Fractions, decimals and percentages
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課程筆記
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%.
投影片
練習題
免費預覽——32 題中的 8 題。註冊即可查看全部。
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}
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