Factors, Multiples, and Divisibility

Transcription

1 Factors, Multiples, and Divisibility R - You can use these divisibility rules to determine if a number is divisible by another number. A whole number is divisible by if the ones digit is,,, 6, or. if the sum of the digits of the number is divisible by. if the last two digits of the number are divisible by. if the ones digit is or. 6 if the number is divisible by both and. if the sum of the digits of the number is divisible by. if the ones digit is. Examples,,, 6, Last two digits are. 6 ; ;,; Divisible by because ones digit is Divisible by because, ; ; ;, Tell whether each number is divisible by,,,, 6,, or.... Tell whether the first number is a multiple of the second.. ;. ; 6. ; 6. ;. Number Sense Name factors of. There are members in the U.S. Senate. There are members in the U.S. House of Representatives.. Is the total number of U.S. senators divisible by,,,, 6,, or?. Could the members of the U.S. House of Representatives be evenly divided into committees with members on each? members on each? members on each? Use with Lesson -.

2 Prime and Composite Numbers R - A prime number has exactly two factors: and itself. Example: is prime. Its factors are and. Composite numbers have more than two factors. Example: is composite. Its factors are,,, and. You can make a factor tree to find the prime factorization of a number Begin with any two factors of the number.. Continue to write factors until all the factors are prime.. Circle the prime factors.. Write the prime factors from least to greatest.. Write the factors in exponential form. Tell whether each number is prime or composite Write the prime factorization of each number Number Sense How can you tell that 6 is divisible by? Use with Lesson -.

3 Greatest Common Factor R - Here are two different ways to find the greatest common factor (GCF) of and. List the Factors Step : List the factors of each number. :,,,, 6, :,,,,,,, Step : Circle the factors that the numbers have in common. :,,,, 6, :,,,,,,, Step : Select the greatest factor the numbers have in common. The numbers have and in common, but is greater. The GCF is. Use Prime Factorization Step : List the prime factors of each number. : : Step : Circle the factors that the numbers have in common. : : Step : Multiply the common prime factors. The GCF is. Find the GCF for each set of numbers..,.,.,.,. 6, 6.,. Number Sense Name two numbers that have a greatest common factor of.. Name two numbers that have a greatest common factor of.. Name two numbers that have a greatest common factor of.. The swim team has members and the diving team has members. If the coaches wished to divide the teams into groups and have all of the groups from both teams be the same size, what is the greatest number of team members who could be in a group? Use with Lesson -.

4 Least Common Multiple R - There are different ways to find the least common multiple (LCM) of two numbers. Here are two ways of finding the LCM of and : List Multiples Step : List multiples of each number. :,,, 6,,,,, 6,,, :,,,,,,,,, Step : Check the multiples the numbers have in common. :,,, 6,,,,, 6,,, :,,,,,,,,, Step : Determine which of the common multiples is the least. and are both common multiples, but is the least. The LCM of and is. Use Prime Factors Step : List the prime factors of each number. : : Step : Circle the greatest number of times each different factor appears. : : Step : Find the product of the factors you circled. The LCM of and is. Find the LCM of each set of numbers.. 6,.,.,.,,. 6, 6.,.,.,,.,. Number Sense If you know the LCM of and, how could you find the LCM of and?. Peter says the least common multiple of, 6, and is. Do you agree or disagree? Explain. Use with Lesson -.

5 PROBLEM-SOLVING STRATEGY: Make a Table R - Some problems can be solved by making and using a table. Dan can cut lawns per day in the summer. How many lawns can he cut if he works days? Here is how to make and use a table for this problem: Step : Set up the table with the correct labels. Day Lawns Step : Enter known data into the table. Day Lawns 6 Step : Look for a pattern. Extend the table. Day Lawns Step : Find the answer in the table. Day Lawns Dan can cut lawns in days. Make a table to solve the problem. Write the answer in a complete sentence.. Marie studied seeds in science class. She noticed that seeds sprouted at F. She also noticed that for every degree warmer she kept the seeds, 6 more sprouted than at the previous temperature. How many seeds sprouted at 6 F?. Lee did chores for his neighbor each week. For the first chore he received $.. For each additional chore he earned $.. If he did 6 chores one week, how much money did he earn? 6 Use with Lesson -.

6 Understanding Fractions R -6 Fractions are used to show parts of a whole, or parts of a set. They can also indicate division. Situation Fraction Division Expression INCHES Write a fraction for the shaded portion of each picture..... INCHES Draw a picture to show each fraction.. as a part of a set 6. as a part of a whole. Number Sense If you show as a part of a set by shading, what portion of the set is not shaded? Use with Lesson -6.

7 Equivalent Fractions R - Two fractions that are equivalent will always be the same when expressed in simplest form. How to Write Equivalent Fractions One Way: Use multiplication. Multiply both the numerator and the denominator by the same nonzero number. Example: How to Write Fractions in Simplest Form One Way: Use divisibility rules. Divide the numerator and the denominator by a common factor. Repeat until is the only common factor They are equivalent. 6 Another Way: Use division. Divide both the numerator and the denominator by the same nonzero number. Choose a common factor to divide by They are equivalent. is a common factor, so divide 6 and by. Another Way: Divide by the GCF. Divide the numerator and the denominator by the greatest common factor (GCF). 6 6 The GCF of 6 and is. Find two fractions equivalent to each fraction.... Rewrite each pair of fractions with a common denominator..,., 6., 6 Write each fraction in simplest form Number Sense If two fractions have the same denominator, how can you determine if they are equivalent? Use with Lesson -.

8 Improper Fractions and Mixed Numbers R - A mixed number combines a whole number with a fraction. It is greater than one. An improper fraction has a numerator that is larger than its denominator. How to Write an Improper Fraction as a Mixed Number Write as a mixed number. Divide the numerator by the denominator. The quotient is the whole number in the mixed number. The remainder is the numerator. The denominator stays the same. How to Write a Mixed Number as an Improper Fraction Multiply the denominator by the whole number. Then add the numerator. Write this number for the numerator. Use the original denominator.. Draw a picture to show. Write each improper fraction as a whole number or mixed number in simplest form Write each mixed number as an improper fraction Reasoning Write 6 as an improper fraction with a denominator of. Use with Lesson -.

9 Estimating Fractional Amounts R - You can use benchmark, or common, fractions to estimate fractional amounts. Some benchmark fractions are,,,, and. About of the square is shaded. You can also use rounding to estimate fractional amounts. out of 6 workers surveyed said they prefer to drive to work. About what fraction prefer to drive? 6 is close to. 6 is close to. is close to, and 6, so is about. 6 of the workers prefer to drive. Estimate the shaded part of each.... Which benchmark fraction is close to?. Which benchmark fraction is close to?. Which benchmark fraction is close to 6? 6. Which benchmark fraction is close to?. Reasoning The state of Rhode Island has an area of, sq mi. It has sq mi of land that is covered by water. About what fraction of the state s land is covered by water? Use with Lesson -.

10 Connecting Fractions and Decimals R - A fraction and a decimal can both be used to represent the same value. of the ths. are shaded. fraction decimal How to Convert Decimals to Fractions Write. as a fraction.. hundredths Write in simplest form. So.. Write. as a mixed number.... hundredths So.. How to Convert Fractions to Decimals Write as a decimal. Divide the numerator by the denominator. Apply zeros if necessary... The decimal. is a repeating decimal. Place a bar over the repeating digit. So.. Write a decimal and a fraction in simplest form for each shaded portion... Write each decimal as a fraction or a mixed number in simplest form Write each fraction or mixed number as a decimal Use with Lesson -.