Decimal Review – Adding – Subtracting - Multiplying
Tips to remember:
*A dot is used to represent a decimal point.
*Whole numbers precede the decimal point, and any fractional part follows the decimal point.
*Decimals are fractions divided into tenths, hundredths, or some power of 10.
*Sample of place value names:
hundred thousands - ten thousands - thousands, hundreds - tens - ones. Tenths – hundredths – ten thousandths, hundred thousandths – ten thousandths
*example: 325, 211.6849; this number is read as three hundred twenty-five thousand, two hundred eleven AND six thousand, eight hundred forty nine ten thousandths.
Note: The word “and” represents the decimal point.
Adding and Subtracting Decimals
Key: Line up the decimals
Also, whole numbers have an implied decimal behind the last digit.
Step 1 – Write the numbers vertically with the decimals lined up
Step 2 – If necessary, use zeros as placeholders
Step 3 – Add or Subtract. The decimal in the answer must line up with the decimal in the problem. In other words, one should be able to draw a straight line beginning with the decimal in the first number through the decimal in the answer.
Example: Add 23.4, 45, and 34.758
23.400 (added two zero place holders)
35.000 (…placed a decimal behind the whole number and added three zero placeholders.)
34.758
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89.158 Note: It is possible to draw a straight line through all of the decimals.
Multiplying Decimals:
Key: To count the total digits behind all decimal points
Step 1 - Temporarily ignore the decimal point and multiply
Step 2 – After multiplying, it’s time to replace the decimal point by counting the number of digits behind all decimal points.
Step 3 - start from the right of the product and move forward(left) the same number of times to place the decimal point.
Example: 4.56 X .3 =
Step 1: 456 x 3 = 1368
Step 2:
4.56 ( has 2 digits behind or following the decimal point)
X .3 (has 1 digit behind the decimal point)
----- Therefore, there are a total of 3 digits behind the decimal point
Step 3: 4.56 X .3 = 1.368 (The answer has 3 digits behind the decimal point)
Practice:
1) Write the numeral: three hundred sixty-two and forty-eight thousandths
2) find the sum: 67.3 + 19 + 43.211
3) find the sum: 34 + .56 + 5.32
4) Subtract 398.1 from 697.34
5) Find the product: 39 X .32
6) Find the product: 239.22 X .12
Answers:
1) 362.048
2) 129.511
3) 39.88
4) 299.24
5) 12.48
6) 28.7064
What is a Fact Family?
Has your child come home with something similar to a problem stating: Write the fact family for 5, 13, 8 with no examples in sight? Well, this article is for parents who have to help their children with fact family homework. Let’s look at an example:
8 + 5 = 13
5 + 8 = 13
13 – 8 = 5
13 – 5 = 8
Generally, the word family means certain people are related. Likewise, fact family implies that certain numbers and facts are related.
For starters, they are only three numbers in each family. In the above fact family, the members are 5, 8, and 13.
How are they related?
*** You can add two of the numbers together to get the third number.
8 + 5 = 13
*** You can switch the order of the two numbers added above to equal the third number again. In math, this is referred to as the commutative property of addition.
5 + 8 = 13
Cousin Operators or Operands
*** Just as your sister/brother’s children are your children’s cousins, addition is related to subtraction via the term inverse property. Subtraction is the inverse property of addition. In other words, subtraction is the opposite of addition. We can do undo the work of addition by subtracting. This is very important to remember for problem solving.
How to get the last two math facts of the family . . .
So far we’ve recreated 8 + 5 = 13 and 5 + 8 = 13
Since we now know the inverse (opposite) of addition is subtraction, start with the sum (or the larger number), 13, and subtract one of the addends. 13 – 8 = 5 Of course, your answer is the third number. In this case, the answer is 5. Thus the next fact would be, 13 – 5 = 8.
Usefulness:
Consider this word problem:
Susan had 5 pencils. Her grandmother gave her more pencils for her collection. Susan now has 13 pencils. How many pencils did Susan’s grandmother give her?
If a student has an understanding of fact family concept, he/she could rebuild the family.
You know that Susan started out with 5 pencils and ended up with 13 pencils. Thus, you know two of the family members. 5 and 13. In math language that translates,
5 pencils + ____ more pencils = 13 pencils or 5 + ? = 13
Let’s look at the fact family again.
5 + ? = 13
? + 5 = 13
13 – 5 = ?
13 - ? = 5
Which equation above would give me the value of ‘?” ? Answer: The third equation. Hey, we just need to subtract 5 from 13 to learn that her grandmother gave her 8 pencils.
If your child did not know their addition and subtraction facts well, teaching them concept would definitely help.
What about Multiplication and Division?</b>
Yes, there related. Division is the inverse property of Multiplication. Thus, the same principle applies. Study the example below.
6 x 4 = 24
4 x 6 = 24
24 / 6 = 4
24/ 4 = 6
(The “/” represents division.)
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How to Find the Slope
What is a slope? The slope represents the change in the y coordinates over the change in the x coordinates between two points on a line. In other words, slope = change in y / change in x
Standard form of a linear equation.
Ax + By = C
Slope intercept form of a linear equation
Y= mx + b (m represents the slope; b represents the y-intercept)
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HOW TO FIND THE SLOPE GIVEN AN EQUATION
1) Change equation to slope intercept form by isolating Y
2) Observe equation for “ m” which is the slope
Example 1:
Y = 3X + 5 ======= > Already in slope intercept form
Y = mx + b
Slope = 3 or 3/1 or m = 3 or m = 3/1; normally it is written as m = 3
Example 2:
8x + 4y = 12
8x – 8x + 4y = 12 – 8x ===== > Subtract 8x from both sides
4y = 12 – 8x
4y/4 = 12/4 – 8x/4 ======= > Divide both sides by 4
Y = 3 – 2x
Y = -2x + 3 ============== > Slope Intercept Form
Y= mx +b
Thus slope = -2 or m = -2
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FINDING THE SLOPE GIVEN TWO POINTS: (X1, Y1) and (X2, Y2)
As usual, there is a formula for this task ==== > m = Y2 – Y1 / X2 – X1
Remember, slope represents the change in the y- coordinates which is the numerator over the change in the x- coordinates which is the denominator.
The word “change” tells us to find the difference or to subtract the first coordinate from the second coordinate.
Example 3:
(3, 1) and (5, 4)
Let’s identify the coordinates.
X1 = 3
Y1 = 1
X2 = 5
Y2 = 4
Next, plug into the formula
M = 4 - 1 / 5 - 3
M = 3 / 2
Note: Something, you may not have considered. Take a moment and look at the slope formula again. m = Y2 – Y1 / X2 – X1
Notice Y2 is first in the numerator and X2 is first in the denominator. However, it’s okay to subtract the second coordinate from the first coordinate, but you must be consistent and do it for the numerator and denominator. Let’s try it.
M = Y1 – Y2 / X1 – X2
M = 1 – 4 / 3 - 5
M = -3 / -2
M = 3/2