Understanding Factors in Math

• When two or more numbers are multiplied together to get the product, each number is called a factor of the product.
• The factors of 12 are 1, 2, 3, 4, 6, and 12.
• For example, 5 cannot be multiplied by any other number to get the product 12, so 5 is not a factor of 12.
• The numbers 1, 2, 4, 8, and 16 are all factors of 16 because 1×16=16, 2×8 = 16, 4 × 4 = 16 and 16 × 1 = 16
• The numbers 1, 3, 9, and 27 are all factors of 27 because 1 x 27 = 27, 3 x 9 = 27, 9 x 3 = 27 and 27 x 1 = 27
• When a number is divided by its factor, it leaves no remainder.
• 2 and 9 are factors of 18 because 18/2 has no remainders (R = 0) and 18/9 has no remainders (R = 0)
• 3 and 9 are factors of 27 because 27/3 has no remainders (R = 0) and 27/9 has no remainders (R = 0) with 27/2 giving a R = 1 hence is no factor
• 7 and 5 are factors of 35 because 35/7 and 35/5 have no remainders (R = 0)
• 2, 3, and 4 are not factors of 35 when dividing 35 and results in remainders (R)

Facts About Factors

• A factor of a number will always be smaller than or equal to the number.
• 1 and the number itself are factors of any number.
• The number 1 has only one factor-the number "1" itself.
• All the other numbers will have at least two factors.
• Division of a number by any of its factors leaves no remainder.

Finding Factors

• Factors can be obtained by multiplication, finding the numbers that can be multiplied to give the required product
• Factors can be obtained by division, finding the divisors that can divide the given number without leaving any remainder
• E.g. the numbers 1, 2, 4, 5, 10, and 20 can form the product 20 using mulitiplication, so are all factors of 20
• E.g. divisors 1, 2, 3, 6, 9, and 18 divide 18 without remainders, so are all factors of 18

Finding out if a number is a factor of another number

• A smaller number will be a factor of another number if the division by that number leaves O as the remainder.
• Find out if 5 is a factor of 95 by working out if 955 leaves any remainder; the remainder is 0, so 5 is a factor of 95
• Find out if 3 is a factor of 17 by working out if 17/3 leaves any remainder; 17+ 3 leaves 2 as the remainder, 3 not a factor of 17

Prime and Composite Numbers

• Prime numbers have only two factors-1 and the number itself.
• Numbers that have more than two factors are called composite numbers.
• The number 1 is neither prime nor composite.
• It is called a unique number because it has only 1 factor.
• Prime Numbers between 1 and 20 are -2, 3, 5, 7, 11, 13, 17, 19
• Composite Numbers between 1 and 20 are -4, 6, 8, 9, 10, 12, 14, 15 ,16, 18 ,20
• The smallest prime number is 2

Prime Factorisation

• Writing a number as a product of its factors is called factorisation.
• Writing a number as a product of its prime factors only is called prime factorisation.
• Methods to find the prime factors of a number are Factor tree method and Short division method

Factor Tree Method

• Factorise the numbers in such a way that at least one of the factors is a prime factor.
• Factorise the composite factor further to get at least one prime factor.

Short Division Method

• Write the target number as the dividend.
• Divide it by the smallest prime factor.
• Divide the new dividend by a prime number until 1 is achieved
• Prime factorisation is the product of the prime number divisors

Common Factors

• Common factors are the factors that are common for two or more numbers.

Twin primes

• Prime numbers 3 and 5 have a composite number in between; such prime numbers are called twin primes.
• Prime numbers 2 and 3 come one after the other. So, they are called consecutive prime numbers.

Multiples

• A multiple contains many more units of the number
• A number can have unlimited number of multiples; count by "x" to get all the multiples of "x."

Facts About Multiples

• Each number is a multiple of itself.
• Every number is a multiple of 1.
• A multiple is a product of two numbers; the product is a multiple of each of these two numbers.
• Multiples of any number are countless, there is no last multiple of a number.

Finding Multiples

• Multiples obtained by multiping the target number with natural mumbers
• Test if one number is a multiple of the other by dividing the bigger number by the smaller number

Common Multiples

• Common multiples are the multiples which are common for two or more numbers.

Test of Divisibility

• Divisibility rules enable us to find out if one number is divisible by another, without carrying out the actual division.

Test of Divisibility by 2

• A number is said to be divisible by 2 when it does not leave any remainder when divided by 2; has 0, 2, 4, 6, or 8 in its ones place.

Simple Closed Curves

• There can be many different types of simple closed figures.
• Simple closed curves can be made of line segments only, curved lines only or both line segments and curved lines

Polygons

• A simple closed figure made of three or more line segments is called a polygon.
• The line segments of a polygon are known as its sides.
• The meeting point of two line segments is called a corner or a vertex.
• Polygons get its name from the number of sides it has.
• Examples are Triangle ('Tri' means 3 sides i.e Three sides), Quadrilateral ('Quad' means 4 sides i.e. Four sides), Pentagon ('Penta' means 5 sides i.e. Five sides) and Hexagon('Hexa' means 6 sides i.e. Six sides)

Point, Line, Line Segment, and Ray

• A point is a position on a plane surface.
• A point is usually denoted by a capital letter.
• A line is a straight path which extends on both sides.
• The length of a line cannot be measured.
• A part of a line that is between two end points is called a line segment.
• A line segment has fixed length.
• A ray is part of a line that has one end point and extends in one direction without ending.
• Arrows indicate that there are no end points.

Triangles

• A traingle has 3 vertices (A, B, C) and 3 sides (AB, BC, CA)
• A triangle with three unequal sides is called a scalene triangle.
• A triangle with two equal sides is called an isosceles triangle.
• A triangle with three equal sides is called an equilateral triangle.

Quadrilaterals

• A polygon with four sides is called a quadrilateral.
• A quadrilateral has four sides and four vertices.
• A quadrilateral with opposite sides equal is called a rectangle.
• A quadrilateral with all sides equal is called a square.

Circle

• A circle is a closed figure made of a single curved line and has no corner or vertex.
• The curved line is the boundary or outer edge of the circle and is called circumfrence.
• The center is a fixed point inside the circle that is equal distance from every point on the boundary of the circle
• The radius is a line drawn from the Centre to any point on the circumference of the circle.
• The diameter is straight line that passes through the centre and joins two different points on the circumference of the circle.

Relationship between the Diameter and Radius of a Circle

• The radius of the circle is half its diameter.

Symmetry and Mirror Reflection

• A figure that can be divided into halves such that the two halves match exactly is called a symmetrical figure.
• Some shapes have more than one line of symmetry.
• Reflection symmetry is when a figure matches in proportion when reflected using a mirror; the dotted line which divides is knowm as line of symmetry.

Tessellations

• A repeating pattern of shapes that fit perfectly together, with no overlaps or gaps, is known as a tessellation.
• Tessellations can be created by repeating some polygons.
• Examples are Triangles, Squares, Hexagons etc.

Fractions

• Numerator is that part of whole which being referred
• Denominator is entire whole which can have multiple parts
• Written as numerator/denominator.

Equivalent Fractions

• Equivalent fractions are fractions that have the same value, even though they may look different e.g. 1/4 and 2/8
• We can get equivalent fractions of a given fraction by either multiplying or dividing the numerator as well as the denominator by the same number.

Like Fractions

• Fractions with the same denominators

Unlike Fractions

• Fractions with different denominators

Comparison of Like Fractions

• When comparing two or more fractions with the same denominators, the larger fraction is the one with the greater numerator because the whole is divided into the same number of parts.

Addition/Substraction of Like Fractions

• Keep the denominator same and just add or subtract the numerators.

Finding a Fraction of a Number

• "x/y" refers to "x" parts out of "y" equal parts

Reducing Fractions

• Reducing a fraction means making the fraction as simple as possible.
• Denominator and numerator are divided by common factor to simplify

Proper Fraction

• A fraction where the numerator is smaller than the denominator

Improper Fraction

• A fraction where the numerator is greater than or equal to the denominator.

Mixed Fraction

• A fraction which is made up of a whole number and a proper fraction
• Improper Fractions can be converted into Mixed Fractions
• Mixed Fractions can be converted into Improper Fractions

Decimals

• A way of writing a number that is not 'whole'; in-between numbers i.e. 2.5.
• Has Decimal point

Decimals on a Number Line

• Point is defined by it's location between 2 integers and it's relative proximity to integers.
• Each relative location can then be described as a decimal
• Relationship

Conversion of Fractions to Decimals

• Fractions with denominators of 10, 100, 1000 are called decimal fractions
• Decimals are called special fractions
• Conversions can occur from either form to the other

Conversion of decimal to fraction

• Write decimal number as numerator without decimal point
• In denominator write 1 followed by as many zeros as number of digits after decimal point in decimal number.
• Simplify fraction

Reading Decimals

• Read whole value then add then suffix point then all decimal places
• Write it out numerically

Metric Conversions

• Conversions that transform the metric unit from one value to another by multiplication m/cm g/kg km/m ml/l kg/mg

Scales

• Units and magnitude of conversion
• Linear relationship

Common length units

• Kilometre (km), 1000 m
• Metre (m), Base unit Im
• Centimetre (cm), 1/100 m

Units of Capacity

• Capacity is defined as the quantity that something can hold.
• The basic unit of capacity is litre (l).
• A smaller unit of capacity is millilitre(ml).
• Conversions - 1 litre = 1000 millilitres

Units of Mass

• Mass defined as the quantity of matter of a substance.
• Unit of mass is gram (g).
• Kilogram is used for measuring the weight of heavy things.
• Kilogram written in short as kg, so 20 kg means 20 kilograms.
• Conversions - 1000 g = 1 kg or 1 kg = 1000 g

Observing Line Segments

• Line segments part of a line, ends have specific points

The Perimeter

• Perimeter defined as the length of the boundary of any shape
• Perimeter can be by adding length of lines around the shape.

Timeline

• A timeline is like a number line which features some basic dates or times in a chronological order.

Calculating time elapsed

• am -ante meridiem which means before noon in Latin
• pm -post meridiem which means after noon in Latin
• calculate minutes and hours between two times

Bar graph

• A bar graph is a visual interpretation of data either in the form of vertical or horizontal bars.
• The longer the bar, the greater is its value.

Scale

• It links unit and real value