Chapter 1 Fractions Review

Copyright © 2007 by Mosby, Inc. Objectives Adding, subtracting, multiplying fractions and mixed numbers Reducing factions to the lowest common denominator Copyright © 2007 by Mosby, Inc. All rights reserved.

Fractions – review of terms A fraction is a part of a whole Numerator: The top number in a fraction the dividend – the number being divided Denominator: The bottom number of a fraction – the divider the divisor What is the definition of a fraction? A fraction is a method of expressing the division of a whole into equal parts. Every fraction has a numerator and a denominator. What is the numerator? The numerator indicates the number of parts that you have of a divided whole. What is the denominator? The denominator indicates the number of parts into which the whole has been divided. Copyright © 2007 by Mosby, Inc. All rights reserved.

Copyright © 2007 by Mosby, Inc. Fractions (cont’d) Proper fraction 3/8 1/4 14/15 4/5 the top number is smaller than the bottom number Improper fraction 3/2 7/4 15/15 the top number is bigger than (or equal to) the bottom number What is the definition of a proper fraction? A proper fraction is a fraction in which the numerator is smaller than the denominator. What is the definition of an improper fraction? An improper fraction is a fraction in which the numerator is larger than or equal to the denominator. Copyright © 2007 by Mosby, Inc. All rights reserved.

Copyright © 2007 by Mosby, Inc. Fractions (cont’d) Complex fraction A complex fraction is a fraction where the numerator, denominator, or both contain a fraction Mixed number 2 3/8 7 1/4 1 14/15 each example is made up of a whole number and a proper fraction together What is the definition of a complex fraction? A complex fraction is one that has a fraction in its numerator, its denominator, or both. What is the definition of a mixed number? A mixed number is produced when a whole number is combined with a fraction. What is the definition of lowest common denominator? It is the smallest number that can be divided evenly by all denominators in a problem. Copyright © 2007 by Mosby, Inc. All rights reserved.

Lowest common denominator The least common denominator of two or more denominators is actually the smallest whole number that is divisible by each of the denominators. To find the lowest common denominator (LCD): Simply list the multiples of each denominator (multiply by 2, 3, 4, etc.) then look for the smallest number that appears in each list. 1/3 + 1/6 = What is the LCD? Copyright © 2007 by Mosby, Inc. All rights reserved.

Changing an Improper Fraction to a Mixed Number Convert: Dividing 23 by 7, you get 3 with a remainder of 2. Placing the remainder (2) over the denominator (7), you get a proper fraction of 2/7. Combining the proper fraction with the whole number obtained by dividing in the first step, you get a final answer of 3 2/7. Convert: 23/7 Dividing 23 by 7, you get 3 with a remainder of 2. Placing the remainder (2) over the denominator (7), you get a proper fraction of 2/7. Combining the proper fraction with the whole number obtained by dividing in the first step, you get a final answer of 3 2/7. Copyright © 2007 by Mosby, Inc. All rights reserved.

Changing a Mixed Number to an Improper Fraction Convert Multiplying the denominator (7) by the whole number (3), you get 21. Adding 21 to the numerator of the fraction (1), you get 22. Therefore, the final answer is 22/7. Convert: 3 1/7 Multiplying the denominator (7) by the whole number (3), you get 21. Adding 21 to the numerator of the fraction (1), you get 22. Therefore, the final answer is 22/7. Copyright © 2007 by Mosby, Inc. All rights reserved.

Changing a Fraction to an Equivalent Fraction with the LCD Example: Dividing the LCD (12) by the denominator of the fraction to be converted (3), you get four. Multiplying 4 by the numerator of the fraction to be converted (4), you get 16. Therefore, the final answer is 16/12. Convert: 4/3 = ?/12 Dividing the LCD (12) by the denominator of the fraction to be converted (3), you get four. Multiplying 4 by the numerator of the fraction to be converted (4), you get 16. Therefore, the final answer is 16/12. Copyright © 2007 by Mosby, Inc. All rights reserved.

Changing a Mixed Number to an Equivalent Fraction with a LCD Example: and Converting 10 2/3 to an improper fraction, you get 32/3. Dividing the LCD (9) by the denominator (3) of the fraction to be converted (32/3), you get 3. Multiplying 3 by the numerator of 32/3, you get 96. Therefore, the final answer is 96/9. Convert: 10 2/3 and 1/9 Converting 10 2/3 to an improper fraction, you get 32/3. Dividing the LCD (9) by the denominator (3) of the fraction to be converted (32/3), you get 3. Multiplying 3 by the numerator of 32/3, you get 96. Therefore, the final answer is 96/9. Copyright © 2007 by Mosby, Inc. All rights reserved.

Adding Fractions Having the Same Denominator Example: Add: Adding the numerators, 2 and 1, you get 3. Placing the sum (3) over the common denominator, you get 3/9. Reducing 3/9 to lowest terms, you get the final answer, 1/3. Add: 2/9 + 1/9 Adding the numerators, 2 and 1, you get 3. Placing the sum (3) over the common denominator, you get 3/9. Reducing 3/9 to lowest terms, you get the final answer, 1/3. Copyright © 2007 by Mosby, Inc. All rights reserved.

Adding Fractions Having Unlike Denominators Example: Add: Converting the fractions to equivalent fractions with the LCD (9), you get 6/9 and 1/9. Adding the numerators, 6 and 1, you get 7. Placing the sum (7) over the common denominator, you get 7/9. Reducing 7/9 to lowest terms, you get the final answer, 7/9. Add: 2/3 + 1/9 Converting the fractions to equivalent fractions with the LCD (9), you get 6/9 and 1/9. Adding the numerators, 6 and 1, you get 7. Placing the sum (7) over the common denominator, you get 7/9. Reducing 7/9 to lowest terms, you get the final answer, 7/9. Copyright © 2007 by Mosby, Inc. All rights reserved.

Adding Fractions Involving Whole Numbers and Unlike Denominators Example: Add: You have already added the fractions in the last exercise, getting 7/9 for the sum of 2/3 and 1/9. Therefore, the next step is to write the reduced fraction next to the sum of the whole numbers (5 + 1 = 6). The answer is 6 7/9. Add: 5 2/3 + 1 1/9 In this case, you have already added the fractions in the last exercise, getting 7/9 for the sum of 2/3 and 1/9. Therefore, the next step is to write the reduced fraction next to the sum of the whole numbers (5 + 1 = 6). The final answer is 6 7/9. Copyright © 2007 by Mosby, Inc. All rights reserved.

Subtracting Fractions Having the Same Denominator Examples: Subtract: The final answer is 1/9. The difference between the two fractions is 2/8. After reducing the resulting fraction, the final answer is 1/4. Subtract: 2/9 – 1/9 The final answer is 1/9. Subtract: 7/8 – 5/8 The difference between the two fractions is 2/8. After reducing the resulting fraction, the final answer is 1/4. Copyright © 2007 by Mosby, Inc. All rights reserved.

Subtracting Fractions with Unlike Denominators Examples: Subtract: Changing the fractions to equivalent fractions gives 6/9 for 2/3 and 1/9 for 1/9. The difference between the two fractions is 5/9. After reducing the resulting fraction, the final answer is 5/9. Subtract: 2/3 – 1/9 Changing the fractions to equivalent fractions gives 6/9 for 2/3 and 1/9 for 1/9. The difference between the two fractions is 5/9. After reducing the resulting fraction, the final answer is 5/9. Copyright © 2007 by Mosby, Inc. All rights reserved.

Subtracting Fractions Involving Whole Numbers and Unlike Denominators Changing the fractions to equivalent fractions gives 4/14 for 2/7 and 1/14 for 1/14. The difference between the two fractions is 3/14, which is already in lowest terms. The difference between the whole numbers is 5. The answer is 5 3/14. Subtract: 5 2/7 – 1/14 Changing the fractions to equivalent fractions gives 4/14 for 2/7 and 1/14 for 1/14. The difference between the two fractions is 3/14, which is already in lowest terms. The difference between the whole numbers is 5. Therefore, the final answer is 5 3/14. Fractions Aren't So Scary Fraction song Copyright © 2007 by Mosby, Inc. All rights reserved.

Copyright © 2007 by Mosby, Inc. Time to practice! Ch 1 Work sheet starts on page 21. Do the first 6 problems of each of these sets (24 problems total) Change improper fractions to mixed numbers Change mixed numbers to improper fractions Add and reduce fractions Subtract and reduce fractions Read pages 9 – 16 in text for example problems Check your answers in the back of the text Turn in to bin (this is homework if you don’t finish in class) Copyright © 2007 by Mosby, Inc. All rights reserved.

Question: Solve & reduce!     Copyright © 2007 by Mosby, Inc. All rights reserved.

Multiplying Fractions and Mixed Numbers Converting the mixed numbers to improper fractions gives 55/4 for 13 3/4 and 21/10 for 2 1/10. The product of the numerators is 1155, and the product of the denominators is 40. The resulting fraction is 1155/40. Therefore, reducing to lowest terms, the answer is 28 7/8. Multiply: 13 3/4 × 2 1/10 Converting the mixed numbers to improper fractions gives 55/4 for 13 3/4 and 21/10 for 2 1/10. The product of the numerators is 1155, and the product of the denominators is 40. The resulting fraction is 1155/40. Therefore, reducing to lowest terms, the final answer is 28 7/8. Copyright © 2007 by Mosby, Inc. All rights reserved.

Dividing Fractions and Mixed Numbers Example: Divide: Converting the mixed numbers to improper fractions gives 55/4 for 13 3/4 and 2/1 for 2. The inverted divisor is 1/2, and the product of the resulting fractions (55/4 and 1/2) is 55/8. Therefore, reducing to lowest terms, the answer is 6 7/8. Divide: 13 3/4 ÷ 2 Converting the mixed numbers to improper fractions gives 55/4 for 13 3/4 and 2/1 for 2. The inverted divisor is 1/2, and the product of the resulting fractions (55/4 and 1/2) is 55/8. Therefore, reducing to lowest terms, the final answer is 6 7/8. Copyright © 2007 by Mosby, Inc. All rights reserved.

Reducing a Complex Fraction with Mixed Numbers Example: Converting the mixed numbers to improper fractions gives 38/7 and 6/5. Rewriting this as a division problem, you have 38/7 ÷ 6/5. Invert the divisor and the product of the fractions is 190/42. Reducing to lowest terms, the answer is 4 11/21. Reduce: (5 3/7) / (1 1/5) Converting the mixed numbers to improper fractions gives 38/7 for 5 3/7 and 6/5 for 1 1/5. Rewriting this as a division problem, you have 38/7 ÷ 6/5. The inverted divisor is 5/6, and the product of the fractions is 190/42. Therefore, reducing to lowest terms, the final answer is 4 11/21. Copyright © 2007 by Mosby, Inc. All rights reserved.

Copyright © 2007 by Mosby, Inc. Time to practice! Ch 1 Work sheet on page 23. Do all the problems of each of these sets (24 problems total) Multiply and reduce fractions Divide and reduce fractions Read pages 17-19 in text for example problems Check your answers in the back of the text Turn in to bin (this is homework if you don’t finish in class) Copyright © 2007 by Mosby, Inc. All rights reserved.

Do you know your stuff? Complete Post Test 1 on page 25 & 26 (30 problems) Check your work at the back of the text You will also see problems like those we did yesterday. Let’s check your answers to these too! Turn in to the bin .

Ch 1 Quiz    

Time to show what you know! Get a calculator, a pencil, and spread out. Chapter 1

Copyright © 2007 by Mosby, Inc. Fractions in the world Math magician Copyright © 2007 by Mosby, Inc. All rights reserved.