Fractions, decimals and percentages

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Notes de leçon Diapos Questions d'entraînement

Notes de leçon

Fractions, decimals and percentages are linked

They are three ways of writing the same part of a whole: \frac{1}{4} = 0.25 = 25\%.
Fraction to decimal: divide the numerator by the denominator. \frac{3}{8} = 3 \div 8 = 0.375.
Decimal to percentage: multiply by 100. Percentage to decimal: divide by 100.
Learn the common equivalents: \frac{1}{2} = 0.5 = 50\%, \frac{1}{5} = 0.2 = 20\%, \frac{3}{4} = 0.75 = 75\%, \frac{1}{3} = 0.\dot{3}.

One quarter in three forms

Operations with fractions

Add/subtract: use a common denominator. \frac{2}{3} + \frac{1}{4} = \frac{8}{12} + \frac{3}{12} = \frac{11}{12}.
Multiply: multiply numerators and denominators. \frac{2}{3} \times \frac{3}{5} = \frac{6}{15} = \frac{2}{5}.
Divide: multiply by the reciprocal. \frac{3}{4} \div \frac{2}{5} = \frac{3}{4} \times \frac{5}{2} = \frac{15}{8}.
For mixed numbers, convert to improper fractions first.
A reciprocal exists only for a nonzero number. Division by zero is undefined.

Percentages of amounts

Find 10% by dividing by 10 and build up: 15% of 80 = 8 + 4 = 12.
Using a multiplier: 15% of 80 = 0.15 \times 80 = 12.
To write one amount as a percentage of another, divide and multiply by 100: 18 out of 40 is \frac{18}{40} \times 100 = 45\%.

Recurring decimals

A recurring decimal repeats forever: 0.\dot{3} = \frac{1}{3}, 0.\dot{1}\dot{8} = 0.181818....
To convert to a fraction, let x equal the decimal, multiply to line up the repeat, then subtract. For x = 0.\dot{4}: 10x - x = 4, so x = \frac{4}{9}.

Ordering and comparing

Convert everything to the same form (usually decimals) before comparing.
Compare \frac{3}{5}, 0.58 and 62%: they are 0.6, 0.58 and 0.62, so the order is 0.58, \frac{3}{5}, 62%.

Diapos

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Questions d'entraînement

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1.What is 50% as a fraction in its simplest form?
Easy
- A\frac{1}{5}
- B\frac{1}{2}
- C\frac{5}{10}
- D\frac{1}{4}
2.Write 0.6 as a percentage.
Easy
- A6%
- B0.6%
- C60%
- D600%
3.Write 35% as a decimal.
Easy
- A3.5
- B0.35
- C0.035
- D35
4.What is \frac{3}{4} as a percentage?
Easy
- A34%
- B75%
- C43%
- D60%
5.Work out \frac{1}{3} + \frac{1}{6}.
Easy
- A\frac{2}{9}
- B\frac{1}{2}
- C\frac{2}{6}
- D\frac{1}{9}
6.Work out \frac{5}{6} - \frac{1}{4}.
Easy
- A\frac{4}{2}
- B\frac{7}{12}
- C\frac{4}{10}
- D\frac{1}{3}
7.Work out \frac{2}{3} \times \frac{3}{5}.
Easy
- A\frac{5}{8}
- B\frac{2}{5}
- C\frac{6}{8}
- D\frac{10}{9}
8.Work out 2\frac{1}{2} \times 3.
Easy
- A6\frac{1}{2}
- B7\frac{1}{2}
- C6 1/3
- D5\frac{1}{2}

Plus de questions

9.What is 15% of 80?
Easy
- A8
- B12
- C15
- D120
10.What is 35% of 200?
Easy
- A35
- B70
- C7
- D700
11.Write 18 out of 40 as a percentage.
Easy
- A18%
- B40%
- C45%
- D22%
12.Work out \frac{3}{5} \div \frac{9}{10}.
Medium
- A\frac{27}{50}
- B\frac{2}{3}
- C\frac{3}{2}
- D\frac{5}{9}
13.Work out 1\frac{2}{3} + 2\frac{3}{4}.
Medium
- A3\frac{5}{7}
- B4\frac{5}{12}
- C3\frac{5}{12}
- D4\frac{1}{7}
14.Which is the largest: \frac{3}{5}, 0.58 or 62%?
Medium
- A\frac{3}{5}
- B0.58
- C62%
- DThey are equal
15.Which list is in ascending order?
Medium
- A\frac{1}{2}, 0.4, 45%
- B0.4, 45%, \frac{1}{2}
- C45%, 0.4, \frac{1}{2}
- D\frac{1}{2}, 45%, 0.4
16.Which fraction equals 0.\dot{4}?
Medium
- A\frac{4}{10}
- B\frac{4}{9}
- C\frac{4}{99}
- D\frac{2}{5}
17.Write 0.\dot{1}\dot{8} as a fraction in its simplest form.
Medium
- A\frac{18}{99}
- B\frac{2}{11}
- C\frac{1}{8}
- D\frac{9}{50}
18.A coat costing £80 is reduced by 15%. What is the sale price?
Medium
- A£12
- B£68
- C£65
- D£92
19.In a class of 30, 12 are boys. What percentage are girls?
Medium
- A40%
- B60%
- C18%
- D12%
20.\frac{3}{5} of a number is 18. What is the number?
Medium
- A10.8
- B30
- C24
- D90
21.What is the reciprocal of \frac{2}{7}?
Easy
- A\frac{2}{7}
- B\frac{7}{2}
- C-\frac{2}{7}
- D\frac{5}{7}
22.Which method gives 8% of 250?
Medium
- A8 \times 250
- B0.08 \times 250
- C0.8 \times 250
- D250 \div 8
23.Which is the equivalent fraction to \frac{2}{3}?
Easy
- A\frac{4}{9}
- B\frac{4}{6}
- C\frac{3}{2}
- D\frac{2}{6}
24.What is \frac{7}{20} as a percentage?
Easy
- A7%
- B20%
- C35%
- D3.5%
25.\frac{1}{4} is the same as 25%.
Easy
True or false?
26.To divide by a nonzero fraction, multiply by its reciprocal.
Easy
True or false?
27.\frac{2}{5} + \frac{3}{5} = \frac{5}{10}.
Easy
True or false?
28.0.07 is the same as 70%.
Easy
True or false?
29.0.\dot{3} is exactly equal to \frac{1}{3}.
Medium
True or false?
30.Which of these are equal to \frac{3}{4}?
Medium
- A0.75
- B75%
- C\frac{6}{12}
- D\frac{9}{12}
- E0.34
31.Which are recurring decimals?
Medium
- A\frac{1}{3}
- B\frac{1}{4}
- C\frac{2}{9}
- D\frac{1}{5}
- E\frac{5}{11}
32.Explain how to convert 0.\dot{6} to a fraction.
Medium

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