Work out 2 1/3 ÷ 1 5/9, giving the answer as a mixed number.
- Change to improper fractions: 2 1/3 = 7/3 and 1 5/9 = 14/9.
- Turn the second fraction over and multiply: 7/3 × 9/14 = 63/42.
- Simplify: 63/42 = 3/2 = 1 1/2.
Answer: 1 1/2
Fractions, decimals and percentages
Maths · Number. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
The idea
A fraction, a decimal and a percentage are three ways to write the same value: 3/4 = 0.75 = 75%. You must be able to change any one into the others and to choose the form that makes a question easiest.
In a fraction the top number is the numerator and the bottom is the denominator. A mixed number such as 2 1/3 has a whole part and a fraction part. Change it to an improper fraction (7/3) before you multiply or divide.
Some fractions give decimals that stop (terminate). Others give recurring decimals, where digits repeat for ever. Every recurring decimal can be turned back into a fraction.
Rules to remember
- Fraction to decimal: numerator ÷ denominator. Decimal to percentage: × 100.
- Add or subtract: change to a common denominator first, then add or subtract the numerators.
- Multiply: (a/b) × (c/d) = (a × c)/(b × d)
- Divide: (a/b) ÷ (c/d) = (a/b) × (d/c)
- Mixed number to improper fraction: 2 1/3 = (2 × 3 + 1)/3 = 7/3
- A fraction in lowest terms terminates only if its denominator has no prime factors other than 2 and 5.
- Recurring decimal: let x be the decimal, multiply by 10, 100, … to line up the repeating part, then subtract.
Common mistake
Adding numerators and denominators separately, such as 1/2 + 1/3 = 2/5. Use a common denominator: 3/6 + 2/6 = 5/6.
Worked example
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