Chapter 3 Fractions PDF

FRACTIONS CHAPTER 3  In this chapter, we will discuss Types of fractions Differentiate proper fraction from improper fraction Compare and contrast mixed numbers and fractions Change mixed numbers to improper fractions and vice versa Reduce fractions to lowest terms and bui...

FRACTIONS CHAPTER 3  In this chapter, we will discuss Types of fractions Differentiate proper fraction from improper fraction Compare and contrast mixed numbers and fractions Change mixed numbers to improper fractions and vice versa Reduce fractions to lowest terms and build fractions to higher terms. Target Skills Perform operations on integers. Apply rules on signed numbers in word problems. Define prime, composites, factors and multiples based on given examples. List the prime factors of an integer Find the GCF and LCM of two or more integers.  TYPES OF FRACTIONS TOPIC 1 Recall: Fractions Represent a part of a whole a , a and b are integers and b ≠ 0 b 5 numerator denominator 7 vinculum Examples 1. There are 25 animals in JoJo's farm. 14 of them are cows and the rest are goats. What fraction of the animals were goats? How about cows? SOLUTION: a. 25 – 14 = 11 There are 11 goats out of 25 animals b. 14 are cows Examples 2. What fraction of the pizza was left? Examples 3. What fraction of each shape is shaded? Types of Fractions 1. Proper Fraction - If the numerator is less than the denominator 7 18 5 11 19 91 2. Improper Fraction - If the numerator is greater than the denominator 84 12 44 11 5 17 3. Mixed number - Combination of a whole number and a proper fraction 2 4 1 4 2 9 12 3 18 Examples: 5 2 1. Proper Fraction 5. 1 Mixed Number 14 9 54 2. 12 Proper Fraction 6. Improper Fraction 50 13 11 3. 7 7 Mixed Number 7. Proper Fraction 29 11 17 4. 15 Improper Fraction 8. Proper Fraction 83 8 Rules on Fractions If you divide a number by itself, then the quotient is equal to 1 3 100 28 =1 100 =1 28 =1 3 If you divide a number by 1, the quotient is the same number 5 1000 =5 1 = 1000 1  CHANGING MIXED NUMBERS TO IMPROPER FRACTIONS TOPIC 2 Steps: 1. Multiply the whole number to the denominator of the fraction. 2. Add the product to the numerator of the fraction. 3. Write the sum as the numerator of the new fraction then copy the same denominator. Example: 2 1. Change 4 to improper fraction. 9 a. Multiply the denominator and the whole number 9 × 4 = 36 b. Add the product to the numerator of the original fraction. 36 + 2 = 38 c. Use the sum as a numerator of the new fraction, then copy the denominator 2 4 = 9  1 2. Change 16 to improper fraction. 12 a. 16 × 12 = 192 b. 192 + 1 = 193 1 c. 16 12 = 7 3. Change 4 to improper fraction. 17 a. 17 × 4 = 68 b. 68 + 7 = 75 7 c. 4 = 17  8 4. Change 5 to improper fraction. 31 a. 5 × 31 = 155 b. 155 + 8 = 163 8 c. 5 = 31 16 5. Change 2 to improper fraction. 23 a. 23 × 2 = 46 b. 46 + 16 = 62 16 c. 2 = 23 CHANGING IMPROPER FRACTION TO MIXED NUMBERS TOPIC 3 Changing Improper Fraction to Mixed Numbers STEPS: 1. Divide the numerator by the denominator 2. The quotient will be the whole number of the mixed number 3. The remainder will be the numerator of the mixed number, then copy the denominator. Example: 35 1. Change to mixed numbers. 4 a. Divide the numerator by the denominator 35 ÷ 4 = 8 r. 3 b. Use the quotient as the whole number and the remainder as the numerator 3 8 4 c. Copy the denominator 35 3 = 8 4 4  183 2. Change to mixed numbers. 7 a. 183 ÷ 7 = 26 remainder 1 1 b. 26 7 183 c. = 7 123 3. Change to mixed number. 18 a. 123 ÷ 18 =6 remainder 15 15 b. 6 18 123 c. = 18  68 4. Change to mixed number. 10 a. 68 ÷ 10 = 6 remainder 8 8 b. 6 10 68 c. = 10 92 5. Change to mixed number. 15 a. 92 ÷ 15 = 6 remainder 2 2 b. 6 15 92 c. = 15 REDUCING FRACTIONS TO LOWEST TERM TOPIC 4 Definition: Equivalent Fractions - Fractions that have the same numerical value but have different forms. 8 1 = 16 2 0.5 = 0.5  How? Find the GCF of the numerator and the denominator and divide it on them Example: 64 1. Reduce 18 64 = 2 × 2 × 2 × 2 × 2 × 2 18 = 2 × 3 × 3 GCF: 2 64÷2 32 = ∴ = 18÷2 9 Example: 140 2. Reduce 24 140 = 2 × 2 × 5 × 7 24 = 2 × 2 × 2 × 3 GCF: 2 × 2 = 4 140÷4 35 = ∴ = 24÷4 6 Example: 246 3. Reduce 48 246 = 2 × 3 × 41 48 = 2 × 2 × 2 × 2 × 3 GCF: 2 × 3 = 6 246÷6 41 = ∴ = 48÷6 8 Using Prime Factors to reduce fractions 35 1. 14 35 5×7 = 14 2×7 35 = 14  81 2. 36 81 3 ×3 ×3 ×3 = 2 × 2 ×3 ×3 36 81 = 36 228 3. 36 228 2 × 2 × 3 × 19 = 2 ×2 ×3 ×3 36 228 = 36  236 4. 28 236 2 × 2 × 59 = 28 2 × 2 × 7 236 = 28 312 5. 56 312 2 × 2 × 2 × 3 × 13 = 56 2 × 2 × 2 × 7 312 = 56 RECAP 1. Types of fraction Proper Fraction Improper Fraction Mixed Numbers 2. Changing Mixed Numbers to Improper Fraction 3. Changing Improper Fraction to Mixed Numbers 4. Reducing Fraction to Lowest Term GCF Prime Factorization