Module for grade 5 * Place Value * Ordering decimal numbers * Computations * Fractions, decimals, and percents * Negative and positive integers

I. Place Value
Numbers, such as 495,784, have six digits. Each digit is a different place value.
The first digit is called the hundred thousands' place. It tells you how many sets of one hundred thousand are in the number. The number 495,784 has four hundred thousands.
The second digit is the ten thousands' place. In this number there are nine ten thousands in addition to the four hundred thousands.
The third digit is the one thousands' place which is five in this example. Therefore there are four sets of one hundred thousand, nine sets of ten thousand, and five sets of one thousand in the number 495,784.
The fourth digit is called the hundreds' place. It tells how many sets of one hundred are in the number. The number 495,784 has seven hundreds in addition to the thousands.
The next digit is the tens' place. This number has are eight tens in addition to the four hundred thousands, nine ten thousands, five thousands and seven hundreds.
The last or right digit is the ones' place which is four in this example. Therefore there are four sets of one hundred thousand, nine sets of ten thousand, five sets of one thousand, seven sets of one hundred, eight sets of ten, and four ones in the number 495,784 A. Place Value Extended Forms
There are 4 sets of one hundred thousand, 9 sets of ten thousand, 5 sets of one thousand, 7 sets of one hundred, 8 sets of ten, and 6 ones in the number 495,786.
Expanded form shows the number expanded into an addition statement. The expanded form of 495,786 is 400,000 + 90,000 + 5,000 + 700 + 80 + 6.

Pre- test Name _____________________________ | | | Date ___________________ |
Place Value
Write each number in standard form.

1. | 4 millions 6 hundred thousands 9 ten thousands 1 thousand 1 hundred 3 tens 1 one | | 2. | 900,000 + 10,000 + 3,000 + 40 + 3 | | 3. | seventeen million, nine hundred thirty-four thousand, eight hundred seventy-five | | 4. | 300,000 + 90,000 + 3,000 + 400 + 2 | | 5. | nine hundred thirty million, four hundred fifty-six thousand, five hundred forty-two | | 6. | four hundred six thousand, three hundred fifty-one | | 7. | 4 thousands 4 hundreds 4 tens 8 ones | | 8. | 20,000 + 9,000 + 200 + 40 + 5 | | 9. | 10,000 + 5,000 + 900 + 90 + 1 | | 10. | one thousand, three hundred sixty-eight | |
Answer key: 1. 4,691,131 2. 9 hundred thousands 10 ten thousands 3 thousands 40 tens 3 ones 3. 17,934,875 4. 3 hundred thousands 90 ten thousands 3 thousands 4 hundreds 2 ones 5. 930,456,542 6. 406,351 7. 4,448 8. 2o ten thousands 9 thousand 2 hundreds 4 tens 5 ones 9. 10 ten thousands 5 thousands 9 hundreds 9 tens 1 ones 10. 1,368

II. Ordering Decimal Numbers
Numbers have an order or arrangement. The number two is between one and three. Three or more numbers can be placed in order. A number may come before the other numbers or it may come between them or after them.
Example: If we start with the numbers 4.3 and 8.78, the number 5.2764 would come between them, the number 9.1 would come after them and the number 2 would come before both of them.
Example: If we start with the numbers 4.3 and 4.78, the number 4.2764 would come before both of them, the number 4.9 would come after them and the number 4.5232 would come between them.
The order may be ascending (getting larger in value) or descending (becoming smaller in value).
Pre-test
Finding Digit Value with Decimals

Answer Key:
1. 8,000
2. 1 ⁄ 1000 3. 3 ⁄ 100
4. 4 ⁄ 10
5. 2 ⁄ 100
6. 8 ⁄ 1000
7. 1 ⁄ 1000
8. 5 ⁄ 1000
9. 5 ⁄ 100
10. 6 ⁄ 10
1) 8 ,644.58
2) 344.181
3) 61.83
4) 95.4
5) 152.42
6) 618,252.778
7) 3,455,287.351
8) 1,953.175
9) 2,990.85 10) 139,996.6

III. Computation
The practice section of this page contains addition, subtraction, multiplication and division problems. Refer to the appropriate lesson if you find that you need extra practice or explanation for any of these operations. A. Addition
Addition is ...
... bringing two or more numbers (or things) together to make a new total.

Here 1 ball is added to 1 ball to make 2 balls: | | | Using Numerals it is: | | 1 + 1 = 2 | | | | And in words it is: | | One + one = two | B. Subtraction is ... taking one number away from another.

| | Start with 5 apples,

then subtract 2,

we are left with 3 apples. | | This can be written:5 − 2 = 3 | | C. Basic multiplication
If 3 kids each have two robot possums, how many total robot possums do we have? You liked addition, but now you're ready to go to the next level. Depending on how you view it, multiplication is about repeated addition or scaling a number or seeing what number you get when you have another number multiple times. If that last sentence made little sense, you might enjoy this tutorial. *
Number line 1(Video) *
Whole numbers on the number line(Exercise) *
Basic multiplication(Video) *
Multiplying 1-digit numbers(Exercise) *
Multiplication 2: The multiplication tables(Video) *
Example: Ways to represent multiplication(Video) *
Multiplication 3: 10,11,12 times tables

D. Division is splitting into equal parts or groups.
It is the result of "fair sharing".

Example: there are 12 chocolates, and 3 friends want to share them, how do they divide the chocolates? | | | 12 Chocolates | | 12 Chocolates Divided by 3 |

Answer: 12 divided by 3 is 4

Pre-test
Answer key: 1. 243 2. 45 3. 44 4. 14 5. 68 6. 36 7. 12 8. 4 9. 476 10. 3
Answer the following equations. 1. 231+12 2. 43+2 3. 67-23 4. 23-9 5. 34*2 6. 12*3 7. 48/4 8. 24/6 9. 453+23 10. 2+1

IV. Fractions, Decimals and Percent A. Converting a fraction to a percent

Do the following steps to convert a fraction to a percent:
For example: Convert 4/5 to a percent. * Divide the numerator of the fraction by the denominator (e.g. 4 ÷ 5=0.80) * Multiply by 100 (Move the decimal point two places to the right) (e.g. 0.80*100 = 80) * Round the answer to the desired precision.
Follow the answer with the % sign (e.g. 80%) B. Converting a Percent into a Fraction
Do the following steps to convert a percent to a fraction:
For example: Convert 83% to a fraction. * Remove the Percent sign * Make a fraction with the percent as the numerator and 100 as the denominator (e.g. 83/100) * Reduce the fraction if needed
For example: Convert 0.83 to a percent. C. Convert Decimal to a Percent * Multiply the decimal by 100 (e.g. 0.83 * 100 = 83) * Add a percent sign after the answer (e.g. 83%)

D. Convert Percent to Decimal
How to convert a percent to a decimal:
For example: Convert 83% to a decimal. * Divide the percent by 100 (e.g. 83 ÷ 100 = 0.83)

E. Converting Fraction to Decimal
Do the following steps to convert a fraction to a decimal:
For example: Convert 4/9 to a decimal. * Divide the numerator of the fraction by the denominator (e.g. 4 ÷ 9=0.44444) * Round the answer to the desired precision.
Pre-test
Answer key: 1. 0.625 2. 0.375 3. 0.333 4. 0.67 5. 0.67 6. 0.6 7. 0.56 8. 0.75 9. 0.25 10. 0.333

Convert the the ff into decimal. 1. 5/8 2. 3/8 3. 2/6 4. 6/9 5. 4/6 6. 3/5 7. 5/9 8. 6/8 9. 1/4 10. 3/9

V. Negative and Positive Integers A. Adding Positive and negative integers
If one of the integers is negative, subtract the absolute value of it from the other number. Example: 14 + (-6) = 14 - 6 = 8
If both of the integers are negative, add their absolute values and prefix the number with a negative sign.

B. Two-Digit Integer Addition Equations
An equation is a mathematical statement that has an expression on the left side of the equals sign (=) with the same value as the expression on the right side. An example of an equation is 2 + (- 6) = - 4.
One of the terms in an equation may not be known and needs to be determined. The unknown term may be represented by a letter such as x (e.g. 2 + x = - 4). The equation is solved by finding the value of the unknown x that makes the two sides of the equation have the same value.
Use the subtractive equation property to find the value of x in addition equations. The subtractive equation property states, "The two sides of an equation remain equal if the same number is subtracted from each side."
We may also use the additive equation property which says: "The two sides of an equation remain equal if the same number is added to each side."
Example:
-5 | + | x | = | 4 | +5 | | | | +5 | | | x | = | 9 |
Check the answer by substituting (9) for x in the original equation. The answer is correct if the expressions on each side of the equals sign have the same value.
-5 + 9 = 4
4 = 4 (Correct!)
Example:
x | - | -5 | = | 4 | x | + | 5 | = | 4 | | | -5 | | -5 | | | x | = | -1 |
Check the answer by substituting (-1) for x in the original equation. The answer is correct if the expressions on each side of the equals sign have the same value.
-1 - (-5) = 4
4 = 4 (Correct!)

C. Subtracting Positive and Negative Integers
To subtract integers, change the sign on the integer that is to be subtracted. * If both signs are positive, the answer will be positive.
Example: 14 - (-6) = 14 + 6 = 20 * If both signs are negative, the answer will be negative.
Example: -14 - (+6) = -14 - 6 = -20
If the signs are different subtract the smaller absolute value from the larger absolute value. The sign will be the sign of the integer that produced the larger absolute value.
Example: 14 - (+6) = 14 - 6 = 8
Example: -14 - (-6) = -14 + 6 = -8
Answers:
1. (-2) 2. (+7) 3. (-4) 4. (-2) 5. (+12) 6. (-8) 7. (+15) 8. (-4) 9. (0) 10. (+4)
Pre-test
1. (+5) + (-7) =
2. (-2) + (+9) =
3. (+2) + (-6) =
4. (0) + (-2) =
5. (+6) + (+6) =
6. (-7) – (+1) =
7. (+9) – (-6) =
8. (-1) – (+3) =
9. (-9) – (-9)
10. (-3) – (-7)