whole number that divides exactly into another whole number is called a factor of that number.

The factors of 7 are: 1, 7

1, 7 are factors of 7.

7 is god’s number and its factors are …

List all the factors of … Haz una lista de todos los divisores de …

Work out all the factors of … Calcula todos los divisores de …

Point out which of these numbers have exactly three factors Señala cuáles de los siguientes números tienen exactamente tres divisores.

Euclid –/iuclid/ Euclides The sieve of Eratosthenes – La criba de …

To factor – Factorizar Factor tree – Arbol de factorización.



PRIMO – PRIME / COMPOSITE - COMPUESTO

PRIME: number that has exactly two factors 1 and itself. COMPOSITE NUMBER: number that has more than two factors.

The number 5 is prime, because it has exactly two factors 1 and 5.

12 is a composite number, because it has more than two factors.

List all the factors of … Haz una lista de todos los divisores de …

Work out all the factors of … Calcula todos los divisores de …

Point out which of these numbers have exactly three factors Señala cuáles de los siguientes números tienen exactamente tres divisores.

M.C.D - GREATEST COMMON FACTOR (G.C.F.) The highest (greatest) common factor of several numbers is the largest number that evenly divides into all of them.

4 is the greatest common factor to 16, 24 and 36. To find GCF

o Find the prime factor descomposition

o Choose only the common factor with the least exponents (orders)

m.c.m. – LEAST COMMON MULTIPLE (L.C.M.)

The least common multiple of several numbers is the smallest number that is multiple of all of them.

The least common factor of 4 and 3 is 12. To find LCM

o Find the prime factor descomposition.

o Choose the common factor and the not common factor with the greatest exponents

6

2

4

3




UNIDAD DIDÁCTICA 3: ENTEROS. INTEGERS.

RECTA NUMÉRICA – NUMBER LINE

8 is greater (bigger) than -2 8 > 2 - 4 is smaller (less) than - 2 - 4 < - 2

I have zero in the center, the positive numbers go to the right, and the negative numbers go to the left.

We can order the integers from least to greatest by using a number line. Podemos ordenar los enteros de menor a mayor usando una recta numérica.

I have the tick marks by increments or intervals of 5. Tomo las marcas con incrementos o intervalos de 5 (unidades)

To be right here. – The number 6 is going to be right about here. Estar aquí. (situar en la recta numérica). – El nº 6 va a estar por aquí.

- 6 is to the left of negative 5. - 6 está a la izquierda del - 5.

Sort these negative numbers, greatest first. Ordena estos números negativos, el más grande primero. (de mayor a menor)

Plot on the number line and after order them from less to great: 5, - 2, 0, - 5, 7. Dibuja en la recta numérica y después ordenalos de menos a más. …

VALOR ABSOLUTO – ABSOLUTE VALUE

The absolute value of a number is the distance between the number and zero. It’s represented by these 2 bars | |.

The absolute value of – 5 is 5. |- 5| = 5

“- 7” is 7 away from zero.

THE OPPOSITE – EL OPUESTO

The opposite of an integer is another integer with the same absolute value but different sign.

The opposite of – 5 is 5.

Large - Grande longitud Great – Grande cantidad Big – Grande tamaño.



SUMANDO Nº POSITIVOS – ADDING POSITIVE NUMBERS Para sumar un positivo nos desplazamos a la derecha.

SUMANDO Nº NEGATIVOS – ADDING NEGATIVE NUMBERS

Para sumar un negativo nos desplazamos a la izquierda.

When adding integers with the same sign…

… We add their absolute values, and give the result the same sign Enteros con el mismo signo sumamos sus valores absolutos y el mismo signo.

When adding integers with the opposite signs … … We subtract the smallest from the largest and give the result the sign the sign of the integer with the largest absolute value. Distinto signo se resta y se coloca el signo del mayor.

MULTIPLICANDO ENTEROS - MULTIPLYING INTEGERS

Two like signs become a positive sign, two unlike signs become a negative sign




UNIDAD DIDÁCTICA 4: FRACCIONES. FRACTIONS.

FRACCIÓN – FRACTION

FRACCIONES EQUIVALENTES – EQUIVALENT FRACTIONS

If the cross-products are the same, then the fractions are equivalent.

the first cross-product is 2 · 15 = 30 . The second cross-product is 5 · 6 = 30. So, these fractions are equivalent.

½ is the simplest fraction SIMPLIFICANDO FRACCIONES – SIMPLIFYING FRACTIONS

If we keep dividing until we can't go any further, then we have simplified the fraction (made it as simple as possible).

FRACTION

BAR



MULTIPLICANDO FRACIONES - MULTIPLYING FRACTIONS

Multiply the top numbers (the numerators).

Multiply the bottom numbers (the denominators).

DIVIDIENDO FRACCIONES - DIVIDING FRACTIONS

Multiply the first fraction by the reciprocal of the second fraction. Multiply the cross-product.

COMPARANDO Y ORDENANDO – COMPARING AND ORDERING THE SAME DENOMINATORS.

The largest fraction is the one with largest denominator. DIFERENT DENOMINATORS.

If the cross-products are equal, then the fractions are equivalent.

If the first cross-product is the largest, then the first fraction is the largest.

If the second cross-product is the largest, then the second fraction is the largest

SUMANDO FRACCIONES – ADDING FRACTIONS THE SAME DENOMINATORS.

Add only the top numbers (numerators) DIFERENT DENOMINATORS.

Find the LCM of the denominators. It’s the new denominator of both fractions.

We divide every new denominator by the previous one, and we multiply the result by each numerator.




UNIDAD DIDÁCTICA 5: LOS NÚMEROS DECIMALES. DECIMAL NUMBERS

Unidades de millón

Centenas De mil

Decenas de mil

Unidades de mil

Centenas Decenas Unidades

7 5 3 0 2 1 6

Unidades Décimas Centésimas Milésimas Diez

milésimas Cien

milésimas Millonésimas

7 5 3 0 2 1 6

La coma decimal se simboliza con el punto.

3.45 Three point four five. Three units, and forty- five hundredths.

El punto nuestro de miles o de millones es una coma.

7, 530,216 Seven million, five hundred and thirty thousand, two

hundred and sixteen.

EXPRESIONES. - EXPRESSIONS

The decimal point appears between the ones and the tenths position. El punto decimal aparece entre las unidades y las décimas.

We need to place a zero in the thousandths position. Necesitamos colocar un cero en la posición de las milésimas.

0.0934 Nine hundred and thirty – four ten-thousandths. Novecientos treinta y cuatro diez - milésimas.

To line up Alinear los decimales en la misma columna. Amount – cantidad. Withdrawn – Retirado (dinero banco) Deposit – Deposito.

Regular number Decimal exacto

Repeating decimal Decimal periódico

Irrational numbers Números irracionales

2/5 = 0’4 = 0.4 1/3 = 0’3333… = 0.333… π= 3.141592…



SUMA ADDITION RESTA SUBTRACTION

Line up the decimal points and then follow the rules for adding or subtracting whole numbers, placing the decimal point in the same column. When one number has more decimal places than another, use zeros to give them the same number of decimal places. Add: 43.67 + 2.3

1) Line up the decimal points and adds a 0 on the right of the second. 2) Then add. 43. 67

2.30 45.97

MULTIPLICACIÓN MULTIPLICATION DIVISIÓN DIVISION

How many digits to leave to the right of the decimal point. Add the number of digits to the right of the decimal point in both factor.

10.2 2.3 306

204 _ 23.46 _

Continue the whole division adding zeros to the right of the number being divided until you get the amount of decimal digits required.

FRACTION CONVERTER.




UNIDAD DIDÁCTICA 6: POTENCIAS Y RAÍCES. POWERS AND ROOTS

LAWS OF POWERS – PROPIEDADES DE LAS POTENCIAS

MULTIPLICATION - Multiplicación When powers with the same base are multipled, the base remains unchanged and the exponents are added. X n · X m = X n + m

Se deja la misma base y se suman los exponentes.

DIVISION - División When powers with the same base are divided, the base remains unchanged and the exponents are subtracted. X n : X m = X n - m Se deja la misma base y se restan los exponentes.

POWER OF A POWER – Potencia (X n )m = X n · m The exponents must be multiplied. Se multiplican los exponentes

(x2)3 = x2 · x2 · x2 = (x·x) · (x·x) · (x·x) = x6

So (x2)3 = x6



X 1 = X If the exponent is 1, then you just have the number itself

(example 91 = 9) X 0 = 1 If the exponent is 0, then you get 1 (example 90 = 1)

32 / 32 = 9 / 9 = 1

32 / 32 = 3 2 – 2 = 30

So 30 = 1

A square root of a number is ...

... a value that can be multiplied by itself to give the original number.

A square root of 9 is ...

... 3, because when 3 is multiplied by itself you get 9.

… - 3, because when -3 is multiplied by itself you get 9

The cube root of a number is ...

... the special value that when cubed gives the original number.

The cube root of 27 is ...

... 3, because when 3 is cubed you get 27.



BLOQUE GEOMETRÍA - GEOMETRY UNIDAD DIDÁCTICA 7:

SISTEMA MÉTRICO DECIMAL. METRIC SYSTEM OF MEASUREMENT

LENGTH / LONGITUD



MASS/MASA

VOLUME / CAPACITY – VOLUMEN O CAPACIDAD




UNIDAD DIDÁCTICA 8: RATIO, PROPORTIONS AND PERCENTS. RAZON,

PROPORCIONES Y PORCENTAJES

RATIO - RAZON

A ratio shows the relative sizes of two or more values.

There are three grey squares to two white squares. We can write ratios in different ways:

3 : 2 (three to 2) 3 es a 2. Por cada 3 … hay 2 …

3/5 as a fraction (three over five) - tres sobre cinco que es el total.

0.75 as a decimal - como un decimal del total.

75% as a percentage – como un porcentaje.

PROPORTION – PROPORCIÓN When two fractions are equal to each other we can say that they are in proportion.

La igualdad de dos fracciones es una proporción.

The quotient of the fractions is called the proportionality constant.

El cociente de las fracciones se llama: constante de proporcionalidad.

When one of the four numbers in a proportion is unknown, cross products may be used to find the unknown number. This is called solving the proportion. Letters are frequently used in place of the unknown number.

Example: Solve for n

Using cross products: 1 · 4 = 2 · n ; 4 = 2 n; n = 2

DIRECT PROPORTION – PROPORCIONES DIRECTAS

There are relationships where as one quantity decreases the other decreases too. Or one quantity increases and the other increases too. When this type of relationship is satisfied we can say that the two quantities

are directly proportional.

INVERSE PROPORTION – PROPORCIÓN INVERSA.



There are relationships where as one quantity decreases the other

increases

When this type of relationship is satisfied we can say that the two quantities

are inversely proportional.

One example of this is when we travel by car. The faster the speed, the less

time it takes us to travel a certain distance.

120 km/h ------------- 2 h

60 km/h -------------- x h

PERCENTAGE – PORCENTAJE

A percent is a ratio of a number to 100. A percent is expressed using the symbol %.

A percent is also equivalent to a fraction with denominator 100.



BLOQUE ALGEBRA - ALGEBRA

UNIDAD DIDÁCTICA 9: EQUACIONES. EQUATIONS

EQUATION - ECUACIÓN

To solve an equation is to find all its solutions.

A solution to an equation is the number that makes the equality true when we replace the unknown or variable with that number.

Unknown – Incógnita. - x

ADDITION AND SUBTRACTION PROPERTY – PROPIEDAD DE LA SUMA Y RESTA

If you add (subtract) the same number to each side of an equation, the two sides

remain equal.

Si sumas o restas el mismo número a cada lado de una ecuación, los dos lados

permanecen igual.

Solve: x + 2 = 6

We subtract 2 to each side. x + 2 – 2 = 6 – 2

Remove the equivalent terms. x = 4

The solution of this equation is 4.

Left side Write side



MULTIPLICATION AND DIVISION PROPERTY – PROPIEDAD DE LA MULTIPLICACIÓN Y DIVISIÓN. If you multiply (divide) each side of an equation by the same nonzero number, the

two sides remain equal.

Si multiplicas o divides cada lado de una ecuación por el mismo número no nulo,

los dos lados permanecen igual.

Solve: 5m = 15

Divide each side by 5 ;

Simplify. x = 3

The solution of this equation is 3.

SOLVING MULTI-STEP EQUATIONS –

RESOLVIENDO ECUACIONES DE VARIOS PASOS 1º Remove any parentheses.

(1º Eliminar parentesis)

2º Clear any fraction.

(2º Eliminar denominadores)

3º Group like terms on each side of the equal sign.

(3º Agrupar terminus semejantes a cada lado)

4º Isolate the variable.

(4º Despejar la incognita o variable)

5º Simplify.

(5º Simplificar)

Solve:

Clear out the parenthesis.

Clear the fraction

15x + 15 – 10 = 4x + 16

Group like terms together. 15x – 4x = 16 – 15 + 10

Isolate the variable 11x = 11

Solution: x = 1



BLOQUE GEOMETRÍA- GEOMETRY

UNIDAD DIDÁCTICA 10: ELEMENTOS BÁSICOS EN EL PLANO. ANGULOS

Línea recta – Line * Largo y ancho - length and height

Segmento - Line segment * Plano - Plane

Semirrecta – Ray * Punto - Point

they "Supplement" each other

Angulo

A. Agudo

A. Recto

A. Obtuso

A. Llano

A. Convexo

A. Completo

Angle

Acute A.

Right A.

Obtuse A.

Straight A.

Reflex A. Full Rotation A.

Supplementary Angles ,because they add up to 180°

Complementary Angles, because they add up to 90°.

they "Complement" each other

Measuring Degrees- Midiendo ángulos

Protractor - Transportador de ángulos

Degrees – grados sexagesimales

o Minute – Minuto

o Second - Segundo

Radians – grados en radianes

Ruler – Regla Escuadra - drafting triangle

Vertically Opposite Angles –

Ángulos opuestos por el vértice



Perpendicular – Perpendicular Paralelo –

Parallel

SÍMBOLOS MÁS UTILIZADOS EN GEOMETRÍA

Common Symbols Used in Geometry

Symbol Meaning Example In Words

Triangle

ABC has 3

equal sides

Triangle ABC has three equal

sides

Angle ABC is 45° The angle formed by ABC is

45 degrees.

Perpendicular AB CD The line AB is perpendicular

to line CD

Parallel EF GH The line EF is parallel to line

GH

Degrees

360° makes a

full circle

Right Angle (90°) is 90° A right angle is 90 degrees

Line Segment "AB" AB The line between A and B

Line "AB"

The infinite line that includes

A and B

Ray "AB"

The line that starts at A, goes

through B and continues on

Congruent (same

shape and size)

ABC

DEF

Triangle ABC is congruent to

triangle DEF

Similar (same shape,

different size)

DEF

MNO

Triangle DEF is similar to

triangle MNO

Therefore a=b b=a a equals b, therefore b equals

a

http://www.mathsisfun.com/triangle.html

http://www.mathsisfun.com/angles.html

http://www.mathsisfun.com/perpendicular-parallel.html

http://www.mathsisfun.com/perpendicular-parallel.html

http://www.mathsisfun.com/geometry/degrees.html

http://www.mathsisfun.com/rightangle.html

http://www.mathsisfun.com/geometry/congruent.html

http://www.mathsisfun.com/geometry/similar.html




UNIDAD DIDÁCTICA 11: TRIÁNGULOS. TEOREMA DE PITAGORAS. TRIANGLES. PYTHAGORAS THEOREM.

Vértice – Vertex, Corner * Ángulo - Angle

Lado(s) –Side(s) * Vértices -Vértices

Un triángulo tiene tres lados y tres ángulos - A triangle has three sides and three angles

Los tres ángulos suman 180º - The three angles always add to 180

Equilateral Triangle

Three equal sides

Three equal angles, always 60°

Isosceles Triangle

Two equal sides

Two equal angles

Scalene Triangle

No equal sides

No equal angles

Acute Triangle

All angles are less than 90°

Right Triangle Has a right angle (90°)

Obtuse Triangle

Has an angle more than 90°

ÁREA DE UN TRIÁNGULO.- TRIANGLE’S AREA

El área es la mitad de la base por la altura.

The area is half of the base times height.

“b” es la medida de la base

"b" is the distance along the base

“h” es la altura (medida en perpendicular a la base)

"h" is the height (measured at right angles to the base)

“b” = base “h” = height AREA = b · h / 2



TEOREMA DE PITÁGORAS – PYTHAGORAS THEOREM

El lado más largo del triángulo rectángulo se llama Hipotenusa, así la definición

formal es:

En un triángulo rectángulo el cuadrado de la hipotenusa es igual a la suma de los

cuadrados de los otros dos lados (En español se llaman catetos)

The longest side of the triangle is called the "hypotenuse", so the formal definition

is:

In a right angled triangle the square of the hypotenuse is equal to the sum of the

squares of the other two sides.

a2 = b

2 + c

2

Hipotenusa “a”-

Hypotenuse “a” Cateto “b”-

Side “b”

Cateto “c”-

Side “c”




UNIDAD DIDÁCTICA 12: POLÍGONOS. CIRCUNFERENCIA. POLYGONS. CIRCUMFERENCE.

CUADRILATEROS - QUADRILATERALS

Pentagon Hexagon

CIRCLE



Name Sides Shape Interior Angle

Triangle (or Trigon) 3

60°

Quadrilateral (or Tetragon) 4

90°

Pentagon 5

108°

Hexagon 6

120°

Heptagon (or Septagon) 7

128.571°

Octagon 8

135°

Nonagon (or Enneagon) 9

140°

Decagon 10

144°

Hendecagon (or Undecagon) 11

147.273°

Dodecagon 12

150°

Triskaidecagon 13 152.308°

Tetrakaidecagon 14 154.286°

Pentadecagon 15 156°

Hexakaidecagon 16 157.5°

Heptadecagon 17 158.824°

Octakaidecagon 18 160°

Enneadecagon 19 161.053°

Icosagon 20

162°




UNIDAD DIDÁCTICA 13: AREAS Y PERÍMETROS. POLYGONS. CIRCUMFERENCE.

Area of Plane Shapes

Triangle

Area = ½b×h

b = base

h = vertical

height

Square

Area = a2

a = length of side

Rectangle

Area = b×h

b = breadth

h = height

Parallelogram

Area = b×h

b = breadth

h = height

Trapezoid (US)

Trapezium (UK)

Area = ½(a+b)h

h = vertical

height

Circle

Area = πr2

Circumference=2πr

r = radius

Ellipse

Area = πab

Sector

Area = ½r2θ

r = radius

θ = angle in radians

Circumference = 2 × π × Radius - Longitud de la circunferencia

Perimeter - Perimetro The distance around a two-dimensional shape.

http://www.mathsisfun.com/triangle.html

http://www.mathsisfun.com/quadrilaterals.html





http://www.mathsisfun.com/geometry/circle.html

http://www.mathsisfun.com/geometry/ellipse.html

http://www.mathsisfun.com/geometry/circle-sector-segment.html



Common Big and Small Numbers

Name The Number Prefix Symbol

thousand 1,000 kilo k

hundred 100 hecto h

ten 10 deka da

unit 1

tenth 0.1 deci d

hundredth 0.01 centi c

thousandth 0.001 milli m

These are the most common measurements::

Millimeters

Centimeters

Meters

Kilometers

These are the most common measurements of area (from smallest to largest):

Square Millimeter

Square Centimeter

Square Meter

Hectare

Square Kilometer

30 ft2 = 2.79 m2

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BASIC MATH VOCABULARY 1º ESO