Working With Fdp

遊んで学ぼう

問題に答えてエネルギーを集めたら、釣りや探検を楽しもう。アカウント不要。

先生の方へ： Working With Fdp（Maths [CIE]、Extended）向けのすぐ使えるレッスンスライド, 復習ノート, 図解 — レッスンで使うか、生徒がライブゲームとして遊ぶインタラクティブなクラス活動としてトピックを実施できます。

レッスンノート

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.).

スライド

Step through every slide for this topic — plus flashcards and revision notes — with a free account.

登録 — 無料ログイン

練習問題

無料プレビュー — 45問中8問。すべて見るには登録を。

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

もっと問題

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 = ____%

復習ノート

## 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.

Unlock all 45 questions & more

無料アカウントを作って、このトピックのすべての問題・スライド・フラッシュカード・復習ノートを見よう。

登録 — 無料ログイン

過去問

このトピックの過去問練習は近日公開。

近日公開