15,11,14,4,1
answer (11-4) (15-14) x 1 = 6
Tuesday 16 April 2013
Sunday 17 March 2013
Wednesday 13 March 2013
Monday 11 March 2013
Sunday 10 March 2013
Sunday 3 March 2013
Tuesday 26 February 2013
Sunday 10 February 2013
Krypto Question
13,7,1,5,6=2
Mrs.Boughton put the answer on the board to be 3, but on the post it said 2. I got an answer for both, it's just for the answer to be 2 i could only get 4 numbers in the equation.
1. (Answer for 3) (13+1)'/.7+6-5=3
2. (Answer for 2) 13-7-5+1=2
'/. -- this is suppose to be a division sign, there was no divisions signs on my laptop.
Saturday 9 February 2013
Monday 4 February 2013
Pattering: Graphing, T-charts, Variables, etc.
Variables
Variables can be either a dependent variable or an independent variable. Variables are numbers but used in unknown. An unknown is a variable that is introduced to stand for a constant value that is not initially known. Its like finding whats the unknown number, like if you had a t-chart and a person gets a variable.You find whats the variable. Like if you gave the person the number 1 then person will give you a number. You need at least 3 guesses or so to find the variable.
ex.
you picked the number 1 then the person gave the number 2 then you picked another number like 2 then the person gave 4 then you picked the number 6 then the person gave 12. etc.
tip. to find the number you may want to start with numbers 1 - 10. But the variable their is 2x=y, it like multiplying the term/figure etc. number 2 times to get the final answer.
Graphing
For graphing you need to ALWAYS label your graph or else you wont get a mark on labeling the graph. Also you must make a diagonal line on the dots you made. In the graph you must also make it even like if you put number 2 you cant you like 2 7 9 13 etc you its like 2 4 6 8 10 etc.
Variables can be either a dependent variable or an independent variable. Variables are numbers but used in unknown. An unknown is a variable that is introduced to stand for a constant value that is not initially known. Its like finding whats the unknown number, like if you had a t-chart and a person gets a variable.You find whats the variable. Like if you gave the person the number 1 then person will give you a number. You need at least 3 guesses or so to find the variable.
ex.
you picked the number 1 then the person gave the number 2 then you picked another number like 2 then the person gave 4 then you picked the number 6 then the person gave 12. etc.
tip. to find the number you may want to start with numbers 1 - 10. But the variable their is 2x=y, it like multiplying the term/figure etc. number 2 times to get the final answer.
Graphing
For graphing you need to ALWAYS label your graph or else you wont get a mark on labeling the graph. Also you must make a diagonal line on the dots you made. In the graph you must also make it even like if you put number 2 you cant you like 2 7 9 13 etc you its like 2 4 6 8 10 etc.
Tuesday 29 January 2013
Rounding & Estimating
Rounding:
When it comes to rounding, it's really simple. If you were asked to round, go by these rules.
1) If it's 5 and higher: round UP
2) If it's any number lower than 5: round down.
For example, I chose the number 126. In this case, we're rounding it up to the nearest ten. Since it ends in a "6", we would have to go up. The number would now be 130.
If the number was 124, we would round it to 120 since 4 is lower than 5.
Estimating:
In some or most cases, estimating has to do with rounding. To estimate is to take a smart guess, but there has to be a reason.
For example:
- Adding: 126+163
I could round 126 to 130 and I could round 163 to 160. So now the two numbers are 130 and 160.
130+160= 190.
Now if you calculate the actual number, it would be 289.
-Subtracting: 352-221
I could round 352 to 350 and 222 to 220.
350-220= 130
Now if you calculate the actual number, it would be 131.
In some cases, the two answers could be pretty close.
When it comes to rounding, it's really simple. If you were asked to round, go by these rules.
1) If it's 5 and higher: round UP
2) If it's any number lower than 5: round down.
For example, I chose the number 126. In this case, we're rounding it up to the nearest ten. Since it ends in a "6", we would have to go up. The number would now be 130.
If the number was 124, we would round it to 120 since 4 is lower than 5.
Estimating:
In some or most cases, estimating has to do with rounding. To estimate is to take a smart guess, but there has to be a reason.
For example:
- Adding: 126+163
I could round 126 to 130 and I could round 163 to 160. So now the two numbers are 130 and 160.
130+160= 190.
Now if you calculate the actual number, it would be 289.
-Subtracting: 352-221
I could round 352 to 350 and 222 to 220.
350-220= 130
Now if you calculate the actual number, it would be 131.
In some cases, the two answers could be pretty close.
Rounding and Estimating
Rounding- To round you need to take your number that your working with, so lets say I'm working with the number 63. If your number is 0 - 4 your going to round to a lower number, so if you want to round to your nearest tenth you look for the number after your tenths unit which is a 3, since 3 is under 4 your going to round down to 60. Say my number was 67, you're going to round up to 70, your going to do this because any number from 5 - 9, is going to be rounded up since these numbers are closer to the next tenth.
Estimating- To estimate, what I do is I round first. Lets say I want to add 56 and 32, to estimate this I round first. So, 56 rounded to the nearest tenth would be 60 because it's a greater number than 4, then we take the 32 and round it to the nearest tenth, which is 30. It's rounded to 30 because it's a lower number than 4. After you round your numbers you can add, subtract, multiply, etc. Now lets take the numbers we rounded, which is 60 and 30, add them together making 90. Since it's an estimation it is not going to be exact.
Estimating- To estimate, what I do is I round first. Lets say I want to add 56 and 32, to estimate this I round first. So, 56 rounded to the nearest tenth would be 60 because it's a greater number than 4, then we take the 32 and round it to the nearest tenth, which is 30. It's rounded to 30 because it's a lower number than 4. After you round your numbers you can add, subtract, multiply, etc. Now lets take the numbers we rounded, which is 60 and 30, add them together making 90. Since it's an estimation it is not going to be exact.
Monday 28 January 2013
Adding fraction
1.) Adding fraction with proper with like denominators.
You just add both numerators.
Examples:
7/20 + 2/20 = 9/20
2.) Adding fraction with proper with unlike denominators.
You have to make them equal by changing the denominators.For example, if it's 30 and 50, you have to make 50.
Estimating and Rounding
Rounding:
If you are estimating you have to ask yourself some questions. For example if you had the number 218 you can either choose to round to the nearest one, ten, or hundred since it's a three digit number. Now let's say you are rounding to the nearest ten, you look at the digit beside the tens place value which is 8. Now you ask yourself is 8 higher than 5? Or lower than 5? Or you can ask yourself is 8 closer to ten? Or closer to 1? Of course 8 is closer to ten so now the number 218 turns into 220.
Estimating:
Estimating, when you are estimating maybe for an assignment or a test it's almost the same concept with rounding. For example, if you have a question asking you, estimate the total cost of the T.V and the sofa. T.V costs $499.99 and the sofa costs $239.99. Let's round the cost of the T.V to the nearest hundred, now you look at the next digit beside the hundreds place which is 9, so is 9 closer to 10? Or closer to 1? 9 is closer to 10, so now $499.99 tunrs into $500. Now when you are estimating the cost of the sofa which is 239.99, it is pretty much the same concept, you look at the digit beside the hundreds place, which is 3, so is 3 closer to 10? Or closer to 1? 3 is closer to 1. Now, 239.99 turns into $200. After you are done rounding the prices you add them together. 500+200= $700.00 and that is your estimated answer. If you calculate the real price 499.99+239.99= $739.98, so this estimate is close to the real answer.
If you are estimating you have to ask yourself some questions. For example if you had the number 218 you can either choose to round to the nearest one, ten, or hundred since it's a three digit number. Now let's say you are rounding to the nearest ten, you look at the digit beside the tens place value which is 8. Now you ask yourself is 8 higher than 5? Or lower than 5? Or you can ask yourself is 8 closer to ten? Or closer to 1? Of course 8 is closer to ten so now the number 218 turns into 220.
Estimating:
Estimating, when you are estimating maybe for an assignment or a test it's almost the same concept with rounding. For example, if you have a question asking you, estimate the total cost of the T.V and the sofa. T.V costs $499.99 and the sofa costs $239.99. Let's round the cost of the T.V to the nearest hundred, now you look at the next digit beside the hundreds place which is 9, so is 9 closer to 10? Or closer to 1? 9 is closer to 10, so now $499.99 tunrs into $500. Now when you are estimating the cost of the sofa which is 239.99, it is pretty much the same concept, you look at the digit beside the hundreds place, which is 3, so is 3 closer to 10? Or closer to 1? 3 is closer to 1. Now, 239.99 turns into $200. After you are done rounding the prices you add them together. 500+200= $700.00 and that is your estimated answer. If you calculate the real price 499.99+239.99= $739.98, so this estimate is close to the real answer.
Estimating And Rounding
To estimate you would have to round to the nearest 1's, 100's, 1000's etc.
To know what number to round just round to the nearest numbers it says on the paper and once you figure that out then you have to look at the right (beside your number).
If your numbers are 5 to 9 the you would have to round it up, but if it is 1 to 4 then you would have to round down.
For example.....
Estimating with Decimals
Its just like the same thing but its just with decimals. But this time you have to round to the nearest tenth's, hundredth's, thousandth's etc.
You just have to remember 5 or higher your have to round up, but if its 4 and lower then round it down.
For example...
To know what number to round just round to the nearest numbers it says on the paper and once you figure that out then you have to look at the right (beside your number).
If your numbers are 5 to 9 the you would have to round it up, but if it is 1 to 4 then you would have to round down.
Estimating with Decimals
Its just like the same thing but its just with decimals. But this time you have to round to the nearest tenth's, hundredth's, thousandth's etc.
You just have to remember 5 or higher your have to round up, but if its 4 and lower then round it down.
For example...
Over Estimating and Under Estimating
For over estimating that means you had to much of the right answer. For under estimating you got less of your answer.
For example.....
Sunday 27 January 2013
mix and improper fractions
to turn a mix fraction to an improper fractions you have to this steps:
step 1: multiply your denominator to the whole
step 2: after multiplying the denominator to the whole, add it to the numerator
(reminder: your denominator will stay desame)
example: 4 5/9 (your denominator is nine, four is your whole and five is your numerator)
9x4= 36+5=41 (so your numerator is 41)
so your improper fraction is 41/9
step 1: multiply your denominator to the whole
step 2: after multiplying the denominator to the whole, add it to the numerator
(reminder: your denominator will stay desame)
example: 4 5/9 (your denominator is nine, four is your whole and five is your numerator)
9x4= 36+5=41 (so your numerator is 41)
so your improper fraction is 41/9
Mixed & Improper Fractions
Mixed and Improper Fractions
For mixed and improper fractions, let's start with knowing what a fraction is. A fraction is showing a division from part and whole. It shows how much the whole is divided up to in equal parts.
For mixed and improper fractions, let's start with knowing what a fraction is. A fraction is showing a division from part and whole. It shows how much the whole is divided up to in equal parts.
Numerator: In ½ , the 1 is represented as the part of the whole, meaning it's the numerator.
The numerator shows the equal parts in the fraction. 1/2 also means half because 1 is half of 2.
Denominator: In the fraction ¾, the 4 is represented as the denominator. The denominator shows how much the whole is, or the total.
Divide: In fractions, there is the numerator ( In simplest terms, the number at the top ), and the denominator ( The number at the bottom ), but what does the line represent? The line in fractions represents divide. When you divide the numerator to the denominator, you'll turn the fraction into a decimal. If you turn a
fraction like ¾ into a decimal, divide 3 to 4 to equal 0.75.
Mixed Fractions:
Mixed Fractions is when there is a whole number mixed with a proper fraction. This happens when there is an improper fraction, but showed in a different way.
2¾ In this fraction, the 2 is the whole number. The 3 is the parts in the whole. The 4 is how much parts the whole is divided up to, or the total.
Improper Fractions:
Improper Fractions is when the numerator is greater than the denominator, making it improper. You could easily convert improper fractions into mixed fractions, and vice versa.
11/4 In this fraction, you could tell it's improper by seeing that the numerator is greater than the denominator. 11 is greater than 4 so you can also tell that it's more than a whole. 4/4 is a whole, and 11/4 is greater.
Converting Mixed to Improper and Improper to Mixed:
2¾ For mixed to improper, you can take the whole number (2) and then multiply that by the denominator (4), then adding the numerator (3). Equation: 2x4+3 = 11. Once you have the answer, just simply input the denominator. Remember, the denominator never changes. Your answer should be the numerator. This equals up to 11/4.
11/4 For improper to mixed, you'll have to use your division facts. Find out how much the denominator (4) could fit into the numerator (11). So how I thought of it is 4x3 equals 12 but 12 is greater than 11, so then 2x4. 2x4 = 8. After that, figure how much you need to get to the previous numerator, so 8 to 11, you add 3. 3 is the leftover number. The leftover number will be the numerator on the new mixed number and the denominator will stay the same. The whole will be the number you multiplied by the denominator, in this case, the 2, equaling 2 3/4.
Hope this helps! ^_~~
- Pam Joseph 7-09
Converting Review ( percent,fractions,decimals)
How to convert Percent to Decimals:
Eg.
25% and 2.5% are examples of percent.
- so we need to find the decimal form of both of 25% & 2.5%
1. To do that, we first need to find the decimal point of the percent/number.
Remember: if you can't see thr decimal point of the percent/number, the decimal point is at the right end of the number.
Eg.
37% ( 37. <--- decimal point )
2. After we find the decimal point of the percent/number, we now move the decimal point 2x to the left then remove the percent sign.
Eg. #1
25.% -> 25. = 0.25 ( final answer )
^ <-- move the dec. p. to the left (2x)
Decimal point
Eg. # 2
2.5% -> 2.5 = 0.025
^ <-- move the dec. p. to the left (2x)
Decimal point
* always move the decimal point 2x to the left.
* if there's a gap/space when you move the decimal point like example number 2, just fill the gap with the number 0.
How to convert Decimals to Percent:
Eg.
0.25 and 2.5
- we need to convert 0.25 and 2.5 to percent.
1. First thing we need to do is to find the decimal point.
Eg.
0.25 2.5
^ ^
\ /
Decimal points
2. After that, we now move the decimal point 2x to the right then just add a percent sign (%).
Eg#1
0.25 ----> 0.25 + % = 25% ( final answer )
^ --->Move to the right (2x)
Decimal point
* if there's the number zero in front of the decimal numbers, just remove it.
Eg#2
2.5 ---> 2.5 = 250% ( final answer )
^ ---> move to the right (2x)
Decimal Point
* If there's a space when you move the decimal point just add zero to the space.
How to convert Percent to Fraction:
1. We turn the percent to decimal. ( You can see that in "How to turn Percent to Decimal".
Eg.
3.7 = 0.037
2. Now we need to identify the place value of the last number of decimal.
Eg.
0.037
0- tenths
3- hundredths
7- thousandths
Remember: The first number after the decimal point always starts with the place value of tenths.
3. After you 've identified the place value of the last number, we now make the decimal number a numerator and the denominator is based on the place value of the last decimal number.
Eg.
0.037 = 37/1000
^
Thousandths
* if there's a zero in front of the number, just remove it.
4. If the fraction can be simplified, simplify it. To do that, we must need to find a number that can divide both the numerator and the denomintor.
Eg.
25/100 divided both by 25 = 1/4
How to convert Fraction to Decimal:
1. We divide the numerator by the denominator.
Eg#1
5/8 = 5 divide by the number 8. --> 0.625
5- numerator
8- denominator
Eg#2
3 3/5 ( mixed fraction )
= 3 divide by the number 5
= 0.6 + 3
= 3.6
Remember: if you have a mixed fraction, just add the whole number to the answer of the numerator and denominator.
3 3/5
3- whole number
3- numerator
5- denominator
How to convert Decimal to Fraction:
1. We identify the place value of the last number of decimal.
Eg.
0.625
6- tenths
2- hundredths
5- Thousandths
2. We now place the decimal number(s) as the numerator of the fraction and the denominator is based by the place value of the last decimal number .
Eg.
0.625 --> 625/1000 = 5/8 ( final answer )
^
Thousandths Divide both numbers by 125
* if you can simplify the fraction, simplify.
Eg.
25% and 2.5% are examples of percent.
- so we need to find the decimal form of both of 25% & 2.5%
1. To do that, we first need to find the decimal point of the percent/number.
Remember: if you can't see thr decimal point of the percent/number, the decimal point is at the right end of the number.
Eg.
37% ( 37. <--- decimal point )
2. After we find the decimal point of the percent/number, we now move the decimal point 2x to the left then remove the percent sign.
Eg. #1
25.% -> 25. = 0.25 ( final answer )
^ <-- move the dec. p. to the left (2x)
Decimal point
Eg. # 2
2.5% -> 2.5 = 0.025
^ <-- move the dec. p. to the left (2x)
Decimal point
* always move the decimal point 2x to the left.
* if there's a gap/space when you move the decimal point like example number 2, just fill the gap with the number 0.
How to convert Decimals to Percent:
Eg.
0.25 and 2.5
- we need to convert 0.25 and 2.5 to percent.
1. First thing we need to do is to find the decimal point.
Eg.
0.25 2.5
^ ^
\ /
Decimal points
2. After that, we now move the decimal point 2x to the right then just add a percent sign (%).
Eg#1
0.25 ----> 0.25 + % = 25% ( final answer )
^ --->Move to the right (2x)
Decimal point
* if there's the number zero in front of the decimal numbers, just remove it.
Eg#2
2.5 ---> 2.5 = 250% ( final answer )
^ ---> move to the right (2x)
Decimal Point
* If there's a space when you move the decimal point just add zero to the space.
How to convert Percent to Fraction:
1. We turn the percent to decimal. ( You can see that in "How to turn Percent to Decimal".
Eg.
3.7 = 0.037
2. Now we need to identify the place value of the last number of decimal.
Eg.
0.037
0- tenths
3- hundredths
7- thousandths
Remember: The first number after the decimal point always starts with the place value of tenths.
3. After you 've identified the place value of the last number, we now make the decimal number a numerator and the denominator is based on the place value of the last decimal number.
Eg.
0.037 = 37/1000
^
Thousandths
* if there's a zero in front of the number, just remove it.
4. If the fraction can be simplified, simplify it. To do that, we must need to find a number that can divide both the numerator and the denomintor.
Eg.
25/100 divided both by 25 = 1/4
How to convert Fraction to Decimal:
1. We divide the numerator by the denominator.
Eg#1
5/8 = 5 divide by the number 8. --> 0.625
5- numerator
8- denominator
Eg#2
3 3/5 ( mixed fraction )
= 3 divide by the number 5
= 0.6 + 3
= 3.6
Remember: if you have a mixed fraction, just add the whole number to the answer of the numerator and denominator.
3 3/5
3- whole number
3- numerator
5- denominator
How to convert Decimal to Fraction:
1. We identify the place value of the last number of decimal.
Eg.
0.625
6- tenths
2- hundredths
5- Thousandths
2. We now place the decimal number(s) as the numerator of the fraction and the denominator is based by the place value of the last decimal number .
Eg.
0.625 --> 625/1000 = 5/8 ( final answer )
^
Thousandths Divide both numbers by 125
* if you can simplify the fraction, simplify.
subtracting fractions
1.SUBTRACTING WITH LIKE DENOMINATORS
You just subtract the numerators together.
EX.4/5-1/5=3/5
2.SUBTRACTING WITH UNLIKE DENOMINATORS
You have to find the lowest common denominator for both denominators in the the times tables. You have to multiply the the numerator by how much you multiplied the denominator.
EX.5/6-4/8
You just subtract the numerators together.
EX.4/5-1/5=3/5
2.SUBTRACTING WITH UNLIKE DENOMINATORS
You have to find the lowest common denominator for both denominators in the the times tables. You have to multiply the the numerator by how much you multiplied the denominator.
EX.5/6-4/8
6x4=24 5x4=20
8x3=24 4x3=12
20/24-12/24=8/24
3.SUBTRACTING MIXED WITH LIKE DENOMINATORS
subtract the numerator then the whole numbers
EX.4 4/5-2 1/5
4-1= 3
4-2=2
so 4 4/5-2 1/5= 2 3/5
4.SUBTRACTING MIXED WITH UNLIKE DENOMINATORS
You have to find the lowest common denominator for both denominators in the the times tables. You have to multiply the the numerator by how much you multiplied the denominator. subtract the numerator then the whole number.
EX.2 1/2-1 2/4
2x2=4 1x2=2
4x1=4 2x1=2
2-2=0
2-1=1
2 1/2-1 2/4=1
Mixed Numbers and Improper Fractions
Today, we will be talking about mixed numbers and improper fractions, but before that, lets talk about what a fraction is.
A fraction describes a part of a whole. The number on the bottom of the fraction is called a denominator, and it denotes how many equal parts the whole is divided into. The number on the top of the fraction is called a numerator, and it denotes how many parts we are taking. For example, the fraction 3/4 denotes 3 of 4 equal parts. 3 is the numerator and 4 is the denominator.
Now, that to know what a fraction is, we will be talking about mixed numbers.
A mixed number is composed of a whole number and a fraction. 6 2/3, 18 3/4 and 2 2/5 are all examples of mixed numbers.
Converting Improper Fractions into Mixed Numbers:
Divide the numerator by the denominator. The resultant becomes the whole number, and the remainder becomes the numerator of the new fraction. The denominator of the new fraction is the same as the old denominator. If there is no remainder, then there is no fraction, the result is simply a whole number.
For example, we can convert 22/5 into a mixed number.
22/5= 4
Remainder= 2
Mixed Number: 4 2/5
Converting Mixed Numbers into Improper Fractions:
To convert a mixed number into an improper fraction, multiply the whole number by the denominator and add it to the numerator. This becomes the numerator of the improper fraction; the denominator of the new fraction is the same as the original denominator.
For example, we can convert 7 8/3 into an improper fraction.
7 x 3= 21
21+8= 29
Improper Fraction: 29/3
Now, that to know what a fraction is, we will be talking about mixed numbers.
A mixed number is composed of a whole number and a fraction. 6 2/3, 18 3/4 and 2 2/5 are all examples of mixed numbers.
Converting Improper Fractions into Mixed Numbers:
Divide the numerator by the denominator. The resultant becomes the whole number, and the remainder becomes the numerator of the new fraction. The denominator of the new fraction is the same as the old denominator. If there is no remainder, then there is no fraction, the result is simply a whole number.
For example, we can convert 22/5 into a mixed number.
22/5= 4
Remainder= 2
Mixed Number: 4 2/5
Converting Mixed Numbers into Improper Fractions:
To convert a mixed number into an improper fraction, multiply the whole number by the denominator and add it to the numerator. This becomes the numerator of the improper fraction; the denominator of the new fraction is the same as the original denominator.
For example, we can convert 7 8/3 into an improper fraction.
7 x 3= 21
21+8= 29
Improper Fraction: 29/3
Rounding/Estimating
To estimate, first round the numbers. Then add it or subtract it.
When estimating, first decide what
rounding will take place and look at the digit to its right.
Round it up if the number is like this;
= 5, 6, 7, 8, 9
Change it to 0 (zero)/round it down if the number is less than 4
For Example:
You can estimate numbers to the nearest ten, hundreds,
thousands, ten-thousands, etc.
Estimating Decimals
Estimation is a good tool for making a rough calculation. There are many estimation strategies that you could use to estimate the sum of these decimals. Let's look at the front-end strategy and the rounding strategy. We will round to the nearest tenth.
To round a decimal to a designated place value, first underline or mark that place. If the digit to the right of that place is 5 through 9, then round up. If the digit to the right of that place is 1 through 4, then round down, leave the digit in the designated place unchanged, and drop all digits to the right of it.
An overestimate is an an estimate that is too high: it exceeds the actual answer. An underestimate is an estimate that is too low: it is lower than the actual answer.
When estimating, first decide what
rounding will take place and look at the digit to its right.
Round it up if the number is like this;
= 5, 6, 7, 8, 9
Change it to 0 (zero)/round it down if the number is less than 4
For Example:
Estimate the sum.
|
Estimate the difference.
| ||
36
+44
?
|
40
+40
80
|
52
-25
?
|
50
-30
20
|
You can estimate numbers to the nearest ten, hundreds,
thousands, ten-thousands, etc.
Estimating Decimals
Estimation is a good tool for making a rough calculation. There are many estimation strategies that you could use to estimate the sum of these decimals. Let's look at the front-end strategy and the rounding strategy. We will round to the nearest tenth.
Example 1: Front-End Strategy | Rounding Strategy | |
| Add the front digits and then adjust the estimate. | Round each decimal to a designated place value, then add to estimate the sum. | |
3.75 3.75  about+ 4.29 + 4.29 17 7 + 1 = 8 | 3.75 3.8+ 4.29 + 4.3+ 4.29  + 8.1 | |
| 3 + 4 = 7 and .75 plus .29 is about 1. Thus, $7+ $1 = $8. The estimated sum is $8. | Rounding each decimal to the nearest tenth, we get an estimated sum of 8.1 or $8.10. |
| Note the difference between the two strategies used in Example 1: The front-end strategy uses the first digit to estimate a sum and then considers the other digits to adjust the estimate. In the rounding strategy, addition does not occur until after the numbers have been rounded. In both strategies, you must line up both decimals before proceeding. |
Example 2: | Estimate the sum of each pair of decimals by rounding to the specified place. | ||||
| a) | Estimate 4.203 + 6.598 by rounding to the nearest hundredth. | ||||
| 4.203 4.20 + 6.598 + 6.60 10.80 | |
| |||
| b) | Estimate $12.96 + $7.19 by rounding to the nearest one. | ||||
| $12.96 $13 + $ 7.19 + $ 7 $20 | |
| |||
| c) | Estimate 11.79 + 4.58 by rounding to the nearest tenth. | ||||
| 11.79 11.8 + 4.58 + 4 6 16.4 |
| ||||
An overestimate is an an estimate that is too high: it exceeds the actual answer. An underestimate is an estimate that is too low: it is lower than the actual answer.
| Estimate | Actual Sum | Overestimate or Underestimate? | ||
| a) | + $36.23+ $36.20 + $63.44 + $63.40+ $99.60 + $99.60 | $99.67 | Underestimate since $99.60 < $99.67 | |
| b) | $57.65 $ 57.70 + $43.31 + $ 43.30 $101.00 | $100.96 | Overestimate since $101.00 > $100.96 | |
| c) | $24.89 $24.90 + $72.15 + $72.20 $97.10 | $97.04 | Overestimate since $97.10 > $97.04 |
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