What is a fraction?So far we have dealt with whole numbers or integers, as found by counting.A fraction is one whole number divided by another.We write fractions as one number over another, with a horizontal line between them, like this: 3 – 4or in a line of text as one number with a slash or solidus then the other number, like this: 3/4.The fraction 3/4 or three quarters means 3 parts out of 4.The upper number, 3, is called the numerator and the lower number, 4, is the denominator.To calculate a fraction of something, multiply by the numerator and divide by the denominator.For example, 3/4 of 12 is 9: 3 – × 12 = (3 × 12) ÷ 4 = 36 ÷ 4 = 9 4
Exercise: fractionsWhat is a half as a fraction?What is four fifths of 20?Check answer to fractions exercise.
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Simplifying fractionsSometime the numerator and denominator have a common factor. We can make the fraction simpler by dividing top and bottom by the factor.For example: 15 3 × 5 3 –– = –––––– = –– 20 4 × 5 4because the common factor of 15 and 20 is 5. We divide top and bottom by 5.
Exercise: simplifying fractionsSimplify 27/30.Check answer to simplifying fractions exercise.
Improper fractionsFractions which are between 0 and 1 are called proper fractions.Improper fractions are those greater than 1.For example, 7/4 is an improper fraction.We can also express this as a whole number and a proper fraction: 1¾.
Exercise: improper fractionsExpress five and two thirds as an improper fraction.Express 17 –– 5as an integer and proper fraction.Check answer to improper fractions exercise.
ReciprocalsThe reciprocal of a number is one divided by the number.The reciprocal of 2 is ½.Conversely, the reciprocal of ½ is 2.To find the reciprocal of a fraction we turn it over, so that the numerator becomes the denominator and the denominator becomes the numerator. 4 5 For example, the reciprocal of –– is –– 5 4 We can convert this to an integer and a proper fraction as 1¼.
Exercise: reciprocalsWhat are the the reciprocals of 4 and of 5/6?Check answer to reciprocals exercise.
Multiplying fractionsTo multiply two fractions we simply multiply their numerators,multiply their denominators, and simplify if necessary: 2 1 2 × 1 2 1 –– × –– = ––––– = –– = –– 3 2 3 × 2 6 3
Exercise: multiplying fractionsMultiply four fifths by three quarters.Check answer to multiplying fractions exercise.
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