MATH 6

VI

MISOSA MODULESMATHEMATICS VI LIST OF TITLES TITLE OF MODULE NO. OF PAGES1. Meaning of Expressions and Equations 62. Exponents 63. Expressions Involving Addition and Subtraction 44. Expressions Involving Multiplication and Division 35. Expressions Involving Exponents 56. Evaluating an Expression with more than Two Operations without 5 exponents 57. Evaluating an Expression with Two Different Operations with 7 Exponents 68. Rename fractions with Power of 10 59. Place Value/Value of Decimals 510. Read and Write Decimals 511. Standard/Expanded Notation of Decimals 512. Comparing and Ordering Decimals 413. Rounding off Decimals14. Subtracting Mixed Decimals through Ten Thousandths without 4 4 Regrouping 415. Estimating Products of Whole Numbers and Decimals 316. Multiplying Hundredths and Hundredths 517. Estimating Quotients of Decimals 618. Dividing Whole Numbers by Decimals 419. Terminating and Repeating Decimals 420. Division of Mixed Decimals by Whole Numbers 521. Equivalent Fractions 422. Solving for the Missing Terms in Equivalent Fractions 523. Estimating Fractions 524. Comparing Fractions25. Subtraction of Dissimilar Fractions in Simple Forms 526. Subtraction of Dissimilar Fractions in Mixed Forms without 6 Regrouping 427. Subtraction of Dissimilar Fractions in Mixed Forms with Regrouping 528. Word Problems involving Subtraction of Dissimilar Fractions in 6 7 Simple and Mixed Forms 529. Simplifying Fractions 430. Multiplication of Fractions in Mixed Forms31. One-Step Word Problems involving Multiplication of Fractions32. Two to Three-Step Word Problems involving Fractions33. Division of a Fraction by a Whole Number34. Division of a Fraction by a Fraction 1

TITLE OF MODULE NO. OF PAGES35. Division of Mixed Numbers 536. Word Problems using Direct Proportion 537. Word Problems using Partitive Proportion 538. Word Problems using Inverse Proportion 439. Finding the Percentage 740. Finding the Rate 741. Finding the Base 642. Solving Word Problems involving Percentage 643. Surface Area of a Cube 644. Surface Area of a Rectangular Prism 745. Surface Area of a Triangular Prism 1146. Surface Area of a Pyramid with a Square Base 647. Surface Area of a Pyramid with a Rectangular Base 748. Surface Area of a Cylinder 749. Volume of a Cube and Rectangular Prism 650. Volume of a Triangular Prism 651. Volume of a Pyramid with a Square Base 652. Volume of a Pyramid with a Rectangular Base 553. Volume of a Cylinder 554. Reading and Interpreting a Circle Graph 755. Constructing a Circle Graph 7 2

GRADE VI MEANING OF EXPRESSIONS AND EQUATIONSObjectives: Define expressions and equations. Distinguish between an expression and an equation.REVIEWSolve the following. Write the answers in your notebook.1. 492 + 3674 6. 11 256 + 25892. 123 – 67 7. 25 006 – 36403. 18 x 9 8. 136 x 984. 21  3 9. 230 x 565. 11 x 236 10. 37 107  63Have you answered these correctly?STUDY AND LEARNLook closely at the following examples:A) 12 880 D) 11 256 + 2 589 = 13 845B) 11 256 + 2 589 E) 230 x 56 = 12 880C) 230 x 56What do you notice about A, B and C in Column A and D and E in Column B?A, B and C are examples of what we call NUMERICAL EXPRESSIONS. 1

How will you describe a numerical expression?A numerical expression is a combination of numbers and symbols of operationnumber or a group of symbols and numbers.Example A is purely a number while B is a combination of the numbers 11 256and 2 589 and the addition symbol (+), while example C is a combination of thenumbers 230 and 56, and the multiplication symbol (x).Let us now look at example A. A. 12 880Can we say that 12 880 is a numerical expression?Going back to the description of numerical expression. 12 880 is a symbol 12 880 represents a numberThe example simply gives us a number. So by being a number, according to thedescription above, 12 880 is a numerical expression.Therefore, 12 880 is a numerical expression.From the previous examples, we have identified the following as numericalexpressions:a. 12 880b. 11 2556 + 2 589c. 230 x 56Is 36 + 4 x 8  2, a numerical expression?Let us analyze this closely: 36 + 4 x 8  2We can see the numbers 36, 4, 8 and 2.We can also see the operation symbols +, x and .These numbers and operation symbols are grouped together.When we solve 36 + 4 x 8  2 it will give us an answer, meaning, it represents anumber.36 + 4 x 8  2 are numbers and symbols put together to represent a number.Therefore, 36 + 4 x 8  2 is a numerical expression. 2

Look again at the following examples given previously.A. 12 880B. 11 256 + 2 589C. 230 x 56D. 11 256 + 2 589 = 13 845E. 230 x 56 = 12 880Take a closer look at D and E.How are D and E similar to B and C?How are they different?Let us take B and D.B. 11 256 + 2 589D. 11 256 + 2 589 = 13 845B and D are similar in the sense that B and D are different because only Dboth have the same numerical has the equal sign (=) and the numberexpressions 11 256 + 2 589. 13 845.Now, let us look at examples C and E.C. 230 x 56E. 230 x 56 = 12 880Do C and E have similarities and differences with B and D?Both C and E contain the same numerical expression 230 x 5, so, in a way, they are similar.They are also different because only E has the equality sign and 12 880.What symbol is common to 11 256 + 2 589 = 13 845 and 230 x 56 = 12 880?If you answered that both have the equal sign (=), then you are right!11 256 + 2 589 = 13 845 and 230 x 56 = 12 880 are examples of EQUATIONS.Equation is a mathematical sentence with the equal sign(=) showing equal relationship between the left and the right expressions.Because of the equal sign (=), the equation tells us that the numerical expression 11256 + 2 589 has the same value as 13 845.Similarly, the left side of E, which is 230 x 56, is equal to the number on the rightside, which is 12 880. 3

See if you can distinguish the equations from the expressions on the list.TRY THESEA. Copy the boxes in your notebook. Then write the expressions inside the EXPRESSION box, the equations inside the EQUATION box.EXPRESSION EQUATION76 = 35 + 41 9 81 7 + 3 – (8 x 7)  4893 x 496 87 = 87+  5 886  654 = 94 x 2 = 520  65 864 231 847  2 36 = 408 – 372B. Copy the numerical expressions from the following list in your notebook. 36 x 814 76 – 9 = 67 93  2 1 + 93 = 47 x 2 8 102 364C. Copy the equations from the list in your notebook. 46 – 8 x 7 70 + 300  10 = 100 999 + 637  2 83 – 2 + 25 = 106 1 = (76 – 6)  70 4

WRAP UP Remember:  A numerical expression is a symbol, a number, or a group of symbols and numbers.  An equation is a number sentence with an equal sign (=) to show that the expression on the left side has the same value as the expression on the right side.  An equation is a mathematical sentence showing two expressions that are equal. Just keep these in mind and you are ready for the test. ON YOUR OWNAnswer the test honestly. Try not to look at the previous pages. Write your answers inyour notebook.A. Choose the letters that belong to the description. 1. A numerical expression a. is made up of numbers and operations. b. can be a number. c. has operations only. d. represents a number. e. uses the equal sign. 2. An equation a. is made up of expressions and the equal sign. b. shows equality of two expressions c. has a left side and right side with the same value. d. is a sentence. e. is a group of numbers and operation signs. 5

B. Draw a heart (♥) if it is a numerical expression, a crescent moon () if it is an equation, and a flower () if it is neither of the two.1) 75 - 4 6) 8762)  7) 90  3 = 30 x 13) 11 = 26 – 154) 14 x 3 – 8  4 8) x5) 36 x 2 + 9 = 81 9) 36 + 36 + 36 + 36 10) (6 + 2) x 7 = 60 – 4 6

GRADE VI EXPONENTS Objectives: Give the meaning of exponent and base. Identify the base and exponent in a given expression. Rewrite a multiplication phrase using exponent and vice versa. REVIEWDo you still remember your multiplication table?A. Find the product of each of the following. 1) 100 x 100 2) 35 x 35 3) 9 x 9 x 9 4) 4 x 4 x 4 x 4 5) 2 x 2 x 2 x 2 x 2B. Find the products of the following. See if you can get all correctly. 1) 121 x 121 2) 89 x 89 3) 50 x 50 x 50 4) 20 x 20 x 20 x 20 5) 10 x 10 x 10 x 10 x 10Let us try again. This time you will be dealing with bigger numbers. 1

STUDY AND LEARNLook closely at the following:1) 100 x 1002) 35 x 353) 9 x 9 x 94) 4 x 4 x 4 x 45) 2 x 2 x 2 x 2 x 2Look closely at the numbers used in each expression.Let us answer the following questions.A. 100 x 100: Are the factors the identical? (Yes) What are the factors used? (100) How many times is the number used as a factor? (2 times) What operation is used repeatedly? (multiplication)B. 35 x 35: Are the factors the identical? What are the factors used? How many times is the number used as a factor? Are the operations the same? What operation is used repeatedly?C. 9 x 9 x 9: Use the same questions above to answer letters C to J.D. 4 x 4 x 4 x 4:E. 2 x 2 x 2 x 2 x 2:F. 121 x 121G. 89 x 89H. 50 x 50 x 50I. 20 x 20 x 20 x 20J. 10 x 10 x 10 x 10 x 10 2

Look closely at your answers to the questions given for each example.Go back and write down your answers to the following questions. Questions A Examples E BCDAre the factors identical?How many times onefactor is used?What operation is usedrepeatedly?How many times is the number used as a factor?Are your answers to each of the three questions the same from Example A to E?Since all the answers are the same, then we can rewrite the five examples asequations.1) 100 x 100 = 1002 We can write the first expression by using2) 35 x 35 = 352 the factor (100) as the base and the3) 9 x 9 x 9 = 93 exponent is (2) which indicate the number4) 4 x 4 x 4 x 4 = 44 of times the base is used as factor.5) 2 x 2 x 2 x 2 x 2 = 25Are 1002, 352, 93, 44, and 25 expressions?Yes, they are expressions since each one represents a number.What do you observe with these new expressions?In 1002, both 100 and 2 are numbers.How is each one written?The number 100 is written in normal size, but the number 2 is written in a smaller fontsize and placed above the right side of 100. (This is known as superscript).The numbers 100 and 2 are written differently because each one has a differentmeaning.Try to look at this: 1002 exponentbaseThe BASE tells us the number repeatedly used as a factor.The EXPONENT tells us how many times the number (base) is used as a factor.In 352, which is the base? Which is the exponent? How about in 93? 45?Let us now do it the other way around. Let us rewrite expressions with exponents intoa simple multiplication phrase. Let’s try 352. 3

How many times do we need to multiply 35 by itself? Therefore, 352 can be written as 35 x 35. Take a look at the other examples below. 93 = 9 x 9 x 9 45 = 4 x 4 x 4 x 4 x 4 54 = 5 x 5 x 5 x 5 TRY THESERead the direction for each exercise carefully. Write the answers in your notebook.A. Identify the base and exponent. 1) 752 2) 8014 3) 63622B. Rewrite using exponents. 1) 7 x 7 x 7 x 7 2) 30 x 30 x 30 3) 18 x 18 x 18 x 18 x 18 x 18 x 18 x 18 4) 241 x 241 x 241 x 241 5) 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1C. Rewrite as a simple multiplication phrase. 1) 39 2) 957 3) 1863 4) 2464 5) 13752 4

WRAP UP Remember:  The base is the number used repeatedly as factor.  The exponent tells how many times the base is used as a factor. ON YOUR OWNRead the direction for each test carefully. Write your answers in your notebook.A. Choose the letters that do not belong to the meaning. 1. The base a. is used as a factor. b. is used repeatedly. c. is written as a superscript. d. shows the number of times a factor is used. 2. The exponent a. is used as a factor. b. shows the number of times a factor is used. c. is used repeatedly. d. is written as a superscript.B. Underline the best answer for each. 1. In 79, the number 7 is the (base, exponent). 2. In 92, the number 2 is written as a (subscript, superscript). 3. In 37141, the number 41 is the (base, exponent). 4. In 658, the number 65 is written in (normal, small) size. 5. In 4197, the number 419 (is the factor, tells how many times the factor is used). 6. In 632, the number 2 (is the factor, tells how many times the factor is used).C. Rewrite using exponents or as a simple expression. 1) 453 2) 1635 3) 87 x 87 x 87 x 87 x 87 x 87 4) 136 x 136 x 136 x 136 5) 8 x 8 x 8 x 8 x 8 x 8 x 8 x 8 5

GRADE VIEXPRESSIONS INVOLVING ADDITION AND SUBTRACTION Objective: Evaluate an expression with addition and subtraction.REVIEWEvaluate the following expressions. Write your answers in your notebook. 75 ÷ 5 16 + 27 436 + 361 36 - 17 21 x 6 STUDY AND LEARNRemember what addition does? It combines quantities. It puts the elements of two ormore sets together. Like in 16 + 27, 16 and 27 are put together to make a total of 43.What about subtraction? It takes away a part or a number from another number orquantity of the same kind. Like 36 - 17, you take away 17 from 36 to leave 19.Study the two operations. What do you observe and what each operation does? Try to observe the following: 16 + 27 = 43 43 - 16 = 27 43 - 27 = 16 1

What do you notice with the subtrahend and difference of the second and thirdequations? How do you compare them with numbers used in the first equation?43 is the sum of 16 and 27. When 16 or 27 is subtracted from 43 you get the otheraddend.This means that whatever addition joins or just puts together, subtraction separates.This also means that subtraction is the opposite of addition. Since they are oppositeof each other, whatever one of these operations does, the other operation undoes.So it can also be said that whatever subtraction does, addition undoes.Since the two operations are inverses, they are of equal importance.When these two operations are now joined in an expression, either of the two is done(or computed) first, depending on which operation is seen first, from left to right.Consider these examples: A. 36 -12 + 14 B. 36 +12 - 14Notice that the numbers are in the same order but the operations are not.In example A, subtraction is given first, so we subtract first, then we add.so: 36-12 + 14 24 + 14 38Therefore, 36 - 12 +14 = 38.Now, for example B, addition is given first, so we add first, then we subtract.So: 36 + 12 -14 48 - 14 34Therefore: 36 + 12 - 14 = 34 2

Let us try and evaluate 17 - 15 + 30 - 6. We have two subtraction symbols and oneaddition symbol, still they are inverses. 17 - 15 + 30 - 6 2 + 30 - 6 32 - 6 26Therefore, 17 - 15 + 30 - 6 = 26. TRY THESEEvaluate the expressions. Show your solutions. Write the complete equationafterwards, like in the examples. Answer in your notebook. 1) 17 + 9 - 6 2) 75 - 36 + 95 3) 136 + 18 - 25 + 16 4) 171 + 36 - 98 + 3 5) 26 -19 + 121- 7+ 26 WRAP UP To evaluate an expression with both addition and subtraction… - do the operation which comes first. - start from left to right in the order in which the operations appear. 3

ON YOUR OWNEvaluate the following expressions. Write only the answers in your notebook, noneed to show the solutions. 1) 16 - 12 + 13 2) 29 + 16 - 18 3) 64 - 16 + 36 -18 4) 98 + 17 - 19 + 48 5) 120 - 26 - 8 + 96 + 21 6) 135 - 48 - 26 + 12 + 15 7) 129 + 77 + 36 - 79 - 43 8) 215 - 148 + 118 - 132 + 44 9) 95 + 234 - 169 + 87 - 108 10) 548 - 399 + 161 - 204 + 86 4

GRADE VIEXPRESSIONS INVOLVING MULTIPLICATION AND DIVISION Objective: Evaluate an expression with multiplication and division. REVIEW Evaluate the expressions. Write only the answers in your notebook. 1) 24 - 13 + 16 2) 59 - 24 + 17 3) 87 -19 + 40 -12 4) 77- 28 -16 + 35 5) 124 - 35 - 6 + 20 + 18 STUDY AND LEARN Just like addition and subtraction, multiplication and division are also inverses of each other. If multiplication comes first before division, multiplication will be done first but when division comes first before multiplication, division will be done first. Therefore, whichever operation comes first between the two will also be solved first. Let us evaluate the expression 8 x 6 ÷ 4 Multiplication sign (x) comes first before the division sign (÷), so we have to perform multiplication first before division. 8x6÷4 = 48 ÷ 4 = 12 Therefore, 8 x 6 ÷ 4 = 12. Here is another example. 1

Let us evaluate 84 ÷ 12 x 16.Here, we have to divide first before multiplying. 84 ÷ 12 x 16= 7 x 16= 112Therefore, 84 ÷ 12 x 16 =112.More examples:1) 15 x 6 ÷ 5 ÷ 2 x 7 2) 297 ÷ 33 x 15 ÷ 5 = 90 ÷ 5 ÷ 2 x 7 = 9 x 15 ÷ 5 = 18 ÷ 2 x 7 = 135 ÷ 5 = 9x7 = 27 = 63TRY THESEEvaluate the following expressions. Write your answers in your notebook. 1) 13 x 18 ÷ 3 2) 14 ÷ 2 x 20 3) 11 x 26 ÷ 2 x 8 4) 26 ÷2 x 12 ÷ 13 5) 60 ÷ 3 x 10To check your answer, ask your teacher for the answer key.WRAP UP To evaluate an expression involving multiplication anddivision, do whichever operation comes first from left to right in theorder in which they appear. 2

ON YOUR OWNEvaluate the following expressions. Write your solutions and answers in yournotebook.65 ÷ 5 x 12 36 x 4 ÷ 12 7 x 12 ÷ 42 1 2 38x3x7÷4 100 ÷ 2 x 36 ÷ 18 ÷ 5 4 5 3

GRADE VI EVALUATING AN EXPRESSION WITH MORE THAN TWO OPERATIONS WITHOUT EXPONENTS AND PARENTHESIS/GROUPING SYMBOLSObjective: Evaluate an expression with more than two operations without exponents and parenthesis/grouping symbols. REVIEWUse the rules in order of operations to solve the following.1) 12 ÷ 4 x 7 = ________2) 3 – 2 + 5 = ________3) 5 x 2 – 6 = ________4) 9 x 4 ÷ 3 = ________5) (3 x 5) – 24 = ________. STUDY AND LEARNStudy how the expressions below is evaluated. Multiply 4x6÷2–1+4x8 Divide = 24 ÷ 2 – 1 + 4 x 8 Multiply = 12 – 1 + 4 x 8 Subtract = 12 – 1 + 32 Add = 11 + 32 = 43How many operations does the expression have? ( 5)Which operation is done first? (Multiplication)Was the solution clear to you? 1

Let us recall the rules we learned in the previous modules.1. Evaluate powers first.2. Perform operations within grouping symbols, such as parenthesis ( ), brackets [ ], or braces { } starting with the innermost grouping.3. Moving from left to right, perform any multiplications or divisions in the order they occur.4. Moving from left to right, perform any additions or subtractions in the order they occur.Let us evaluate 5 x 8 + 24 ÷ 6 Do we have exponents in the expression? (None) Do we have parentheses or other grouping symbols in the expression? (None) Therefore, we will use only rule 3 and rule 4 in solving the expression. Agree? Yes!5 x 8 + 24 ÷ 6 What operation will you do first? (Multiplication)40 + 24 ÷ 6 What will be the next? (Division)40 + 4 What will be the last? (Addition) 44 What is the final answer? (44) Did you understand now the rule?Remember:You are not allowed to perform any additions or subtractions until all themultiplications and divisions have been performed.Now, you try to solve the expressions below.9 + 4 x 5 – 12 ÷ 6 Which operation will you do first?9 + ___ - 12 ÷ 6 Which will be the next?9 + ___ - ___ Which will be the next?___ - ___ Which will be the last?___ Is your answer 27? Then, you are correct! 2

Let us evaluate another one. Which operation will you do first? 10 ÷ 2 x 7 – 4 x 6 Which will be the next? ___ x 7 - 4 x 6 Which will be the next? ___ - 4 x 6 Which will be the last? ___ - ___ Is your answer 11? Then, you are correct! ___Now, try the exercises below.TRY THESERIDDLE TIME What did one tailpipe say to the other?Use a ruler to connect expressions to the correct answers.Then use the DECODER to get the answer for the riddle.1) 8 x 7 + 3 x 7 36 O 32 M2) 18 ÷ 3 + 2 x 15 72 X3) 48 – 4 x 6 ÷ 8 4 U4) 15 + 7 x 5 – 34 77 B5) 5 x 7 – 12 + 9 11 I6) 15 – 8 + 6 x 8 ÷ 12 16 A7) 35 + 23 – 9 x 5 132 H 45 Y8) 96 ÷ 6 x 4 + 8 7 S 13 E9) 24 + 9 x 8 + 36 6 T 10 D10) 12 x 3 + 8 x 4 68 A11) 32 ÷ 4 – 20 ÷ 5 1 E12) 15 – 3 ÷ 3 – 713) 16 ÷ 8 + 9 – 514) 10 x 3 ÷ 5 + 2 – 715) 3 + 5 x 1 + 4 ÷ 2 3

DECODER 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15Answer: __ __ __, __ __ __ __ __ __ __ __ __ __ __ __ WRAP UPHow do we evaluate an expression with more than 2 operations withoutexponents and parenthesis/grouping symbols?To evaluate such expression, we will follow the following rules:1. Evaluate powers first.2. Perform operations within grouping symbols, such as parenthesis ( ), brackets [ ], or braces { } starting with the innermost grouping.3. Moving from left to right, perform any multiplications or divisions in the order they occur.4. Moving from left to right, perform any additions or subtractions in the order they occur.Note:If the expression has no exponents and/or grouping symbols, the rules tobe followed will only be rule # 3 and rule # 4. ON YOUR OWNEvaluate the following expressions.1) 20 ÷ 4 + 7 x 3 6) 20 ÷ 5 + 8 – 2 x 32) 14 ÷ 2 + 5 – 3 x 4 7) 8 x 7 – 18 ÷ 63) 7 + 3 x 2 – 8 ÷ 2 8) 42 ÷ 6 + 56 – 12 x 34) 15 ÷ 3 x 4 – 6 + 2 x 5 9) 37 – 12 + 49 ÷ 75) 3 x 4 – 2 + 1 x 5 10) 10 + 2 x 4 – 12 ÷ 3 4

GRADE VI EVALUATING AN EXPRESSION WITH TWO DIFFERENT OPERATIONS WITH EXPONENTS AND PARENTHESIS/GROUPING SYMBOLSObjective: Evaluate an expression with two different operations with exponents and parenthesis/grouping symbols.REVIEWEvaluate the expressions below. 6) 54 – 18 ÷ 6 1) 12 + 5 x 7 7) 7 + 4 x 15 2) 45 ÷ 9 x 3 8) 120 ÷ 6 – 3 3) 6 x 11 – 4 4) 14 + 12 ÷ 4 9) 12 ÷ 4 x 2 5) 9 x 6 ÷ 3 10) 56 + 8 – 35STUDY AND LEARNStudy how the expressions below are evaluated.a. (5 + 3) x 6 b. (81 ÷ 92) + 7 c. 17 - (48 ÷ 6) = 17 – 8= 8x6 = (81 ÷ 81) + 7 =9= 48 = 1+7 =8 What did you noticed with the given expressions? How do they differ from the expressions given in the review part? What were added to these expressions that were not present in the previous one? (exponent and parenthesis) Do you want to know the rules in evaluating this kind of expression? 1

To avoid confusion, we shall agree on the following rules fororder of operations.1. Evaluate powers first.2. Perform operations within grouping symbols, such as parenthesis ( ), brackets [ ], or braces { }, starting with the innermost grouping.3. Moving from left to right, perform any multiplication or division in the order they occur.4. Moving from left to right, perform any addition or subtraction in the order they occur.Let us evaluate the expression 2 x (82 ÷ 4). 2 x (82 ÷ 4)  What are you going to do first? (Get the value of 82.)= 2 x (64 ÷ 4)  What will be the next step? (Do the operation inside the parenthesis.)= 2 x 16  What operation will be the last to be done?= 32 (Multiplication)Very good! Let us have another one.Evaluate: 32 + (24 x 5) 32 + (24 x 5)  Evaluate 32 first.= 9 + (24 x 5)  Then perform the operation inside the parenthesis. What= 9 + 120 is the product?  Then do the operation that is left. What is the final answer? 129= 129Now, try to evaluate the expressions below:1) (22 – 1) x 122) (56 ÷ 23) + 52 What is your answer in number 1? number 2? If you got 36 and 32 respectively, then your answers are correct! 2

TRY THESEA. CHECKING ANSWERS Four of Kristine’s answers are wrong. Find and correct the four incorrect answers.1) (7 x 23) – 3 = 53 QUIZ2) (24 ÷ 2) x 3 = 36 6) 24 + (23 ÷ 2) = 283) 52 x (23 – 3) = 75 7) (20 + 8) ÷ 4 = 64) 62 ÷ (6 x 2) = 3 8) (15 + 50) ÷ 5 = 135) (62 – 6) + 3 = 27 9) (15 – 6) x 22 = 36 10) 24 + (6 x 3) = 54B. Copy the exercise. Put in parenthesis to make the sentence true.Example: 45 ÷ 9 x 3 = 15 (45 ÷ 9) x 3 = 151) 6 + 3 x 7 = 632) 14 ÷ 7 x 9 = 183) 9 x 5 – 4 = 94) 54 ÷ 9 x 8 = 485) 6 x 11 – 4 = 42 3

WRAP UPHow do we evaluate an expression with two different operations with exponents andparenthesis/grouping symbols?To evaluate an expression with two different operations with exponents andparenthesis/grouping symbols, we will follow the these rules:1. Evaluate powers first.2. Perform operations within grouping symbols, such as parenthesis ( ), brackets [ ], braces { } starting with the innermost grouping.3. Moving from left to right, perform any multiplications or divisions in the order they occur.4. Moving from left to right, perform any additions or subtractions in the order they occur.ON YOUR OWNMatch the expressions in Column A with the answers in Column B. Write the letterof the correct answer on the blank provided before each number.Column A Column B____ 1) 32 x (4 + 23) A. 0____ 2) 24 + (32 – 7) B. 4____ 3) (32 x 5) – 22 C. 12____ 4) 10 – (8 + 2) D. 16____ 5) (21 – 2) x 4 E. 17 F. 18____ 6) (24 ÷ 3) + 23 G. 32 H. 41____ 7) (54 ÷ 32) x 23 I. 48 J. 76____ 8) (9 x 4) ÷ 3 K. 108____ 9) 62 – (23 – 4)____ 10) (32 – 8) x 22 4

GRADE VI RENAMING FRACTIONS IN DECIMAL FORM Objective: Rename fractions whose denominators are powers of 10 in decimal form. REVIEW Do you still remember the relationship between fractions and decimal numbers?Before you continue, review first these activities. A. Give the fraction name for the shaded portion of the given models.1) _____ 3) _____ 2) _____ 4) _____ 5) _____B. Write as a decimal. 1

1) _____ 2) _____ 3) _____4) _____ 5) _____ STUDY AND LEARNStudy this. Mrs. Reyes, the Edukasyong Pantahanan teacher, divided a rectangular piece ofcloth among the 10 girls for their project in sewing. The illustration below will help youunderstand the given answer to the given questions. 1 11 11 10 10 10 10 10 1 11 11 10 10 10 10 10a. Into how many parts was the piece of cloth divided? 10b. What do we call each part? 1 10c. If 8 girls have already gotten their pieces, what part of the whole piece of cloth was already given? 8 10d. What part was left? 2 10 2

So, all the answers have 10 as the denominator. Again, one-tenth is written as 1 ; 10eight-tenths as 8 ; and two-tenths as 2 . 10 10When the denominator of a fraction is a power of 10; it is easier to write thefraction as a decimal. That is,1 = 0.1 8 = 0.8 2 = 0.210 10 10 In 0.8, the period before the digit 8 is called a decimal point while zero representsthe ones place. We read a decimal in the same way we read the fraction it represents.Thus, 0.1 is read as one-tenth, 0.8 as eight- tenths, and 0.2 as two-tenths. We can also represent decimals on a number line in the same way that werepresent fractions and mixed numbers. Study this number line.0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 200 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10How will you rename 12 and 16 as decimals? We can first change 12 and 16 10 10 10 10into mixed decimals where the fraction part has a denominator of 10. That is, 12 2 2 10 = 110 = 1.2 since 10 = 0.2 16 6 6 10 = 110 = 1.6 since 10 = 0.6 3

How about if a fraction has a denominator of 100? 1 000? 10 000? How can wechange it into decimal? Let’s find out.Study the examples. 6 27 59A. 100 = 0.06 100 = 0.27 7100 = 7.59 84 2 187B. 1000 = 0.084 11000 = 1.002 251000 = 25.187 3 652 35 10 000 = 0.3652 627C. 10 000 = 0.0035 5110 000 = 51.0627In the examples in A, how many zeros are there in the denominator of thefraction? (two) How many places are there to the right of the decimal point? (two)How about in the examples in B? (three)How about in the examples in C? (four)So if the denominator is - 100, the number of places to the right of the decimal point is two. - 1 000, the number of places to the right of the decimal point is three. - 10 000, the number of places to the right of the decimal point places is four.Did you understand the lesson very well? If yes, do your best to answer theactivities in the next page. If not, go over the lesson again. 4

TRY THESEDo these in your notebook.A. Write the missing number.1) 2.6 = 210 63 15 2) 0.63 = 3) 7. ____ = 71000 4) 50.873 = 50 1000 792 5) 42.0792 = 42B. Write as fractions or mixed numbers.1) 0.9 2) 0.08 3) 7.59 4) 61.042 5) 215.784 6) 14.8356C. Copy and complete this place value chart. Write each number as a decimal. hundreds tens ones decimal tenths hundredths thousandths Ten point thousandths1)2) .3)4) .5)6) . . . . 3 2) 207 36 49 629 5) 9 5738 861) 510 100 3) 1000 4) 381000 10 000 6) 26410 000 5

WRAP UP Decimals are just another way of writing fractions whosedenominators are powers of 10. To write a decimal as a fraction, the number of decimal places ordigits to the right of the decimal point is the same as the number ofzeros in the denominator of the fraction and vice versa. ON YOUR OWNAnswer the exercises in your paper.A. Write as decimals.1) 3 6 4) 95 861 10 1000 9 5) 8 26952) 100 10 0003) 11 74 1000B. Write as fractions. 4) 835.062 1) 0.784 5) 92.0005 2) 45.3 3) 5.9078 6

GRADE VI PLACE VALUE/VALUE OF DECIMALSObjective: Identify the place value/value of a digit in a given decimal.REVIEW Can you still remember the different place values of whole numbers throughbillions? What are they? Very Good! Now, let’s have a review of it.A. Name the place value position where the number differs. Number A Number B Place Value1) 13 574 23 5742) 469 875 468 8753) 5 078 578 5 278 5784) 723 896 804 753 896 8045) 65 562 004 397 45 562 004 397B. Give the value of 5 in each number. Choose the letter of the correct answerinside the box.1) 45 826 ____ 4) 840 179 475 ____2) 691 573 ____ 5) 78 152 489 036 ____3) 2 507 834 ____a. five c. 5 thousand e. 50 millionb. five hundred d. 5 hundred thousand f. 50 billion 1

STUDY AND LEARNRead the situation. Raul and Joey love studying. Even though their houses are far from their school,they still attend their classes everyday. The distance of Raul’s house to school is 2kilometres while Joey’s house is 0.75 kilometres away. What good attitude can you learn from the two boys? Do youalso possess that kind of attitude? Why? What numbers are given in the situation? 2 and 0.75 What kind of number is 2? Whole number How about 0.75? Decimal number Do you know the different place value positions of a decimal? Let’s find out. Decimal numbers are parts of a whole or less than a whole and are written with decimal point. And as with whole numbers, decimal numbers can be shown on a place value chart. Study the place value chart of decimal numbers below. 1x 1x 1x 1x1 . 1x 1x 1x 1x 1x1000 100 10 2 48 . 0.1 0.01 0.001 0.0001 0.00001 8 3 76 . 6 1 93 . 693 5 501 2 4 482 7 5 2

What is the purpose of the decimal point? Decimal point distinguishes the decimal numbers from the whole numbers. What are the different place value positions to the right of the decimal point? Tenths, hundredths, thousandths, ten thousandths, hundred thousandths and others In 248.6935, what is the place value of 6? Tenths value of 6? 6 x 0.1 = 0.6 place value of 3? Thousandths value of 3? 3 x 0.001 = 0.003 In 8 376.50124, what is the place value of 3? Hundreds value of 3? 3 x 100 = 300 place value of 2? Ten thousandths value of 2? 2 x 0.0001 = 0.0002 In 6 193.48275, what digit is in the Hundredths place? 8 Thousands place? 6 Hundred thousandths place? 5 Place value is the position of a digit in a number while value is the amount orquantity of the digit in the given number. Do you already understand the concepts of place value and value of decimals? Ifyes, do the next exercises. If not, read the explanation again. 3

TRY THESEDo the following exercises in your notebook.A. In 50 678.39241, identify the digit in the…1) hundreds place ______2) thousandths place ______3) tenths place ______4) ten thousands place______5) hundredths place ______B. Give the place value and value of the underlined digit. Number Place Value Value1) 6.089122) 392.0353) 80.54874) 0.9658235) 4 175.6734C. What Number Am I? I am a number between 1 to 10. My tenths digit is 2 less than my ones digit; myhundredths digit is the sum of my ones and tents; my thousandths digit is 1 more than myhundredths digit. What numbers can I be? 4

WRAP UP A decimal is a number that is written with a decimal point in it. A place value chart can help us see the position and value of each digit of adecimal. tenthousands tenthshundred thousands hundredths thousandths thousands hundreds tenmillions tens ones thousandths1 342 365.1427 decimal point The place value positions to the right of the decimal point are tenths, hundredths,thousandths, ten thousandths and so on. The value of each place value position in the decimal is 10 times greater than thevalue of the place to its right. ON YOUR OWNA. Give the value of 7 in each number. 1) 0.376 2) 38.7934 3) 1.0687 4) 974.3089 5) 5.8173 5

B. Name the place value of the underlined digit. 1) 6.0896 2) 397.92 3) 56.24187 4) 7123.9078 5) 63.025671 6

GRADE VI READING AND WRITING DECIMALSObjective: Read and write decimals through ten thousandths. REVIEW Let’s go back to some of the lessons that you have learned. Are you now ready? Write in words or numerals. 1) 453 679 2) 78 007 650 3) 1 562 700 034 4) seventeen billion, three hundred two thousand, eighty 5) five hundred twenty-six million, nine hundred forty-seven Write the value and place value of 3. 1) 5.038 2) 69.7832 3) 1 241.9563 1

STUDY AND LEARN Read the situation and answer the questions after. Carl and his brother take good care of their bodies. They eat the right kinds of food to maintain their proper weights at their age. Carl weighs 45.8 kilograms while his brother weighs 43.75 kilograms.What good behavior can you learn from Carl and his brother? Why is it importantto take care of your body?What are the given numbers in the situation? 45.8 and 43.75What kind of numbers are they? Mixed DecimalsHow do you read decimal numbers? In general, decimals are just another way ofwriting fractions whose denominators are powers of ten and the proper way toread them is the same as reading the corresponding fractions which theyrepresent.Examples:Decimal Fraction Read as: 0.6 6 Six tenths 0.12 10 Twelve hundredths 12 0.2568 Two thousand five hundred 100 sixty-eight ten thousandths 2568 10 000 Notice that in the examples “zero and the decimal point” are not read norwritten in words anymore. 2

A place value chart can also help you read decimals. If there is a whole number, read the whole number first. Then read the decimal point as “and”. Next, read the decimal just as you would a whole number before reading the place value of the last digit. Let us look at the place value of our decimal number system below. 45 . 8 43 . 75 0 . 6089 How is 45.8 read and written in words? Forty-five and eight tenths How about 43.75? Forty-three and seventy-five hundredths How is 0.6089 read and written in words? Six thousand, eighty-nine tenthousandths. Test the skills and concepts you have learned by answering the next activities. TRY THESEDo the following exercises in your paper. A. Read and write as decimals. 1) thirty-eight thousandths 2) six thousand one hundred fifty-two ten thousandths 3) four and seventy-nine hundredths 4) ninety-five and sixty-two ten thousandths 5) one thousand eighty-nine and five hundred thirty-four thousandths 3

B. Read and write the following decimals in words. 1) 5.9 2) 14.872 3) 6.0281 4) 372.408 5) 92.7825 WRAP UP In reading and writing decimals… - The digits to the left of the decimal point are read as a whole number. - The decimal point is read as “and”. - The digits to the right of the decimal point are read as a whole number followed by the place value of the rightmost digit. ON YOUR OWNRead then write the decimals in words or in figures.1. 6.92. 0.39233. 8.19544. 51.765. 805.00696. seven and eight tenths7. three hundred seventy-six thousandths8. fifteen and eleven hundredths9. eight and five hundred seven ten thousandths10. forty-six and one thousand three hundred ninety-four ten thousandths. 4

GRADE VI STANDARD AND EXPANDED NOTATION OF DECIMALS Objective: Write decimals through ten thousandths in different notations. - Standard notation - Expanded notation REVIEW Read these decimals. Give also the place value of the underlined digit. You may askan elder person to check if you read the numbers correctly. 1. 0.892 2. 0.4506 3. 45.79 4. 7.8650 5. 156.2734 If you get all the items correctly, you can proceed to this lesson. But if not, review again the past lessons. STUDY AND LEARN Read the story problem. Gasoline is important in our daily lives. It helps us to travel to different and far away places. It also helps us transport goods. Nowadays, the price of gasoline is about Php38.75 per liter and sometimes Php39.50 per liter. 1

Give other importance of gasoline in our lives. Why is it important to save gas?What are the given numbers in the story problem? 38.75 and 39.50What kind of numbers are they? Mixed DecimalsDo you know that decimals can be written in different forms or notations? Study them.Standard Form Word Form Expanded Form Exponential Form 38.75 Thirty-eight and 30 + 8 + 0.7 + .05 (3 x 101) + (8 x 100) + seventy-five (7x 10–1) +(5 x 10–2) 39.50 hundredths 30 + 9 + 0.5 Thirty-nine and fifty (3 x 101) + (9 x 100) + hundredths (5 x 10–1) In this lesson, we are going to focus our study on writing decimals in standardform and expanded form.Study the examples given in writing decimals in expanded form. Standard Form Expanded Form 1) 62.058 60 + 2 + 0.05 + 0.008 2) 7.8003 7 + 0.8 + 0.0003 We write decimal in expanded form by writing it as a sum of the value of eachdigit. What do we do if there is a zero in the digits of the decimal number? Since thevalue of zero is zero we do not need to write it anymore. Let us see how decimals in expanded form can be transformed into standard form.Go to the next page to find out. 2

Example 1 Write 20 + 4 + 0.5 + 0.007 in standard form.Expanded Form Standard Form20 + 4 + 0.5 + 0.007 2 4. 5 0 7 tens ones tenths hundredths thousandthsYou notice that in the given expanded form there is no hundredths place but in thestandard form there is a hundredths place, what digit is put there? (Zero)So, 20 + 4 + 0.5 + 0.007 = 24.507Example 2 Write 600 + 50 + 9 + 0.2 + 0.08 + 0.007 + 0.0004 in standard form. What are the different place value positions in the given number? Hundreds, tens, ones, tenths, hundredths, thousandths and ten thousandths Are there any missing place value positions in between digits? None Do we need to put a zero or zeros? No So, 600 + 50 + 9 + 0.2 + 0.08 + 0.007 + 0.0004 = 659.2874 How do we write a decimal in expanded form into standard form? To changedecimals from expanded form to standard form we need to identify the place value ofeach digit in order to put them in their proper position. If a place value is missing, youneed to put a zero or zeros. 3

TRY THESEDo the following exercises in your paper. A. Supply the missing number. 1. 5.689 = 5 + ___ + 0.08 + ___ 2. 43.0821 = ___ + 3 + ___ + 0.002 + 0.0001 3. 168.504 = 100 + 60 + ___ + 0.5 + 0.004 B. Write in expanded form. 1) 7.306 = 2) 84.0802 = 3) 6.3981 = 4) 362.5308 = 5) 76.9124 = C. Write in standard form. 1) 70 + 5 + 0.003 = 2) 200 + 7 + 0.2 + 0.08 + 0.004 + 0.0006 = 3) 0.9 + 0.001 + 0.0005 + 0.00003 = WRAP UP To write decimals in expanded form… - Write the sum of the value of each digit. - If there is a zero or zeros, you do not need to write it anymore. To write decimals in standard form… - Identify the place value of each digit in order to put them in their proper position. - If a place value is missing, a zero or zeros should be added. 4

ON YOUR OWNA. Write in expanded form. 1. 0.903 = 2. 4.8952 = 3. 0.0058 = 4. 51.837 = 5. 190.6792 =B. Write in standard form. 6. 0.5 + 0.03 + 0.0009 = 7. 50 + 6 + 0.07 + 0.006 = 8. 5 + 0.1 + 0.04 + 0.008 = 9. 200 + 30 + 0.6 + 0.0005 = 10. 4 000 + 800 + 60 + 5 + 0.8 + 0.02 + 0.008 + 0.0007 = 5