Skill. 19 Simplify Fractions. Using Skill 19 COMMON ERRORS. 85 Holt Matemáticas. OBJECTIVE Write a fraction in simplest form

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1 Skill 9 Simplify Fractions Using Skill 9 OBJECTIVE Write a fraction in simplest form Write on the board. Ask: What are some factors of the numerator? ( and ) What are some factors of the denominator? ( and ) How many factors do and have in common? (one) What is it? () Direct the students attention to the definition of simplest form. Ask: Why can you say is in simplest form? (because the only common factor of the numerator and denominator is ) Review the definition of simplest form, explaining that is the greatest common factor of both and. For Step, have students tell you the factors of and of. Then for Step, write the pairs of common factors on the board as students name them. (, ;, ;, ;, ; and, ) Ask: What is the greatest common factor? () For Step, help students realize that is equal to. So, when a fraction is divided by, the value of the fraction does not change. Then ask: How can you tell that is in simplest form? (because the only common factor of the numerator and denominator is ) TRY THESE Exercises model the type of exercises students will find on the Practice on Your Own page. Exercises and common factors Exercise more than common factors PRACTICE ON YOUR OWN Review the example for simplifying a fraction greater than at the top of the page. Ask: How can you tell that is greater than? (The numerator is greater than the denominator.) CHECK Determine if students know how to find factors and the greatest common factor of the numerator and denominator and use the GCF to find the simplest form. Success is indicated by out of correct responses. Students who successfully complete the Practice on Your Own and Check are ready to move to the next skill. COMMON ERRORS Students may divide the numerator by one factor and the denominator by a different factor. Students may use a common factor but not the greatest common factor. Students who made more than errors in the Practice on Your Own, or who were not successful in the Check section, may benefit from the Alternative Teaching Strategy on the next page. Minutes Holt Matemáticas

2 Optional Alternative Teaching Strategy Modeling Simplest Forms of Fractions OBJECTIVE Use models to find the simplest form for a fraction MATERIALS fraction circles for halves, fourths, eighths, and sixteenths Minutes An alternate method for finding the simplest form is to use,, or as a trial divisor and keep reducing the fraction until it is in simplest form. Have students use fraction circles. For example, write on the board. Have students find the fraction circle for eighths and shade of the parts. Continue: Suppose we again divide the numerator and denominator by. What is the result? ( ) Have students find the fraction circle for halves and shade of the parts. Say: Suppose we divide the numerator and denominator by. What is the result? ( ) Have students find the fraction circle for fourths and shade of them. The circle models help students to visualize that any further division is not possible. At the same time they see that there can be more than one equivalent fraction for many fractions. Repeat the activity to find the simplest form for. Holt Matemáticas

3 Nombre Simplificar fracciones 9 Una fracción está en su mínima expresión cuando el máximo común divisor, o MCD, del numerador y del denominador es. Escribe en su mínima expresión. Paso Escribe los factores del numerador y del denominador. Paso Busca los factores comunes. Encierra en un círculo el máximo común divisor numerador,,,,, (MCD). denominador,,,, 9, numerador,,,,, denominador,,,, 9, Paso Divide el numerador y el denominador entre el MCD. Inténtalo La mínima expresión de es. Escribe cada fracción en su mínima expresión. Halla el MCD y enciérralo en un círculo. Halla el MCD y enciérralo en un círculo. 0 Halla el MCD y enciérralo en un círculo.,,,,,,,, Divide el numerador y el denominador entre el MCD.,,,,,,, Divide el numerador y el denominador entre el MCD. 0,,,,,, 0 Divide el numerador y el denominador entre el MCD. 0 Ir a siguiente página Holt Matemáticas

4 Nombre Practica por tu cuenta 9 Escribe en su mínima expresión. Paso Haz una lista con todos los factores del numerador y del denominador. Encierra en un círculo el MCD. Paso Divide el numerador y el denominador entre el MCD.,,,,,,,,,, ó Escribe cada fracción en su mínima expresión. 9 Encierra en un círculo el MCD. 9,, 9,,,,, Divide el numerador y el denominador entre el MCD. 9 Encierra en un círculo el MCD.,,,,,, Divide el numerador y el denominador entre el MCD. Encierra en un círculo el MCD.,,,,,9, Divide el numerador y el denominador entre el MCD. Escribe los factores. Halla el MCD. Luego, escribe la fracción en su mínima expresión MCD MCD MCD mínima expresión mínima expresión mínima expresión Escribe la fracción en su mínima expresión. 9 9 Comprueba Escribe la fracción en su mínima expresión Holt Matemáticas

5 Skill Write a Mixed Number as an Improper Fraction Using Skill OBJECTIVE Write an improper fraction for a mixed number Begin by asking: How many halves equal whole? ( halves) How many thirds equal whole? ( thirds) How many fourths equal whole? ( fourths) Help students recall that when the numerator and the denominator of a fraction are the same, the fraction is equal to. Have students discuss the steps on Skill, focusing on how to rename the whole-number part as an equivalent number of s and then how to rename each as an equivalent number of halves. For Step, ask: How many ones equal? ( ones) For Step, ask: How many halves equal each whole? ( halves) For Step, ask: How do you find the number of halves there are in all? (Add the numerators of the fractions.) Note that the fraction for is. TRY THESE Exercises model the type of exercises students will find on the Practice on Your Own page. Exercise Write as. Exercise Write as. Exercise Write as 9. PRACTICE ON YOUR OWN Review the example at the top of the page. Ask: How many ones make wholes? ( ones) How many fifths make each whole? ( fifths) So, how many fifths are there in all? ( fifths) CHECK Determine if students know how to rename the whole-number part of a mixed number as an equivalent number of s and then how to rename each as an equivalent number of parts indicated by the denominator of the fraction part. Success is indicated by out of correct responses. Students who successfully complete the Practice on Your Own and Check are ready to move to the next skill. COMMON ERRORS Students may add the denominator, the whole number, and the numerator to get the numerator for the improper fraction. Students may miscount the number of wholes when renaming them as fractions. Students who made more than errors in the Practice on Your Own, or who were not successful in the Check section, may benefit from the Alternative Teaching Strategy on the next page. Minutes 9 Holt Matemáticas

6 Optional Alternative Teaching Strategy Model Improper Fractions for Mixed Numbers OBJECTIVE Make models of improper fractions for mixed numbers MATERIALS fraction circles for halves and fourths Minutes Have students use fraction circles as models to show fractions for whole numbers and mixed numbers. Begin by asking students to show how many halves are in whole. Students shade halves of whole circle. Then ask them to show how many halves are in wholes and half. Students shade halves using whole circles. wholes + half = whole = Than ask them to show how many halves are in wholes. Students shade halves using whole circles. Next, have students discuss how they might show an improper fraction for. Ask: How many whole circles will you need to show the whole-number part? ( whole circles) How will you show the fraction part? (Shade of the parts of another whole circle.) Have the students make the model. wholes = wholes + = 9 Holt Matemáticas

7 Nombre Escribir un número mixto como fracción impropia Escribe el número mixto como fracción impropia. Paso Escribe el número cabal como una suma de las unidades. Paso Usa el denominador de la fracción para escribir fracciones equivalentes a las unidades. Paso Suma los numeradores para hallar la fracción impropia. Inténtalo Por lo tanto, la fracción correspondiente a es Escribe cada número mixto como fracción impropia. Ir a siguiente página. 99 Holt Matemáticas

8 Nombre Practica por tu cuenta Razona: Escribe el número cabal como una suma de unidades. Escribe fracciones equivalentes a las unidades. Suma los numeradores para hallar la fracción. Escribe cada número mixto como fracción impropia. 9 Comprueba Escribe cada número mixto como fracción impropia Holt Matemáticas

9 Skill Add and Subtract Like Fractions Using Skills OBJECTIVE Add and subtract like fractions Mention to students that Skill reviews addition and subtraction of fractions with like denominators. Determine if they recall that with like fractions, students need only add or subtract numerators. Draw attention to Step. Ask: To add fractions, what has to be true about the fractions? (The denominators must be the same.) What is the denominator in the fraction?? (, ) Are the denominators the same? (Yes) When adding fractions, do you add the numerators or the denominators? (numerators) Explain to the students that a fraction is in simplest form if the greatest common factor of the numerator and denominator is. Do and have any factors in common other than? (no) Continue to ask similar questions as you work through the steps of the other examples for addition and subtraction. TRY THESE Exercises model the type of exercises students will find on the Practice on Your Own page. Exercise Add like fractions Exercise Subtract like fractions Exercise Subtract like fractions and simplify the result PRACTICE ON YOUR OWN Review the example at the top of the page. Ask students to explain why they can add or subtract each fraction and explain how they know if the answer is in simplest form. CHECK Determine if the students can add or subtract fractions and can recognize whether a fraction is in simplest form. Success is indicated by out of correct responses. Students who successfully complete the Practice on Your Own and Check are ready to move to the next skill. COMMON ERRORS Students add the denominators of the fractions. Students simplify fractions by dividing the numerator and denominator by different factors. Students who made more than errors in the Practice on Your Own, or who were not successful in the Check section, may benefit from the Alternative Teaching Strategy on the next page. 0 Minutes Holt Matemáticas

10 Optional Alternative Teaching Strategy Model Adding and Subtracting Like Fractions OBJECTIVE Use fraction strips to add and subtract like fractions MATERIALS fraction strips in halves, fourths, and eighths 0 Minutes You may wish to have the students work in pairs. One student can model the steps for adding or subtracting using the fraction strips and the other student can record the steps on paper. Distribute the fraction strips and have the students model +. Ask: Do both of the fraction strips have the same size parts? (yes) When you combine the two fraction strips how many parts in all are shaded? () Have the students record the sum. Determine if students recognize that the sum is not in simplest form. Say: Try to find other fraction strips that have the same area shaded as the one you have. Ask: What other fraction strips equal? (, ) Which is the simplest form of? ( ) When students show an understanding of adding or subtracting fractions with like denominators, have them summarize by stating a rule for adding or subtracting like fractions. When students use the strips to model subtraction, they will be modeling comparison subtraction. Parts on the two strips are matched, and the part(s) left over is the difference. eigths halves Holt Matemáticas

11 Nombre Sumar y restar fracciones semejantes Antes de sumar o restar fracciones, compara los denominadores para asegurarte de que sean iguales. Suma fracciones semejantes Halla. Resta fracciones semejantes Halla. Paso Los denominadores son iguales. Suma los numeradores. igual denominador Paso Escribe la suma sobre el denominador. Paso Los denominadores son iguales. Resta los numeradores. igual denominador Paso Escribe la diferencia sobre el denominador. Inténtalo Suma o resta. Escribe cada respuesta en su mínima expresión. Los denominadores son iguales? Los denominadores son iguales? Los denominadores son iguales? Suma: Mínima expresión? Resta los numeradores: Mínima expresión? Resta los numeradores: Mínima expresión? Ir a siguiente página Holt Matemáticas

12 Nombre Practica por tu cuenta Suma fracciones semejantes. Los denominadores son iguales. Por lo tanto, suma los numeradores. La respuesta no está en su mínima expresión. Por lo tanto, divide entre el máximo común divisor. Resta fracciones semejantes Los denominadores 9 son iguales. 9 9 Por lo tanto, resta los 9 numeradores. La respuesta no está en su mínima expresión. 9 Por lo tanto, divide entre el máximo común divisor. 9 9 Suma o resta. Escribe cada respuesta en su mínima expresión. Los denominadores son iguales? Suma: Los denominadores son iguales? Resta: 0 0 Los denominadores son iguales? Suma: Mínima expresión? Mínima expresión? Mínima expresión? Mínima expresión? Mínima expresión? Mínima expresión? Comprueba Suma o resta. Escribe cada respuesta en su mínima expresión Holt Matemáticas

13 Skill Multiplication Facts Using Skill OBJECTIVE Use strategies to recall multiplication facts MATERIALS multiplication table Minutes Begin the lesson by reminding students that, just as they can use strategies to help them recall addition facts, they can use strategies to help recall multiplication facts. Direct students attention to the skill. Be sure they are familiar with the words used in multiplication. Ask: What do you call the numbers you multiply? (factors) What do you call the result? (product) Focus on each strategy. For Use Facts You Know, ask: Why do you add in? (There is more group of in than in, so we add.) For Use Patterns, assist students in using the table, showing them how to very carefully read across and down the rows. Help them identify patterns for 0 to 0 9 and to 9. TRY THESE Exercises model using strategies. Exercise Exercise Use facts you know and add to get next fact Use patterns of 0 to multiply PRACTICE ON YOUR OWN Focus on the examples at the top of the page. Be sure students understand when the various strategies can be helpful. Ask: If you know, why add when multiplying? (There is more group of.) Finally, review the patterns for products of 9, 0,, and. CHECK Make sure students understand that multiple strategies are possible and that there is no one correct strategy. Success is indicated by out of correct responses. Students who successfully complete the Practice on Your Own and Check are ready to move to the next skill. COMMON ERRORS When using facts they know, students may forget what to add. For example, when using to find 9, they need to think 0. Students who made more than errors in the Practice on Your Own or were not successful in the Check section, may benefit from the Alternative Teaching Strategy on the next page. Holt Matemáticas

14 Optional Alternative Teaching Strategy Arrays for Multiplication Facts OBJECTIVE Use arrays to model strategies for recalling multiplication facts MATERIALS tiles, chart of multiplication facts Minutes Have students use tiles to model a strategy for recalling multiplication facts. Have students use tiles to model a fact they know. Then have them lay out addition tiles to show the "next fact." For example:. Then, add tiles to make, so,. Have students use a multiplication table to find patterns. What patterns can be found in the table? For facts of, the ones digits repeat: 0,,,,, What other patterns can be found? Repeat with several different facts. Holt Matemáticas

15 Nombre Operaciones de multiplicación Usa estrategias para recordar las operaciones de multiplicación. Usa operaciones que conoces Usa una operación que ya conoces para hallar una operación que no conoces. Si conoces: Entonces también sabes: Si conoces: Entonces puedes hallar: Razona: es ( ) ó ó. Por lo tanto,. Usa patrones Si usas una tabla de multiplicación, puedes buscar patrones en los productos. Multiplica por 9, 0,, Operaciones de 9 a 9 0: Los dígitos de las unidades disminuyen de en. Los dígitos de las decenas aumentan de en. La suma de los dígitos del producto es 9. Operaciones de 0 a 9: Los dígitos de las unidades se repiten: 0,,,,,... Qué otros patrones encuentras? Inténtalo Usa estrategias para multiplicar. Usa las operaciones que conoces. Usa patrones. Por lo tanto, 0 0 Por lo tanto, Ir a siguiente página Holt Matemáticas

16 Nombre Practica por tu cuenta Usa las operaciones que conoces Si conoces: Entonces razona: ( ), ó 0 Por lo tanto, 0. Usa patrones Busca patrones que te ayuden a recordar las operaciones de multiplicación. Para los productos de 9 y del al 9, los dígitos de todos los múltiplos de 9 suman 9. Los productos de 0 terminan en 0. Para los productos de y del al 9, vemos el mismo dígito en la posición de las decenas y de las unidades. Los productos de terminan en, 0,,, u. Usa las operaciones que conoces. Por lo tanto, 9 Por lo tanto, 9 Por lo tanto, 9 Por lo tanto, Por lo tanto, Por lo tanto, Usa patrones Multiplica Comprueba Multiplica Holt Matemáticas