Fractions, decimals and percentages

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शिक्षकों के लिए: Fractions, decimals and percentages (Mathematics, Number) के लिए इस्तेमाल के लिए तैयार लेसन स्लाइड्स, रिवीज़न नोट्स — इन्हें अपने लेसन में इस्तेमाल करें, या टॉपिक को एक इंटरैक्टिव क्लास एक्टिविटी की तरह चलाएं जिसे आपके शिक्षार्थी लाइव गेम की तरह खेलें।

लेसन नोट्स स्लाइड्स प्रैक्टिस सवाल

लेसन नोट्स

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%.

स्लाइड्स

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साइन अप करें — फ्री लॉग इन

प्रैक्टिस सवाल

फ्री प्रीव्यू — 32 में से 8 सवाल। सभी देखने के लिए साइन अप करें।

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}

और सवाल

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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