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What is a Fraction? A fraction is a number, which contains parts of a whole. Fractions can be smaller than or larger than one (one whole). N A fraction is a number with the form D where n and d are two numbers N The number n above the line is called the numerator D The number d below the line is called the denominator. Fraction can be written in different ways A fraction is a number with the form N D Alternative ways of expressing this statement include: "n over d", n ÷ d Example The fraction 5 6 could be expressed as: five-sixths, five over six, 5 ÷ 6 Proper, Improper and Mixed Numbers If the numerator is smaller than the denominator (if n < d), then the fraction is called a proper fraction, and its value is less than 1. 3 7 2 10 17 26 If the numerator is greater than the denominator (if n > d), then the fraction is called an improper fraction, and its value is greater than 1. 31 15 5 10 37 23 If the numerator is equal to the denominator, then the fraction's value is equal to 1. A mixed number (or mixed fraction) is a number that has a whole number part to it, and a fraction part to it. 31 5 1 2 3 12 7 10 Common Fractions A common fraction is simply an ordinary fraction. The numerator and denominator must be integers, or whole numbers, and the denominator cannot equal zero. Common Fractions Not Common Fractions 35 45 5 9 51 16 3.2 4.5 5 0 0.57 1.6 Decimal Fractions A decimal fraction is a fraction where the denominator is a power of ten. 7 10 .7 3 5 5 100 .05 263 500 Are not decimal fractions 537 1000 .537 Are all decimal fractions Equal to Equivalent Fractions Equivalent fractions are fractions, which have the same value as each other. A quick way to tell whether or not two fractions are equivalent is to change them both into decimals using a calculator. If the two decimals are identical, then the fractions have the same value. 2 .66 3 2 = 3 = 4 6 .66 4 6 = 6 9 = 8 = 12 10 15 Each time the fraction is split, both the denominator and the numerator are multiplied by the split. This gives us an equivalent fraction. In other words, if you multiply the numerator and denominator by the same number, you get the same (or equivalent) fraction. And by using the same logic, if we divide the numerator and denominator by the same number, you get an equivalent fraction. Simplifying/ Reducing Fractions This is also sometimes called reducing fractions to their simplest form. This involves dividing both the numerator and denominator by a common factor to reduce the fraction to the equivalent fraction with the smallest possible numerator and denominator. 10 = 100 50 = 60 1 10 5 6 12 = 24 75 = 90 1 2 15 = 18 5 6 Adding and Subtracting Fractions Adding and subtracting fractions works differently from adding and subtracting integers or decimals. If the two fractions have the same denominator, then it is quite easy to add or subtract the fractions by simply adding the numerators together. 1 5 + 3 5 = 4 5 6 + 15 = __ 25 25 4 6 + 1 6 = 5 6 6 + 17 = __ 30 30 If the fractions have different denominators, then they need to be changed into equivalent fractions with the same denominator before they can be added or subtracted. 2 + 6 Multiply by the opposite denominator 7 12 Multiply by the opposite denominator 2 x12 + 7 x6 6 x12 12 x6 Now that both have a common denominator add them together 24 + 42 72 72 66 66 6 72 reduces to 72 6 = = = = 66 72 11 12 Multiplying and Dividing Fractions To multiply two fractions together, simply multiply the two numerators together, then multiply the 2 denominators together. Multiply 7 12 x 5 = 35 10 120 8 32 x 8 = 64 20 640 To divide () one fraction by a second fraction, you need to invert the numerator and denominator of the second fraction so that the 'old denominator' is on the top, and the 'old numerator' is on the bottom half of the fraction. They can then be multiplied together to give an answer. Divide Invert Answer Reduce Regroup if nd 2 needed fraction 7 5 = 7 x 10 = 70 = 7 = 11 12 10 12 5 60 6 6 9 7 = 9 x 20 = 180 32 20 32 7 224 = 45 56