Working With Fdp

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Converting Fractions, Decimals & Percentages

Percentage to decimal: Divide by 100 (move digits two places right). E.g., 6% = 0.06, 350% = 3.5.
Decimal to percentage: Multiply by 100 (move digits two places left, add %). E.g., 0.35 = 35%, 0.004 = 0.4%.
Decimal to fraction: Write digits over 10ⁿ (n = decimal places). E.g., 0.3 = 3/10, 0.07 = 7/100, 0.513 = 513/1000.
Percentage to fraction: Write over 100. E.g., 37% = 37/100.
Fraction to decimal: Convert to fraction over power of 10. E.g., 3/5 = 6/10 = 0.6; 7/20 = 35/100 = 0.35.
Fraction to percentage: Convert to decimal then multiply by 100. E.g., 4/5 = 0.8 = 80%.
Learn simple recurring decimals: 0.333… = 1/3, 0.666… = 2/3.

Recurring Decimals

Recurring decimal: A decimal with a repeating pattern; e.g., 0.323232… = 0.3̇2̇.
Notation: Dot over single repeating digit; dots over first and last of repeating block (e.g., 0.1̇2̇ for 0.121212…).
Converting to fraction: Set x = decimal, multiply by 10ⁿ until two lines have same repeating part, subtract, solve for x.
Worked example: 0.3̇07̇ → x = 0.307307…, 1000x = 307.307…, subtract: 999x = 307, so x = 307/999.
Always simplify fraction to lowest terms.

Ordering Fractions, Decimals & Percentages

Ordering fractions only: Write all with a common denominator, then compare numerators.
Example: 3/5, 1/2, 13/20, 7/12 → common denominator 60 → 36/60, 30/60, 39/60, 35/60 → order: 1/2, 7/12, 3/5, 13/20.
Ordering mixed FDP: Convert everything to decimals (or percentages) for easy comparison.
Example: 7/8, 5/6, 0.8, 78% → decimals: 0.875, 0.833…, 0.8, 0.78 → order: 78% < 0.8 < 5/6 < 7/8.
Use symbols: < (less than), > (greater than), ≤, ≥, =, ≠.

Ordering FDP: the 5-step method

Common Conversions & Tips

Memorise: 1/2 = 0.5 = 50%, 1/4 = 0.25 = 25%, 3/4 = 0.75 = 75%, 1/5 = 0.2 = 20%, 1/10 = 0.1 = 10%.
Calculator tip: Use calculator to check conversions even in non-calculator questions (for verification).
Non-calculator tip: For fractions, use short division or halving (e.g., 7/8 = half of 7/4, etc.).

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Câu hỏi luyện tập

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1.Which of the following is the decimal equivalent of 3/5?
Easy
- A0.35
- B0.6
- C1.67
2.Write 0.45 as a percentage.
Easy
- A4.5%
- B45%
- C0.45%
- D450%
3.Convert 72% to a fraction in its simplest form.
Easy
- A72/100
- B18/25
- C36/50
- D7.2/10
4.Which number has the largest value?
Medium
- A0.3030
- B1/3
- C0.0330
- D3/10
- E33%
5.Mr Mason asks 240 Year 11 students what they want to do next year. 15% want to go to college, 3/4 want to stay at school, and the rest do not know. How many students do not know?
Medium
- A24
- B36
- C60
- D12
6.Karen got 32 out of 80 in a maths test and 38% in an English test. Did she get a higher percentage in maths or English?
Medium
- AMaths
- BEnglish
- CSame
- DCannot tell
7.Prove algebraically that the recurring decimal 0.25̇ (0.25555...) equals which fraction?
Hard
- A23/90
- B25/99
- C23/99
- D25/90
8.Show that the recurring decimal 0.17̇ (0.17777...) equals which fraction?
Hard
- A8/45
- B17/99
- C16/90
- D8/90

Thêm câu hỏi

9.Mr Brown and his 2 children are going to London by train. Adult ticket costs £24, child ticket costs £12. Family Railcard gives 1/3 off adult tickets and 60% off child tickets. Work out the total cost.
Medium
- A£25.60
- B£28.00
- C£22.40
- D£30.40
10.Show that the recurring decimal 0.3̇96̇ equals which fraction?
Medium
- A44/111
- B396/999
- C396/1000
11.Write the recurring decimal 0.26̇ as a fraction.
Medium
- A4/15
- B26/99
- C13/45
12.Write the recurring decimal 0.32̇ as a fraction.
Medium
- A29/90
- B32/99
- C16/45
13.Write the recurring decimal 0.67̇ as a fraction in its simplest form.
Medium
- A61/90
- B67/99
- C67/100
14.Change the recurring decimal 0.18̇ to a fraction.
Medium
- A17/90
- B18/99
- C2/11
15.A shop has a sale. All items are reduced by 15%. A jacket originally costs £80. How much does it cost in the sale?
Easy
- A£68
- B£65
- C£12
- D£72
16.In a school, 180 students are asked about their favourite sport. 1/3 choose football, 25% choose basketball, and the rest choose tennis. How many students choose tennis?
Medium
- A75
- B60
- C45
- D90
17.Which is the largest: 0.45, 2/5, 44%, 0.4?
Easy
- A0.45
- B2/5
- C44%
- D0.4
18.The recurring decimal 0.1̇2̇ is equal to which fraction?
Medium
- A4/33
- B12/99
- C1/8
- D3/25
19.A rectangle has length 8 cm and width 5 cm. What percentage of the area is the area of a square of side 4 cm cut from it?
Medium
- A40%
- B50%
- C32%
- D20%
20.In a class of 30 students, 18 are girls. What percentage are girls?
Easy
- A60%
- B18%
- C30%
- D45%
21.A car costs $12000. Its value depreciates by 12% each year. What is its value after 2 years?
Medium
- A$9292.80
- B$10560
- C$10200
- D$8448
22.Write 7/20 as a decimal.
Easy
- A0.35
- B0.7
- C0.2
- D0.07
23.A pizza is cut into 8 equal slices. You eat 3 slices. What percentage of the pizza have you eaten?
Easy
- A37.5%
- B30%
- C35%
- D40%
24.Show that the recurring decimal 0.0̇9̇ is equal to which fraction?
Medium
- A1/11
- B9/100
- C1/10
- D9/99
25.In a sale, a shirt is reduced by 20% to $32. What was the original price?
Medium
- A$40
- B$38.40
- C$36
- D$42
26.What is 0.65 as a percentage?
Easy
- A65%
- B6.5%
- C0.65%
- D650%
27.A tank contains 300 litres of water. 15% is used, then 1/3 of the remainder is used. How many litres are left?
Medium
- A170
- B150
- C140
- D160
28.Place these in order, smallest first: 0.6, 5/8, 62%, 0.6̇.
Medium
- A0.6, 62%, 5/8, 0.6̇
- B0.6, 0.6̇, 62%, 5/8
- C62%, 0.6, 5/8, 0.6̇
- D0.6, 5/8, 62%, 0.6̇
29.A triangle has base 10 cm and height 6 cm. What is the area as a percentage of a rectangle with same base and height?
Easy
- A50%
- B60%
- C30%
- D40%
30.What is 3/4 as a percentage?
Easy
- A75%
- B34%
- C25%
- D50%
31.What is 0.6 as a fraction in its simplest form?
Easy
- A3/5
- B6/10
- C2/3
- D3/4
32.What is 72% as a decimal?
Easy
- A0.72
- B7.2
- C0.072
- D72.0
33.What is 3/8 as a percentage?
Easy
- A37.5%
- B38%
- C35%
- D40%
34.Show that the recurring decimal 0.38̇ (0.3888...) equals which fraction?
Medium
- A7/18
- B19/50
- C35/99
- D7/20
35.What is 0.75 as a percentage?
Easy
- A7.5%
- B75%
- C0.75%
- D750%
36.What is 20% as a decimal?
Easy
- A0.2
- B2.0
- C0.02
- D20.0
37.What is 3/5 as a percentage?
Easy
- A30%
- B35%
- C60%
- D65%
38.Which of the following is the largest?
Easy
- A0.4
- B2/5
- C38%
- D0.38
39.0.3̇ (0.333...) is equal to 1/3.
Easy
True or false?
40.Write 0.4̇ (0.444...) as a fraction in its simplest form.
Medium
- A4/9
- B2/5
- C4/10
- D44/99
41.Put these numbers in order, starting with the smallest: 0.6, 5/8, 62%, 0.6̇.
Medium
- 0.6
- 5/8
- 62%
- 0.6̇
42.Match each decimal to its equivalent fraction.
Easy
- 0.5
- 0.25
- 0.75
- 0.2
- 1/2
- 1/4
- 3/4
- 1/5
43.Which is the smallest: 0.45, 2/5, 44%, 0.4?
Medium
- A0.45
- B2/5
- C44%
- D0.4
44.Match each decimal to its equivalent percentage.
Easy
- 0.45
- 0.08
- 1.2
- 0.003
- 45%
- 8%
- 120%
- 0.3%
45.Complete the conversion: 0.8 = ___%
Easy
0.8 = ____%

Ghi chú ôn tập

## Working with FDP – Revision Notes ### Converting Fractions, Decimals & Percentages - **Percentage to decimal**: Divide by 100 (move digits two places right). - 6% = 0.06, 40% = 0.4, 350% = 3.5, 0.2% = 0.002 - **Decimal to percentage**: Multiply by 100 (move digits two places left, add %). - 0.35 = 35%, 1.32 = 132%, 0.004 = 0.4% - **Decimal to fraction**: Write digits over 10^n (n = decimal places). - 0.3 = 3/10, 0.07 = 7/100, 0.513 = 513/1000 - **Percentage to fraction**: Write over 100. - 37% = 37/100 - **Fraction to decimal**: Convert to denominator 10, 100, 1000… - 3/5 = 6/10 = 0.6, 7/20 = 35/100 = 0.35 - **Fraction to percentage**: Convert to decimal then multiply by 100. - 4/5 = 0.8 → 80% ### Recurring Decimals - **Definition**: A decimal with a repeating pattern (e.g., 0.333… = 0.3̇). - **Converting to fraction**: 1. Let x = recurring decimal (e.g., x = 0.353535…) 2. Multiply by 10 repeatedly until two lines have same repeating part. 3. Subtract those lines: 100x – x = 35.3535… – 0.3535… → 99x = 35 4. Solve: x = 35/99 (simplify if needed). - **Common ones**: 0.3̇ = 1/3, 0.6̇ = 2/3. ### Ordering FDP - **All fractions**: Write over common denominator, compare numerators. - **Mixed FDP**: Convert everything to decimals, then order. - **Symbols**: < (less than), > (greater than), ≤, ≥, =, ≠. ### Key Tips - Use a calculator to check conversions (if allowed). - For ordering, write decimals to same number of places.

Recurring decimal: A decimal with a repeating pattern of digits, e.g., 0.333… = 0.3̇. It is rational and can be written as a fraction.
Terminating decimal: A decimal that ends, e.g., 0.25.
Lowest common denominator: The smallest number that is a multiple of all denominators in a set of fractions, used to compare or add them.

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