Fractions, Decimals, Ratios and Percentages - - PDF document

Fractions, Decimals, Ratios and Percentages

ةيوئملا بـسنلا و بـسنلا و ةيرشعلا روـسكلا و روـسكلا 3 -1 Fractions

روـسكلا

• A fraction is part of a whole. When something is broken up into

a number of parts, the fraction shows how many of those parts you have.

• For example, the fraction means one part of 4 parts:

2

Numerator Denominator

Fraction Line

SET 1 - Chapter 3 GFP - Sohar University

• Below is a number of examples on fractions:

3

= = = = = = = = =

SET 1 - Chapter 3 GFP - Sohar University

3 - 2 Proper and Improper Fractions ةبسانملا ريغ و ةبسانملا روـسكلا

• An improper fraction is a fraction where the numerator is

greater than or equal to the denominator, such as:

4

• A proper fraction is a fraction where the numerator is less than

denominator, such as:

SET 1 - Chapter 3 GFP - Sohar University

3 - 3 Mixed Numbers

ةطلتخملا دادعلؤا

• An improper fraction can also be written as a mixed number.
• A mixed number is a number that contains both a whole number and

a proper fraction.

5

= =

= =

SET 1 - Chapter 3 GFP - Sohar University

Example 1:

6

Solution:

SET 1 - Chapter 3 GFP - Sohar University

Example 2:

7

Solution:

Example 3:

Solution:

SET 1 - Chapter 3 GFP - Sohar University

3 - 4 Decimals

ةيرـشعلا روـسكلا

• A decimal is a fraction that has a denominator of a power of ten.
• A point or dot is used to separate the whole number part from the

fractional part of a number.

• For example, in the number 17.591, the decimal point separate 17 (the

whole number part) from 591 (the fractional part).

8 SET 1 - Chapter 3 GFP - Sohar University

Example 4:

Solution:

32.65 18.431 24.176 75.257 + So, 32.65 + 18.431 + 24.176 372.18 ‒ 53.64 318.54

318.54

‒ 117.25 201.29 Thus, 372.18 ‒ 53.64 ‒ 117.25 = 201.29 = 75.257

9 SET 1 - Chapter 3 GFP - Sohar University

Example 5:

Solution:

rounded to 4 decimal places rounded to 4 decimal places

10 SET 1 - Chapter 3 GFP - Sohar University

Example 6:

Solution:

rounded to 3 significant places rounded to 3 significant places rounded to 3 significant places

11 SET 1 - Chapter 3 GFP - Sohar University

Example 7: Evaluate (a) 2.134 × 5.16 (b) 18.142 × 10 (c) 18.142 × 100 (d) 18.142 × 1000

Solution:

12

(b) 18.142 × 10 (c) 18.142 × 100 (c) 18.142 × 1000 = 181.42 = 1814.2 = 18142

SET 1 - Chapter 3 GFP - Sohar University

Example 8: Evaluate: (a) 5284.32 ÷ 10 (b) 5284.32 ÷ 100 (c) 5284.32 ÷ 1000

Solution:

13

(a) 5284.32 ÷ 10 (b) 5284.32 ÷ 100 (c) 5284.32 ÷ 1000 = 528.432 = 52.8432 = 5.28432

SET 1 - Chapter 3 GFP - Sohar University

3 - 5 Ratios

بـسـنلا

• A ratio is a comparison of two or more numbers which represent

different objects.

• It can be written with a colon (1:5), or using the word "to" (1 to 5),
• r as a fraction ( ).
• For example, in the following figure

14

• So, the ratio of circles to squares

is (5 : 6)

• r (5 to 6) or ( )

there are 5 circles

• And, the ratio of squares to circles

is (6 : 5)

• r (6 to 5) or ( )

SET 1 - Chapter 3 GFP - Sohar University

and 6 squares.

Example 9: A classroom contains 32 tables and 28 chairs. Find the ratio of tables to chairs and write it in the simplest form.

Solution:

15

Ratio

• r 8 : 7
• r 8 to 7

Thus, tables to chairs ratio

Example 10: The number of students in a Mathematic class is 45. What is

the boys to girls ratio if there are 15 boys in that class, expressed in the simplest form?

Solution:

Number of girls in the class

• r 1 to 2

Boys to girls ratio = 45 ‒ 15 = 30

SET 1 - Chapter 3 GFP - Sohar University

Example 11: Flavours, sugar and milk are used in an ice-cream recipe in the ratio of 2 to 3 to 10 respectively. How much flavours, sugar and milk should be used to produce 60 kg of this type

• f ice-cream?

Solution:

16

Total number of parts = 2 + 3 + 10 = 15 1 part of the 60 kg 2 parts = 2 × 4 = 8 kg 3 parts = 3 × 4 = 12 kg 10 parts = 10 × 4 = 40 kg So, 8 kg of flavours, 12 kg of sugar, and 40 kg of milk should be used to produce 60 kg of this type of ice-cream. (check: 8 + 12 + 40 = 60)

SET 1 - Chapter 3 GFP - Sohar University

3 - 6 Percentages

ةيوئملا بـسـنلا

• Percentage is a ratio with a base of 100.
• Below are two examples on percentages:

17 SET 1 - Chapter 3 GFP - Sohar University

25% of the squares are green 75% of the squares are white 50% of the squares are green 50% of the squares are white

Example 12: Express the following as percentages: (a) 0.32 (b) 2.51 (c) 9.0582 (d) (e) (f)

Solution:

18 SET 1 - Chapter 3 GFP - Sohar University

Example 13: Express the following as decimal fractions: (a) 25% (b) 40% (c) 81.3% (d) 3.75%

Solution:

19 SET 1 - Chapter 3 GFP - Sohar University

Example 14: Express the following as proper fractions: (a) 30% (b) 42% (c) 21.5%

Solution:

20 SET 1 - Chapter 3 GFP - Sohar University

Example 15: Express the following as mixed numbers: (a) 340% (b) 225%

Solution:

21 SET 1 - Chapter 3 GFP - Sohar University

Example 16: Evaluate 12.7% of 257

Solution:

Example 17: A notebook has 250 pages out of which 172 pages were used. What is the percentage of unused pages?

Solution:

22 SET 1 - Chapter 3 GFP - Sohar University

Example 18: In the first semester, 350 students registered an English course and 40% of them were boys. Calculate the number of girls who registered this course.

Solution: