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Transcript of Math
line up you decimals! Standard Form- is the usual way to
write a number. Ex: 0.12
Expanded Form- is a sum of the
products of each digit and its place
value. Ex:(1x0.1) + (2x0.01)
Word Form- writing the decimal in words
instead of numbers. Ex: twelve hundredths Integers -12-(15)= Problems:
What is 0.132 in expanded
form? Answer- (1x0.1) + (3x0.01) + (2x0.001)
What is 0.7 in expanded form? Answer-
Write 17.542 in word form. Answer- seventeen and five hundred forty-two thousandths
Write 0.9 in word form. Answer- nine tenths
Write thirty-five and ninety-six ten-thousandths in standard form. Answer- 35.0096
Write three and twenty-two hundredths
in standard form. Answer- 3.22 -12+(-15)= addition and subtracting rules
same denominator: If they have the same denominator you can just add or subtract the numerators and keep the denominators same.
Different denominators: If you have different denominators you need to change the denominators to common denominators and add or subtract the numerators and keep the denominators the same.
To add and subtract mixed numbers you can add or subtract the whole numbers by themselves and the fractions by themselves. When working with the fractions you need to keep in mind 2 things: the bottom (denominator) numbers of each fraction still need to be the same to add or subtract the top (numerator) numbers; also, if you end up adding fractions together and getting another whole number make sure you add it to the already calculated whole number.
Same Denominators: 1/3+1/3=2/3
Different Denominators:1/6+1/3=1/6+1/6=2/6 or 1/3 in simplest form
mixed numbers:11/9+ 4/9= 15/9
examples for subtracting fractions:
same denominators:8/9 - 7/9= 1/9
Different denominators: 3/4-1/3= 9/12-4/12=5/12
Mixed Numbers:6 1/10 - 4 3/10= 61/10 - 43/10=18/10=1 8/10 or 1 4/5 -27 K.C.C Fractions E Percent E P H
E Simplify. Divide the numerator and denominator by the GCF, 50. Adding And Subtracting When you add or subtract
decimals always line up the decimal
points! Then, add or subtract digits in the same place-value position. Problems:
23.1 +5.8 = 28.9
5.5 + 3.2 = 8.7
5.774 - 2.371 = 3.403
6.00 - 4.78 = 1.22 H
E Multiplying Fractions rules
When you want to multiply fractions all you really need to do is multiply straight across and simplify if you need too. If you have a mixed number you need to change it to improper and then multiply . Then divide the denominator by the numerator to get it back to a mixed number.
multiplying fractions: 2/5 x 1/2 = 2/10 or 11/5 in simplest form
multiplying mixed numbers:1 3/9X 1 3/9 = 12/9 x12/9 = 144/81 or 1 64/81 or 1 7/9
Dividing Fractions Rules
When you want to divide a fraction you need to multiply it by its reciprocal. You should also remember this saying " keep it change it flip it" because that's what you need to do. You keep that first fraction the same, you change the division sign in to a multiplication sign, and you flip the other fraction so that the denominator is on the top and the numerator is on the bottom. If you have a mixed number you need to change to an improper fraction, then multiply by the reciprocal. Then you need to find the greatest common factor that will go into both numbers and divide.
3/8 \ * 1/8 = 3/8 x 8/1 = 24/ 8 = 3
Mixed numbers:5 1/2 * 2 1/2= 11/2 * 5/2 = 11/2 x 2/5 = 22/10 or 2 2/10 or 2 1/5 katie is beast! sergsesesesese y5 Ordering Decimals Rules:
1. Line up the
2. Starting at
the left find the
first place the digits
3. Then compare the
0.4 ? 0.5
25.5 ? 25.50
Order from greatest to least: 1.1, 2.3, 0.3, and 4,5.
Answer- 0.3, 1.1, 2.3, 4.5 Rounding Rules:
1. Underline the digit
being rounded. Then
look at the digit to the
right of the digit being
2. If the digit is 4 or less
the underlined digit stays
If the digit is 5 or higher
add 1 to the underlined
Round 1.324 to the nearest whole. Answer- 1
Round 99.96 to the nearest tenth. Answer- 100.0 Estimating Sums
and Differences Rule:
In estimating addition and subtraction problems, round the numbers to the same place value before adding
or subtracting. Problems:
Multiply the numbers just as if they were whole numbers:
Line up the numbers on the right--do not align the decimal points.
Starting on the right, multiply each digit in the top number by each digit in the bottom number, just as with whole numbers.
Add the products.
Place the decimal point in the answer by starting at the right and moving the point the number of places equal to the sum of the decimal places in both numbers multiplied. For more help go to this link: http://www.khanacademy.org/ Dividing Decimals By Decimals Rules:
convert the number you are dividing by to a whole number first, by shifting the decimal point of both numbers to the right.Now you are dividing by a whole number, and can continue as normal. Problems:
Divide 6.4 by 0.4
Divide 2.4 by 0.2
Answer- 12 Problems:
Change 0.23 to a fraction.
Change 2.56 to a fraction.
Answer- 256/100= 2 14/25 Percents to Fractions Rules:
When you change a percent to a fraction always put it over 100. If it is a bigger number than 100 change the fraction to a improper fraction.
Ex: 75% to 75/100 Problems:
Change 25% to a fraction
Answer- 25/100 = 1/4
Change 50/100 to a percent
Answer- 50% Ratios And Rates How to do:
The ratio is the relationship of two numbers. For example you have 2 flashlights and 5 batteries. To compare the ratio between the flashlights and the batteries we divide the set of flashlights with the set of batteries. The ratio is 2 to 5 or 2:5 or 2/5. All these describe the ratio in different forms of fractions. The ratio can consequently be expressed as fractions or as a decimal. 2:5 in decimals is 0.4. A rate is a little bit different than the ratio, it is a special ratio. It is a comparison of measurements that have different units, like cents and grams. A unit rate is a rate with a denominator of 1. Problems:
What is 3:6 in simplest
What is another way to
Answer- 4:9 or 4 to 9 Ratio Tables Rounding fractions and mixed numbers Rules:
Quantities can be organized into a table. This table is called a ratio table because the columns are filled with pairs of numbers that have the same ratio. Rounding fractions:
If you are rounding to the nearest whole number, you would drop
a fraction less than 1/2, so you would round 1/3 to 0. Something
1/2 or higher, like 2/3, you would round to 1.
1/3=0 4/6=1 Problems:
Cans of corn are on sale at 10 for $4. Use the ratio table to find the cost of ten cans.
Answer- $6 for 15 cans of corn. Rounding Mixed numbers:
The whole number part is 12, so you'll be rounding down to 12 or up to 13.
Take notice of the fraction, 3/8. We know that 4/8 is the same as 1/2 or "one-half". We also know that any fractional part equal to or greater than 1/2 means that the mixed number gets rounded up to the next whole number. Since 3/8 is less than 4/8 = 1/2, then 12 3/8 cannot be rounded up to the nearest whole number, and must then be rounded down. Proportions A proportion is an equation that states that two ratios are equal. A proportion can be written in two ways: 4/8=1/2 or 4:8=1:2 Problems:
What is another way to write 5/6?
What is another way to write 8/11?
Answer- 8:11 Algebra: Solving
Proportions When you find an unknown value in a proportion, you are solving the proportion. As you discovered in lesson 6-3, there are different methods to determine if a relationship is proportional. Yuo can use the same methods to solve a proportion. Problems:
Solve the value of m:
Answer- m= 20
Solve the value of y:
Answer- y= 5 Estimating products of fractions You can estimate products and quotients of fractions and mixed numbers using
rounding and compatible numbers. Compatible numbers are rounded to make
it easy to compute with them mentally.
13 × 17 13 × 1818 and 3 are compatible
numbers since 18 ÷ 3 = 6.
13 × 18 = 618 3 = 6
So, 13 × 17 is about 6. Integers With negative numbers, we have to remember that as the digit gets bigger, the number gets smaller. Think what the number represents. Think what the value is.
The amount of money you have gets lower the more you owe.
The temperature gets lower, the colder it gets
The more you take away, the less you have Comparing and order integers
Put the following numbers in order starting with the least. -23, 17, -32, 2, -4, 0
Start looking at the negative numbers as these are always less than positive numbers. Start with the "biggest" negative number ( -32) as that has the lowest value.
Find the next "biggest" negative number (-23) and continue until the negative numbers are in order.
Zero and positive numbers can then be put into order to give the following complete list:
-32 , -23 , -4 , 0 , 2 , 17 Subtracting Integers There is only one rule that you have to remember when subtracting integers! Basically, you are going to change the subtraction problem to an addition problem.
When SUBTRACTING integers remember to ADD the
What does that mean? Keep - Change - Change is a phrase that will help you "add the opposite" by changing the subtraction problem to an addition problem.
Keep the first number exactly the same. Change the subtraction sign to an addition sign. Change the sign of the last number to the opposite sign. If the number was positive change it to negative OR if it was negative, change it to positive.
Here's an example for the problem: 12 - (-6) = ?
Keep 12 exactly the same. Change the subtraction sign to an addition sign. Change the -6 to a positive 6. Then add and you have your answer! Multiplying and Dividing Integers If the signs are the SAME, then the answer is POSITIVE.If the signs are DIFFERENT, then the answer is NEGATIVE.
That's it - multiply and divide as you normally would and then apply these rules to determine the sign!
7(-6) = -42 The signs are different (positive 7 and
negative 6), so the answer is negative. Absolut Value Absolute Value
The absolute value of an integer is the numerical value without regard to whether the sign is negative or positive. On a number line it is the distance between the number and zero.
The absolute value of -15 is 15. The absolute value of +15 is 15
The symbol for absolute value is to enclose the number between vertical bars such as |-20| = 20 and read "The absolute value of -20 equals 20".
absolute value of an integer is the numerical value without regard to whether the sign is negative or positive. Multiplying Decimals Problems:
What is 5/6x4/6?
What is 2/4x3/5?
Answer- 6/20=3/10 There are two rules that you must follow when adding integers. You must look at the signs of each number that you are adding to determine which rule to use!
Rule #1: When adding signs that are the same, ADD and keep the sign.
Rule #2: When adding signs that are DIFFERENT, SUBTRACT the numbers and keep the sign of the number with the LARGEST ABSOLUTE VALUE
4+(-2) = 2 I SUBTRACTED 4-2 to get 2 and then kept the
sign of the 4 (positive) because it has the
larger absolute value. Percents to Decimals Adding Integers Comparing and ordering Integers Prime Factors When two or more numbers are multiplied,
each number is called a factor of the product. Rules: Problems:
Is 12 prime or composite?
Is 19 prime or composite?
Answer- prime Powers and Exponents Divide the denominator (the bottom part) into the numerator (the top part).
Percent is some portion of 100. To find a decimal number from a percentage, divide by 100.
20% = 20/100 = 0.20
To go the other way, if you have a decimal and need to find percentage, multiply the decimal number by 100 to find percentage.
1.19 x 100 = 119% A product of identical factors can be written using an exponent and a base. The base is the number used as a factor. The exponent indicates how many times the base is used as a factor. Problems:
Write 3x3x3x3 written as an exponent.
Answer- 3 small 4
Write 2x2x2 as an exponent.
Answer- 2 small 3 Greatest Common Factor Factors that are shared by two or more numbers are called common factors. The greatest of the common factors of two or more numbers is the greatest common factor (GCF) of the numbers. Problems:
What are the GCFs of 16 and 24?
Answer- 1,2,4, and 8. Simplifying Fractions Whatever you do to the numerator of a fraction you must also do to the denominator. So if you have to divide the numerator by a number, you must also divide the denominator by the same number. That way you will not change the overall value of the fraction. Problems:
What is 4/6 in simpliest form?
What is 2/4 in simpliest form?
Answer- 1/2 Estimating with Percents To estimate a percent of something, you must imagine that thing being cut up into exactly 100 parts. For example, if you were to estimate the percent of the square that is covered by the shaded figure you would need to imagine the square being cut up into 100 pieces. Then you would need to count the number of pieces that are shaded to estimate the percent. Tips and Discounts To find the amount of a tip, discount, or tax, you can use the formula A = p x r where A is the amount of the tip, discount, or tax; p is the original price; and r is the rate or percent of the tax, tip, or discount. Look at this example.
"A coat is on sale for 20% off the original price of $85. What is the amount of the discount?" In this problem you know the regular price and the rate or percent of the discount. You need to find the amount of the discount. (When computing with percent, remember to change the percent to a fraction or decimal.)
A = p r
A = $85 20%
A = $85 0.20
A = $85 0.20
A = $17
Now that you know the discount is $17, you can find the sale price of the coat by subtracting $17 from $85. The sale price of the coat is $68.00 Interest When we borrow money we are expected to pay for using it – this is called interest.
There are three components to calculate simple interest: principal (the amount of money borrowed), interest rate and time.
Formula for calculating simple interest:
I = Prt
I = interest
P = principal
r = interest rate (per year)
t = time (in years or fraction of a year)
CALCULATING SIMPLE INTEREST EXAMPLES
Alan borrowed $10,000 from the bank to purchase a car. He agreed to repay the amount in 8 months, plus simple interest at an interest rate of 10% per annum (year).
If he repays the full amount of $ 10,000 in eight months, the interest would be:
P = $ 10,000 r = 0.10 (10% per year) t = 8/12 (this denotes fraction of a year)
Applying the above formula, interest would be
I = $ 10,000(0.10)(8/12)
= $ 667
If he repays the amount of $10,000 in fifteen months, the only change is with time. Therefore, his interest would be:
I = $ 10,000 (0.10)(15/12)
= $ 1,250