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number AND algebra • real numbers Percentages as fractions 7A ■■ ■■ ■■ ■■ ■■ ■■ The term per cent means ‘per hundred’. The symbol for per cent is %. For example, 7% means 7 out of 100. Whether a percentage is a whole number, a mixed number, a proper fraction, or a decimal, it can be expressed as a fraction. To convert a whole number percentage into a fraction, write it over 100 and simplify. To convert a mixed number percentage into a fraction: •• change the mixed number into an improper fraction first •• multiply the denominator by 100 •• simplify if possible. If the percentage is a proper fraction, multiply the denominator by 100 and simplify. To convert a percentage containing a decimal number into a fraction: •• place the decimal number over 100 •• change the numerator to a whole number by multiplying both the numerator and the denominator by a required multiple of 10 •• simplify if possible. Worked Example 1 Write 47% as a fraction. Think Write Write the percentage and then change it to a fraction with a denominator of 100. 47 47% = 100 Worked Example 2 Write 20% as a fraction in simplest form. Think 1 2 Write Write the percentage, change it to a fraction with a denominator of 100 and then cancel by dividing numerator and denominator by the same number. 20% = Write the answer and check that the fraction cannot be simplified further. = 20 1 100 5 1 5 Worked Example 3 Write the following percentages as fractions in simplest form. 1 1 a % b 15 % 4 3 Think a 1 Write the percentage and then multiply the denominator by 100. 2 Simplify. Write a 1 % 4 = 1 4 × 100 = 1 400 Chapter 7 Percentages 221 number AND algebra • real numbers b 1 Write the percentage and then change the mixed number to an improper fraction. 2 Multiply the denominator by 100 and simplify by cancelling. Check to make sure that the fraction cannot be simplified further. b 15 13 % = 46 % 3 = = = 46 3 × 100 46 300 23 150 23 150 Worked Example 4 Write 36.4% as a fraction in simplest form. Think Write 1 Write the percentage and change it to a fraction out of 100. 36.4% = 2 Change the numerator to a whole number by multiplying it by an appropriate multiple of 10, multiply the denominator by the same multiple of 10 and simplify the fraction. = = 3 Write the answer. = 36.4 100 36.4 × 10 100 × 10 364 1000 91 250 91 250 remember 1. Per cent means ‘out of 100’. 2. The symbol for per cent is %. 3. To convert a percentage to a fraction, write it as a fraction with a denominator of 100 and simplify. 4. If the percentage is a fraction, multiply the denominator by 100 and simplify. 5. If the percentage is a mixed number, either: (a) change the mixed number to an improper fraction, write it as a fraction out of 100 and simplify the fraction or (b)change the mixed number to an improper fraction, multiply the denominator by 100 and simplify. 6. If the percentage contains a decimal number, place it over 100 and then multiply the numerator and the denominator by an appropriate multiple of 10 to make the numerator a whole number. Simplify where appropriate. 222 Maths Quest 7 for the Australian Curriculum