Decimals, fractions and percentages

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What is a Percentage?

A percentage is a way of showing a part out of 100. The word comes from Latin and means 'by the hundred'.
The percent sign is %. For example, 45% means 45 out of every 100.
45% is the same as the fraction 45/100 or the decimal 0.45.
Percentages are used to compare parts of a whole, like how many students like pizza.

Converting Fractions to Decimals and Percentages

To change a fraction to a decimal, divide the top number by the bottom number. For example, 1/2 = 0.5.
To change a decimal to a percentage, multiply by 100. So 0.5 becomes 50%.
Common conversions to remember: 1/2 = 0.5 = 50%, 1/4 = 0.25 = 25%, 3/4 = 0.75 = 75%.
Also remember: 1/5 = 0.2 = 20%, 2/5 = 0.4 = 40%, 3/5 = 0.6 = 60%, 4/5 = 0.8 = 80%.
Tenths are easy: 1/10 = 0.1 = 10%, 7/10 = 0.7 = 70%.
Hundredths are easy too: 1/100 = 0.01 = 1%, 25/100 = 0.25 = 25%.

Converting Percentages to Fractions and Decimals

To change a percentage to a fraction, write it over 100 and simplify. For example, 25% = 25/100 = 1/4.
To change a percentage to a decimal, divide by 100. So 25% = 0.25.
Remember: 100% = 1 whole. So 100% = 1 as a decimal and 100/100 as a fraction.
Percentages can be more than 100%. For example, 150% = 1.5 as a decimal and 150/100 = 3/2 as a fraction.

Finding a Percentage of an Amount

To find 10% of a number, divide the number by 10. For example, 10% of 80 is 8.
To find 1% of a number, divide the number by 100. For example, 1% of 500 is 5.
To find 25% of a number, divide by 4. For example, 25% of 60 is 15.
To find 50% of a number, divide by 2. For example, 50% of 120 is 60.
For other percentages, first find 1% or 10%, then multiply. For example, to find 15% of 200, find 10% (20) and 5% (10), then add to get 30.
You can also convert the percentage to a decimal and multiply. For example, 15% of 200 = 0.15 × 200 = 30.

Adding and Subtracting Decimals

When adding or subtracting decimals, line up the decimal points.
Write the numbers one under the other, with the decimal points in a column.
Add or subtract like whole numbers, then bring the decimal point straight down.
Example: 3.25 + 1.4 = 4.65. Line up: 3.25 + 1.40 = 4.65.
Example: 5.6 − 2.35 = 3.25. Line up: 5.60 − 2.35 = 3.25.

Multiplying and Dividing Decimals

To multiply decimals, multiply as if they were whole numbers, then count the total number of decimal places in both factors.
Place the decimal point in the answer so it has the same number of decimal places. Example: 0.3 × 0.4 = 0.12 (1+1=2 decimal places).
To divide a decimal by a whole number, divide as usual and bring the decimal point straight up in the answer.
To divide by a decimal, move the decimal point in the divisor to make it a whole number, and move the decimal point in the dividend the same number of places.
Example: 1.2 ÷ 0.3 = 4. Move both decimals one place: 12 ÷ 3 = 4.

Using Percentages in Real Life

Percentages are used in money, like sales tax and discounts. A 10% discount on a $20 toy means you pay $18.
If a price increases by 10%, the new price is 110% of the original. For example, a $200 bike that rises 10% costs $220.
If a price decreases by 10%, the new price is 90% of the original. For example, a $200 bike on sale for 10% off costs $180.
Percentages can be used to compare parts of a group, like '60% of the class are girls'.

Common Mistakes to Avoid

Do not forget to line up decimal points when adding or subtracting decimals.
When converting a percentage to a decimal, divide by 100, not by 10. For example, 5% = 0.05, not 0.5.
When finding a percentage of an amount, do not just take the percentage as a whole number. For example, 20% of 50 is 10, not 20.
Remember that 100% is the whole amount. So 100% of 30 is 30.
Be careful with percentages over 100%. For example, 200% of 10 is 20.

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1.What does the percent sign (%) mean?
Easy
- Aout of 100
- Bout of 10
- Cout of 1000
- Dout of 1
2.Which fraction is equal to 25%?
Easy
- A1/4
- B1/5
- C1/2
- D1/10
3.45% is equal to the fraction 45/100.
Easy
True or false?
4.A class has 500 students. If 50% are male, how many are male?
Medium
- A250
- B50
- C500
- D100
5.A price rises from $2.50 to $2.65. What is the percentage increase?
Medium
- A6%
- B15%
- C0.06%
- D10%
6.Which of the following are equal to 0.4? (select all that apply)
Medium
- A40%
- B4/10
- C4%
- D0.04
- E2/5
7.Put these numbers in order from smallest to largest: 0.3, 30%, 0.03, 3/10
Medium
- 0.3
- 30%
- 0.03
- 3/10
8.Match each fraction to its equivalent percentage.
Easy
- 1/2
- 1/5
- 1/10
- 10%
- 20%
- 50%

Mehr Fragen

9.Put these numbers in order from smallest to largest: 0.6, 55%, 3/5, 0.65
Medium
- 0.6
- 55%
- 3/5
- 0.65
10.Which of the following are equal to 3/4? (select all that apply)
Medium
- A75%
- B0.75
- C7.5%
- D0.075
- E3:4
11.50% of 40 is 20.
Easy
True or false?
12.In a school, 40% of the students walk to school. If there are 350 students, how many walk?
Hard
- A140
- B120
- C160
- D100
13.A book costs $12. The price increases by 25%. What is the new price?
Medium
- A$15
- B$14
- C$16
- D$13
14.Which of these are equivalent to 20%? (select all that apply)
Medium
- A0.2
- B1/5
- C0.02
- D2/10
- E20/100
15.0.6 is greater than 60%.
Easy
True or false?
16.Which of these is equal to 0.07?
Easy
- A7%
- B70%
- C0.7%
- D7/10
17.What is 20% of 45?
Medium
- A9
- B8
- C10
- D15
18.Which of these is NOT equal to 0.5?
Medium
- A5%
- B50%
- C1/2
- D0.50
19.Which of the following are equal to 0.25? (select all that apply)
Medium
- A25%
- B1/4
- C2/5
- D0.250
- E25/100
20.To change a fraction to a percentage, you multiply the fraction by 100.
Easy
True or false?
21.Put these numbers in order from smallest to largest: 0.4, 4%, 1/4, 0.25
Medium
- 0.4
- 4%
- 1/4
- 0.25
22.A bag contains 60 marbles. 30% are blue and the rest are red. How many red marbles are there?
Medium
- A18
- B30
- C42
- D20
23.Which of the following are true? (select all that apply)
Medium
- A0.5 is equal to 50%
- B1/4 is equal to 0.4
- C0.3 is equal to 30%
- D3/5 is equal to 0.6
- E0.75 is equal to 75%
24.If a price increases by 10%, the new price is 110% of the original price.
Easy
True or false?
25.Put these numbers in order from smallest to largest.
Medium
- 0.35
- 35%
- 1/3
- 0.3
26.A rectangle has a length of 12 cm and a width of 8 cm. If the length is increased by 25% and the width is decreased by 25%, what is the new area in square centimetres?
Hard
- A96
- B90
- C72
- D80
27.In a survey, 200 people were asked their favourite sport. 45% chose football, 30% chose basketball, and the rest chose tennis. How many people chose tennis?
Medium
- A50
- B60
- C90
- D40
28.Which of the following is equal to 0.5?
Easy
- A50%
- B5%
- C0.05
- D1/5
29.To convert a percentage to a decimal, you divide by 100.
Easy
True or false?
30.What is 50% of 20?
Easy
- A10
- B5
- C15
- D20
31.Which of the following are equal to 3/5? (select all that apply)
Medium
- A0.6
- B60%
- C0.35
- D6/10
- E35%
32.Put these numbers in order from smallest to largest: 0.25, 25%, 0.5, 1/4
Medium
- 0.25
- 25%
- 0.5
- 1/4
33.Match each fraction to its decimal equivalent.
Easy
- 1/2
- 1/4
- 3/4
- 0.5
- 0.25
- 0.75
34.Which of the following is NOT equal to 0.5?
Medium
- A50%
- B5/10
- C0.05
- D1/2
35.Put these numbers in order from smallest to largest: 0.75, 7/10, 65%, 0.8
Medium
- 0.75
- 7/10
- 65%
- 0.8
36.Which of these are equal to 0.6? (select all that apply)
Easy
- A60%
- B6/10
- C3/5
- D6%
- E0.60
37.What is 10% of 250?
Easy
- A25
- B2.5
- C250
- D0.25
38.If a price increases by 200%, the new price is three times the original price.
Medium
True or false?
39.Match each decimal to its equivalent percentage.
Medium
- 0.05
- 0.2
- 0.35
- 0.9
- 5%
- 20%
- 35%
- 90%
40.Which of the following is equal to 0.7?
Easy
- A7%
- B70%
- C7/100
- D0.07
41.Write 0.75 as a percentage.
Easy
42.Complete the sentence.
Easy
To find 50% of 500, you can find ____ out of every 100, which gives ____.
43.What is 20% of 50?
Medium
44.What does the word 'percent' mean in Latin?
Easy
45.A shirt costs $24. It is on sale with a 25% discount. What is the sale price?
Medium
46.Fill in the missing numbers.
Easy
0.3 = ____% = ____/10
47.What is 0.125 as a percentage?
Medium
48.A pizza has 8 slices. You eat 3 slices. What percentage of the pizza did you eat?
Medium
49.Convert 0.3 to a percentage.
Easy
50.Fill in the blank: The symbol % means 'per ______'.
Easy
The symbol % means 'per ____'.
51.A jacket costs $80. The price increases by 15%. What is the increase in dollars?
Medium
52.Write 3/5 as a percentage.
Medium
53.Explain how to convert the fraction 3/5 to a percentage.
Medium
54.In a class, 60% of students are girls. If 5% of the girls wear glasses, what percentage of the whole class are girls who wear glasses? Show your working.
Hard
55.Explain how to find 15% of 60 using the method of finding 1% first.
Hard
56.Write 0.75 as a percentage.
Easy
- A75 %
- B67 %
- C91 %
- D83 %
57.What is 20% of 50?
Medium
- A11
- B12
- C9
- D10
58.A shirt costs $24. It is on sale with a 25% discount. What is the sale price?
Medium
- A20 $
- B17 $
- C18 $
- D19 $
59.A pizza has 8 slices. You eat 3 slices. What percentage of the pizza did you eat?
Medium
- A41.3 %
- B33.7 %
- C37.5 %
- D45.1 %
60.Convert 0.3 to a percentage.
Easy
- A27 %
- B30 %
- C36 %
- D33 %
61.A jacket costs $80. The price increases by 15%. What is the increase in dollars?
Medium
- A11 $
- B13 $
- C12 $
- D14 $

Lernnotizen

## Decimals, Fractions and Percentages – Quick Revision ### What is a percentage? A **percentage** is a number out of 100. The word comes from Latin *per centum*, meaning 'by a hundred'. The symbol is **%**. So 45% means 45 out of 100, which is the fraction $\frac{45}{100}$ or the decimal 0.45. ### Converting between fractions, decimals and percentages - **Percentage to fraction**: Write the number over 100 and simplify if you can. Example: 25% = $\frac{25}{100}$ = $\frac{1}{4}$. - **Percentage to decimal**: Divide by 100. Example: 25% = 25 ÷ 100 = 0.25. - **Decimal to percentage**: Multiply by 100. Example: 0.75 × 100 = 75%. - **Fraction to percentage**: Divide the top by the bottom, then multiply by 100. Example: $\frac{3}{5}$ = 3 ÷ 5 = 0.6, then 0.6 × 100 = 60%. **Common conversions to remember:** - 1/2 = 0.5 = 50% - 1/4 = 0.25 = 25% - 3/4 = 0.75 = 75% - 1/5 = 0.2 = 20% - 2/5 = 0.4 = 40% - 3/5 = 0.6 = 60% - 4/5 = 0.8 = 80% - 1/10 = 0.1 = 10% - 1/100 = 0.01 = 1% ### Adding and subtracting decimals When you add or subtract decimals, **line up the decimal points**. Then add or subtract like whole numbers, and bring the decimal point straight down. Example: 3.25 + 1.4 = ? 3.25 + 1.40 ------ 4.65 ### Multiplying and dividing decimals - **Multiply**: Multiply like whole numbers, then count the total number of decimal places in both numbers. Put the decimal point in the answer that many places from the right. Example: 0.2 × 0.3 = 0.06 (because 2 × 3 = 6, and there are 2 decimal places in total). - **Divide**: If the divisor (the number you are dividing by) has a decimal, move the decimal point to make it a whole number. Move the decimal point in the dividend (the number being divided) the same number of places. Then divide as usual. Example: 1.5 ÷ 0.5 = 3 (move decimal one place in both: 15 ÷ 5 = 3). ### Finding a percentage of an amount To find a percentage of an amount, convert the percentage to a decimal and multiply. Example: Find 20% of 50. 20% = 0.20, so 0.20 × 50 = 10. ### Percentage increase and decrease When something increases by 10%, the new amount is 110% of the original. When it decreases by 10%, the new amount is 90% of the original. Example: A toy costs $20. Its price rises by 10%. The increase is 10% of $20 = $2, so the new price is $22. ### Money and measures Decimals are used for money (dollars and cents) and for measures like length (metres) and mass (kilograms). Always keep the decimal point in the right place. ### Key tips - Always say what the percentage is **of** – the total matters. - To find 1% of something, divide by 100. To find 10%, divide by 10. - Check your answer makes sense: 50% of a number is half, 25% is a quarter.

percentage: A number out of 100, shown with the % symbol. For example, 45% means 45 out of every 100.
decimal: A number with a decimal point, like 0.45. It shows parts of a whole using tenths, hundredths, etc.
fraction: A way to show part of a whole, like 1/2 or 3/4. The top number is the numerator, the bottom is the denominator.
percent sign (%): The symbol % means 'out of 100'. It comes from the Latin 'per centum'.
convert: To change a number from one form to another, like turning a fraction into a decimal or a percentage.
decimal point: The dot in a decimal number that separates the whole part from the fractional part, like in 3.25.
hundredths: One part out of 100 equal parts. In decimals, the second digit after the decimal point shows hundredths.
percentage increase: When an amount goes up by a certain percentage. The new amount is more than 100% of the original.
percentage decrease: When an amount goes down by a certain percentage. The new amount is less than 100% of the original.

Karteikarten

What does the word 'percent' mean?

It means 'out of 100' or 'by the hundred'. The symbol % is used for percent.

Write 45% as a fraction and as a decimal.

45% = 45/100 = 0.45.

What is 50% of 500 students?

50% means half, so 50% of 500 is 250 students.

How do you convert a fraction to a percentage?

Divide the top by the bottom to get a decimal, then multiply by 100 and add the % sign. For example, 3/4 = 0.75, so 75%.

How do you convert a decimal to a percentage?

Multiply the decimal by 100 and add the % sign. For example, 0.35 becomes 35%.

How do you convert a percentage to a decimal?

Divide the percentage by 100 and remove the % sign. For example, 25% becomes 0.25.

What is 25% as a fraction in simplest form?

25% = 25/100 = 1/4.

What is 20% as a fraction in simplest form?

20% = 20/100 = 1/5.

What is 10% as a fraction and as a decimal?

10% = 10/100 = 1/10 = 0.1.

What is 75% as a fraction and as a decimal?

75% = 75/100 = 3/4 = 0.75.

What is 50% of 80?

50% means half, so 50% of 80 is 40.

What is 10% of 250?

10% means one tenth, so 10% of 250 is 25.

What is 25% of 200?

25% means one quarter, so 25% of 200 is 50.

What is 5% of 60?

5% is 5 out of 100. 5% of 60 = 0.05 × 60 = 3.

What is 20% of 150?

20% is one fifth, so 20% of 150 is 30.

What is 75% of 120?

75% is three quarters, so 75% of 120 is 90.

What is 12.5% as a fraction?

12.5% = 12.5/100 = 1/8.

What is 33⅓% as a fraction?

33⅓% = 33⅓/100 = 1/3.

What is 0.6 as a percentage?

0.6 × 100 = 60%.

What is 0.08 as a percentage?

0.08 × 100 = 8%.

What is 3/5 as a percentage?

3/5 = 0.6, so 60%.

What is 7/10 as a percentage?

7/10 = 0.7, so 70%.

What is 1/4 as a percentage?

1/4 = 0.25, so 25%.

What is 1/2 as a percentage?

1/2 = 0.5, so 50%.

What is 1/5 as a percentage?

1/5 = 0.2, so 20%.

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