Colegio Herma. Maths Bilingual Departament Isabel Martos Martínez. 2015

1. Fraction Is an expression like, where a and b are natural numbers and b is not equal to 0. A fraction can be expressed: As a part of the unit The top number of the fraction tells us how many slices we have. We call it numerator. The bottom number tells us how many parts in the whole unit we have. We call it the denominator As a ratio /quotient To obtain its value you need to divide the numerator by the denominator. YOU MUST DO THE DIVISION. As an operator To obtain its value you need to multiply this number by the numerator and then divide it by the denominator

Fractions can be: Proper fractions: The numerator is less than the denominator This fraction is lower than the unit. Improper fractions The numerator is greater than the denominator This fraction is greater than the unit The improper fraction can be expressed as a MIXED NUMBER

MIXED NUMBER IS A WHOLE NUMBER AND A FRACTION can be expressed as a mixed number because it is an improper fraction. 9 4 = whole number proper fraction

Comparing and Ordering fractions Fractions with the same denominator, look at their numerators. The largest fraction is the one with the largest numerator. Fractions with the same numerator, look at their denominators. The largest fraction is the one with the lowest denominator. If you want to compare more than two fractions with different denominator, you have to find the LCM and this is the new denominator.

2. Equivalent fractions Two fractions are said to be equivalent when simplifying both of them produces the same fraction written in its simplest terms. Equivalent fractions are fractions with identical values. To create a pair of equivalent fractions, you multiply (or divide, cancelling down) the top (numerator) and bottom (denominator) of a given fraction by the same number. Two fractions are equivalent if the cross-products are the same.

THE SIMPLEST FORM FRACTION (FRACCIÓN IRREDUCIBLE) A fraction is in simplest form when the top and bottom cannot be any smaller (while still being whole numbers). The simplest form is a fraction that cannot be reduced, since numerator and denominator have no common divisors. Simplifying (or reducing) fractions means to make the fraction as simple as possible. You always have to obtain the SIMPLEST FRACTION in any operation with fractions. We obtain the SIMPLEST FRACTION by dividing the top and bottom by the highest number that can divide into both numbers exactly (HCD)

REMEMBER: REDUCE A FRACTION WHEN POSSIBLE

Exercises Do ex. 1, 2, 3 and 4 from page 8 and ex. 5, 6 an 7 from page Cancel down the following fractions into their simplest terms: 2. Arrange these fractions in order of size, smallest first: Then, do ex. 9 and 10 from page 10.

3. Operations involving fractions a. Adding and subtracting fractions When adding (or subtracting) fractions with different denominators, they must be rewritten to have the same denominator before starting the addition. b. Multiplying and dividing fractions To multiply: You must simply multiply the two top numbers, and multiply the two bottom ones. To divide one fraction by another, turn the second fraction upside down and then multiply them. (You cross-multiply) Don’t forget: To multiply or divide by a whole number, just treat it like a fraction with a denominator of 1.

Pay atention to order of operation BEDMAS Bedmas song

Now do exercises 12 to 14 from page to 18 from page 12

4. Types of decimal numbers There are three different types of decimal number: exact, recurring and other decimals. An exact or terminating decimal is one which does not go on forever, so you can write down all its digits. For example: 0,125 A recurring decimal is a decimal number which does not stop after a finite number of decimal places, but where some of the digits are repeated over and over again. For example: 0, is a recurring decimal, where '25' is repeated forever.

There exist two types of recurring decimals: Pure recurring decimal: It becomes periodic just after the decimal point. Ex. 1,3535… ( 35 is called the period) Eventually recurring decimal: When the period is not settled just after the decimal point. There is a not repeating number placed between the decimal point and the period. Ex. 1, … ( 6 is called anteperiod, and 35 is called the period) Other decimals are those which go on forever and don't have digits which repeat. For example pi = 3, They are called irrational numbers.

Writing a recurring decimal number as a fraction Now, we are going to convert one recurring decimal number into its corresponding fraction. We will also indicate which kind of recurring decimal it is. You have to use this formula: Where: E: integer part or the whole number portion P: periodic part from the decimal portion A: anteperiod from the decimal portion 9: write as many 9 as digits in the periodic part 0: write as many 0 as digits in the anteperiod part

Now do exercises 27 to 28 from page and 31 from page 16

5. Number sets All the numbers in the Number System are classified into different sets and those sets are called as Number Sets. The set of real numbers is divided into natural numbers, whole numbers, integers, rational numbers, and irrational numbers.

Now do exercises 33 from page 17