Saxon 6/5 math test pdf download

We should be able to read and solve division problems in each form and to change from one form to another. Three numbers are involved in every division problem: 1. The location of these numbers in each form is shown below. To show division with a division bar, we write the dividend on top.

Lesson 20 93 Example 4 In the following equation, which number is the divisor, which number is the dividend, and which number is the quotient? The answer is the quotient, 8. Draw a horizontal number line marked with even integers from —6 to 6. Write two multiplication facts and two division facts for the fact family 4, 9, and Jim reads 40 pages per day. How many pages does Jim read in 4 days?

There are students at Gidley School. If there are girls, how many boys are there? Write an equation and find the answer.

What is the sum of five hundred twenty-six and six hundred eighty-four? Compare: 15 3 4, 20 Try multiplying. What was the total cost of the five notebooks?

Z R 14 — Use digits and symbols to write this comparison: 4 Ten times two is greater than ten plus two. Lesson 20 95 What are the next three terms in this counting sequence?

In this equation, which number is the divisor? Write a multiplication equation 13 that shows the number of squares in this rectangle. We use two numbers to write a fraction. The bottom number, the denominator, shows the number of equal parts in the whole. The top number, the numerator, shows how many of the equal parts are counted. The denominator of the fraction shows the number of equal groups.

We divide the total by the denominator to find the number in each group. Example 1 Half of the 18 students in the class are girls.

We find the number in each group by dividing by 2. This means there are 9 girls in the class. Example 2 a How many cents is one fourth of a dollar? Solution The word fourth means that the whole dollar is divided into four equal parts. Since four quarters equals a dollar, one fourth of a dollar equals a quarter, which is twenty-five cents.

Three fourths of a dollar three quarters equals seventy-five cents. Example 3 One tenth of the 30 students earned an A on the test. How many students earned an A? So 3 students earned an A.

Use this information to answer problems 1—4: There were 20 pumpkins in the garden. One fourth of the pumpkins were too small, one tenth were too large, and one half were just the right size. The rest of the pumpkins were not yet ripe.

How many pumpkins were too small? How many pumpkins were too large? How many pumpkins were just the right size? How many pumpkins were not yet ripe? He could carry a pack F his weight for two miles without resting. Sam weighs 80 pounds. How heavy a pack could Sam carry for 2 miles without resting? How heavy a pack could Sam carry for only half a mile without resting? If you wish to color-code the manipulatives, photocopy each master on a different color of construction paper, or, before cutting, have students color both sides of the fraction circles using different colors for different masters.

Following the activity, each student may store the fraction manipulatives in an envelope or plastic bag for use in later lessons.

Preparation: Distribute materials. Have students separate the fraction manipulatives by cutting out the circles and cutting apart the fraction slices along the lines. Use your fraction manipulatives to help with each exercise below. Show that two quarters equals one half. Two quarters of a circle is what percent of a whole circle?

How many tenths equal one half? Investigation 2 99 Is one quarter plus two tenths more or less than one half? One fourth of a circle plus two tenths of a circle is what percent of a whole circle? One half of a circle plus four tenths of a circle is what percent of a whole circle? Two half circles can be put together to form a whole circle. Use your fraction manipulatives to find other ways to form a whole circle.

Write an equation for each way you find. One fourth of a circle plus one tenth of a circle is what percent of a whole circle? Two fourths of a circle plus two tenths of a circle is what percent of a whole circle? What percent of a circle is one half plus one fourth plus one tenth? What fraction piece covers one half of a half circle? List all the uppercase and lowercase letters that enclose at least one area. Stories about equal groups have a multiplication pattern.

Altogether, how many students are in the four classes? The coach separated the 48 players into 6 teams with the same number of players on each team. How many players were on each team? Monifa raked up 28 bags of leaves. On each trip she could carry away 4 bags. How many trips did it take Monifa to carry away all the bags? The answer is 3. These numbers are related by multiplication.

The total number in all groups is the product. If the total is missing, we multiply to find the missing number. Example 1 At Lincoln School there are 4 classes of fifth graders with 30 students in each class. Altogether, how many students are in the 4 classes?

Solution This story is about equal groups. We are given the number of groups 4 classes and the number in each group 30 students. We write an equation. There are many more students in four classes than in one class, so is reasonable. There are students in all 4 classes. Example 2 The coach separated 48 players into 6 teams with the same number of players on each team.

The groups are teams. We are given the number of groups 6 teams and the total number of players 48 players. We are asked to find the number of players on each team. The answer is reasonable because 6 teams of 8 players is 48 players in all.

Example 3 Monifa raked up 28 bags of leaves. Solution The objects are bags, and the groups are trips. The missing number is the number of trips. We show two ways to write the equation.

On the shelf were 4 cartons of eggs. There were 12 eggs in each carton. How many eggs were in all four cartons? Thirty desks are arranged in 6 equal rows. How many desks are in each row? Twenty-one books are stacked in piles with 7 books in each pile.

How many piles are there? If 56 zebus were separated into 7 equal herds, then how many zebus would be in each herd? The coach separated the PE class into 8 teams with the same number of players on each team. If there are 56 students in the class, how many are on each team? Use a multiplication pattern. Tony opened a bottle containing 32 ounces of milk and poured 8 ounces of milk into a bowl of cereal.

How many ounces of milk remained in the bottle? The set of drums costs eight hundred dollars. The band has earned four hundred eighty-seven dollars. How much more must the band earn in order to buy the drums? Draw an oblique line. Write two multiplication facts and two division facts for the fact family 6, 7, and If a dozen items are divided into two equal groups, how 21 many will be in each group? Use words to show how this problem is read: 20 10 2 What number is the dividend in this equation?

Below is a story problem about equal groups. After you 21 find the answer to the question, use it to rewrite the last sentence as a statement instead of a question. The books arrived in 5 boxes. There were 12 books in each box. How many books were in all 5 boxes? The fraction A is equivalent to what percent?

We can division with use division to find a missing factor. Then we can use a remainder multiplication to check our division. After dividing to get 7, we multiply 7 by 5 and write the product under the This shows that there are exactly 7 fives in Consider this question: If 16 pennies are divided among 5 children, how many pennies will each child receive?

Lesson 22 If we try to divide 16 into 5 equal groups, we find that there is no whole number that is an exact answer. Each child will get 3 pennies. The amount left over is called the remainder. Here the remainder is 1, which means that one penny will be left over.

We subtract to find the amount left over and write this remainder at the end of the answer. Divisibility For some division problems, we can decide whether there by 2, 5, will be a remainder before we begin dividing. Here we show and 10 three rows from a multiplication table. We show the rows for twos, fives, and tens. In each row all the numbers can be divided by the first number of the row without leaving a remainder. If an even number is divided by 2, there will be no remainder.

If an odd number is divided by 2, a remainder of 1 will result. All the numbers in the fives row end in 5 or 0. If a whole number ending in 5 or 0 is divided by 5, there will be no remainder. If a whole number divided by 5 does not end in 5 or 0, there will be a remainder.

All numbers in the tens row end in zero. If a whole number ending in zero is divided by 10, there will be no remainder. If a whole number divided by 10 does not end in zero, there will be a remainder. Example 2 Without dividing, decide which of these division problems will have a remainder.

There might be more than one. Only numbers ending in zero can be divided by 10 without a remainder. Problem D. Only even numbers can be divided by 2 without a remainder. Write each answer with a remainder. Without dividing, decide which of these division problems will have a remainder. Which of these numbers can be divided by 2 without a remainder?

Draw two horizontal lines, one above the other. Huck collected 32 night crawlers for fishing. If he put an equal number in each of his 4 pockets, how many night crawlers did he put in each pocket? Julissa started a marathon, a race of approximately 26 miles.

After running 9 miles, about how far did Julissa still have to run to finish the race? Eight hundred forty mice came in the front door. Four hundred eighteen mice came in the back door. Altogether, how many came in through the front and back doors? Use an addition pattern. Think of an odd number. Multiply it by 2. If the product is divided by 2, will there be a remainder? Grandpa has 10 quarters.

If he gives each of his 22 3 grandchildren 3 quarters, how many quarters will he have left? How many F circles equal a half circle? The fraction F is equivalent to what percent? One prize was behind each curtain.

List all the possible arrangements of prizes behind the curtains. Here we show five fractions equal to one half: 1 2 2 4 3 6 4 8 5 10 Notice that the numerator of each fraction is half the denominator. A fraction is less than A if the numerator is less than half the denominator. A fraction is greater than A if the numerator is more than half the denominator.

The other fraction, e, equals A. Think of a counting number. Double it. Then write a fraction equal to A using your number and its double. Which of these fractions does not equal A? Compare: 5 8 B. How much money should Leo get back? Use a subtraction pattern. What was the cost of the burger and fries together? A week is 7 days. How many days is 52 weeks?

Sumiko, Hector, and Julie divided the money equally. One half of the 20 students had finished the book. One fourth had not yet started the book. Compare: 23 3 10 7. Write two multiplication facts and two division facts for 19 the fact family 7, 9, and Write the numbers 48, 16, and 52 in order from greatest 4 to least.

Draw two vertical lines side by side. Use words to name the number , Write two addition facts and two subtraction facts for the 8 fact family 7, 9, and Which fraction below does not equal A? The fraction H is equivalent to what percent? Mary has nine quarters in her coin purse. Write and 17 answer a multiplication problem that shows the value of the nine quarters.

When there is more than one operation in a problem, parentheses can show us the order for doing the operations. Parentheses separate a problem into parts.

We do the part inside the parentheses first. In the problem below, the parentheses tell us to add 5 and 4 before we multiply by 6. The parentheses show us which step to take first. Then we subtract 6 from 8 and get 2. We follow the proper order on both sides and find that the left-hand side is greater than the right-hand side. So if we have three numbers to add, we decide which two numbers to add first.

Either way, the sum is This property is called the associative property of addition. The associative property also applies to multiplication, but not to subtraction or division. Below we illustrate the associative property of multiplication. Whichever way we group the factors, the product is the same. Name the four operations of arithmetic.

Lesson 24 For each problem, write the proper comparison symbol, and state whether the associative property applies. How much money is one half of a dollar plus one fourth of a dollar? How many horseshoes are needed to shoe 25 horses? Use 21 a multiplication pattern.

Inez removed some eggs from a carton of one dozen eggs. If nine eggs remained in the carton, how many eggs did Inez remove? The auditorium had nine hundred fifty-six seats. Only ninety-eight seats were occupied. How many seats were not occupied? Which pattern did you use? Write two multiplication facts and two division facts for the fact family 5, 10, and Write two addition facts and two subtraction facts for the 8 fact family 9, 5, and Altogether, how much did the postcards cost?

Change this addition problem to a multiplication problem and find the total cost. What is the tenth term of this counting sequence? When any of these odd numbers is divided by 2, there is a 22 remainder of 1. Which of these odd numbers can be divided by 5 without a remainder?

Draw two vertical lines. Write two multiplication facts and two division facts for 19 the fact family 7, 8, and A calendar can help you start. What number was Tom thinking of? For example, the factors of 6 are 1, 2, 3, and 6 because each of these numbers divides 6 without leaving a remainder. Example 1 List the factors of Solution We look for all the whole numbers that divide 20 without leaving a remainder. Which numbers can be put into this box to give us an answer without a remainder?

If we do this, we find that the numbers that divide 20 evenly are 1, 2, 4, 5, 10, and These are the factors of All other whole numbers leave a remainder. Example 2 List the factors of Solution The only factors of 23 are 1 and Every number greater than 1 has at least two factors: the number 1 and itself. Sometimes we can discover some factors of a number just by looking at one or two of its digits. For example, a factor of every even number is 2, and any whole number ending in 0 or 5 has 5 as a factor.

Since 20 is even and ends with zero, we know that both 2 and 5 are factors of Example 3 Which of these numbers is not a factor of 30? So 2 and 5 are factors. And we quickly see that 30 can be divided by 3 without a remainder. The only choice that is not a factor is C. Two is not a factor of which of these numbers? Five is not a factor of which of these numbers? Which of these numbers is not a factor of 40? The Christmas-tree farm planted 9 rows of trees, with 24 trees in each row.

How many trees were planted? How much money should she get back? Altogether, how much did Donna spend? List the factors of Which property of multiplication is illustrated in problem 6? Write two multiplication facts and two division facts for 19 the fact family 10, 12, and How much money is A of a dollar plus F of a dollar plus s of a dollar?

Which number is the divisor in 20 this equation? What is the tenth term in this counting sequence? Think of a whole number. Which property of addition is illustrated by this equation? Write a multiplication equation 18 that shows the number of blocks used to build this figure. The fraction s is equivalent to what percent?

How many cents is 1 quarter? A division algorithm breaks large division problems into a series of smaller division problems that are easier to do.

In each of the smaller problems we follow four steps: divide, multiply, subtract, and bring down. As we do each step, we write a number. Drawing this division chart a few times will help us remember the steps: Division Chart Step 1: Divide and write a number. We continue to divide, multiply, subtract, and bring down until there are no digits left to bring down.

Then we bring down the next digit, which is 5. The 2 of 25 is in the dollars place, and the 5 is in the dimes place. So this division is like dividing 25 dimes by 3. The answer is 8 dimes, which we write above the 5.

We multiply 8 dimes by 3, which is 24 dimes. Then we subtract, get 1 dime, and bring down the 2 cents. Then we multiply and subtract. There are no digits to bring down.

There is no remainder. The three numbers of the multiplication answer should match the three numbers in the division box. Then we multiply, subtract, and bring down. Since there is no other number to bring down, we are finished. The remainder is 4. Thus, the answer is 46 R 4. This means that equals 46 fives plus 4. First we multiply. Then we add the remainder to the product we get.

To check our answer to this division, we multiply 46 by 5 and then add 4. The product is We can find an unknown factor by dividing the product by the known factor. We divide by 5 and find that N is Show how to check this division answer. Find each missing factor: j. How much should she get back in change? Sarita sent 3 dozen cupcakes to school for a party. How many cupcakes did she send? When three new students joined the class, the number of students increased to How many students were in the class before the new students arrived?

Try to answer the comparison without multiplying. Write two multiplication facts and two division facts for 19 the fact family 8, 9, and A checkerboard has 64 squares. The squares are in 8 21 equal rows. How many squares are in each row? How much money is H of a dollar plus u of a dollar? What number is halfway between and ? This equation shows that 7 is a 25 factor of Which other factor of 91 is shown by this equation?

What is the sum of three hundred forty-seven and eight 5, 6 hundred nine? Show how to check the answer. Why or why not? Which of these numbers is not a factor of 15? How many days are in 2 weeks? H of g. It is not necessary to show every whole number on a number line. The locations of unlabeled numbers must be figured out. One use of a number line is as a scale for measuring temperature. Two commonly used temperature scales are the Fahrenheit F scale and the Celsius C scale.

The Celsius scale is a centigrade scale, meaning there are one hundred gradations, or degrees, between the freezing and boiling points of water. The arrow points to a location past the mark and near the mark. Halfway between the and marks is a long mark that stands for The arrow points halfway between the and marks, so it points to Example 3 Draw a horizontal number line from 0 to with only zero and hundreds marked and labeled. Solution We draw a horizontal number line and make marks for 0, , , , , and These marks should be evenly spaced.

We then label the marks. Draw a number line from 0 to with only zero and tens marked and labeled. On the Celsius scale, what temperature is five degrees less than the freezing point of water? Points A and B on this number line indicate two numbers. Write the two numbers, using a comparison symbol to show which is greater and which is less.

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