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: Numerator Fraction Line Denominator 2 GFP - Sohar University SET 1 - Chapter 3

• Below is a number of examples on fractions: = = = = = = = = = SET 1 - Chapter 3 3 GFP - Sohar University 3 - 2 Proper and Improper Fractions ةبسانملا ريغ و ةبسانملا روـسكلا • A proper fraction is a fraction where the numerator is less than denominator, such as: • An improper fraction is a fraction where the numerator is greater than or equal to the denominator, such as: 4 GFP - Sohar University SET 1 - Chapter 3

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. = = = = SET 1 - Chapter 3 5 GFP - Sohar University Example 1: Solution: 6 GFP - Sohar University SET 1 - Chapter 3

Example 2: Solution: Example 3: Solution: SET 1 - Chapter 3 7 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 GFP - Sohar University SET 1 - Chapter 3

Example 4: Solution: 32.65 18.431 + 24.176 75.257 So, 32.65 + 18.431 + 24.176 = 75.257 372.18 318.54 ‒ 53.64 ‒ 117.25 318.54 201.29 Thus, 372.18 ‒ 53.64 ‒ 117.25 = 201.29 SET 1 - Chapter 3 9 GFP - Sohar University Example 5: Solution: rounded to 4 decimal places rounded to 4 decimal places 10 GFP - Sohar University SET 1 - Chapter 3

Example 6: Solution: rounded to 3 significant places rounded to 3 significant places rounded to 3 significant places SET 1 - Chapter 3 11 GFP - Sohar University Example 7: Evaluate (a) 2.134 × 5.16 (b) 18.142 × 10 (c) 18.142 × 100 (d) 18.142 × 1000 Solution: (b) 18.142 × 10 = 181.42 (c) 18.142 × 100 = 1814.2 (c) 18.142 × 1000 = 18142 12 GFP - Sohar University SET 1 - Chapter 3

Example 8: Evaluate: (a) 5284.32 ÷ 10 (b) 5284.32 ÷ 100 (c) 5284.32 ÷ 1000 Solution: (a) 5284.32 ÷ 10 = 528.432 (b) 5284.32 ÷ 100 = 52.8432 (c) 5284.32 ÷ 1000 = 5.28432 SET 1 - Chapter 3 13 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), or as a fraction ( ). • For example, in the following figure there are 5 circles and 6 squares. • So, the ratio of circles to squares is (5 : 6) or (5 to 6) or ( ) • And, the ratio of squares to circles is (6 : 5) or (6 to 5) or ( ) 14 GFP - Sohar University SET 1 - Chapter 3

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: Ratio Thus, tables to chairs ratio or 8 : 7 or 8 to 7 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 = 45 ‒ 15 = 30 Boys to girls ratio or 1 to 2 SET 1 - Chapter 3 15 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 of ice-cream? Solution: 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) 16 GFP - Sohar University SET 1 - Chapter 3

3 - 6 Percentages ةيوئملا بـسـنلا • Percentage is a ratio with a base of 100. • Below are two examples on percentages: 25% of the squares are green 50% of the squares are green 75% of the squares are white 50% of the squares are white SET 1 - Chapter 3 17 GFP - Sohar University Example 12: Express the following as percentages: (a) 0.32 (b) 2.51 (c) 9.0582 (d) (e) (f) Solution: 18 GFP - Sohar University SET 1 - Chapter 3

Example 13: Express the following as decimal fractions: (a) 25% (b) 40% (c) 81.3% (d) 3.75% Solution: SET 1 - Chapter 3 19 GFP - Sohar University Example 14: Express the following as proper fractions: (a) 30% (b) 42% (c) 21.5% Solution: 20 GFP - Sohar University SET 1 - Chapter 3

Example 15: Express the following as mixed numbers: (a) 340% (b) 225% Solution: Example 16: Evaluate 12.7% of 257 Solution: SET 1 - Chapter 3 21 GFP - Sohar University Example 17: A notebook has 250 pages out of which 172 pages were used. What is the percentage of unused pages? Solution: 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: 22 GFP - Sohar University SET 1 - Chapter 3