In this lesson we're going to some more further work in decimals in money.
In most of the exam, like school certificate or major exams, there are 4 operation all the time and the 4 operation decimal is one of them. So what I would like to talk about is not a simple question, a short answer questions.
1. Our first example is "Poppy went to the store and bought toothpaste for $5.32, liquid soap for $3.48, hair shampoo for $4 and razor for 97 cents. How much change will Poppy get from $30?
We add all of the stuffs that Poppy bought and we subtract from the $30.
$5.32 + $3.48 + $4 + $0.97 = $13.77.
$30 - $13.77 = $16.23.
Therefore the answer is $16.23.
2. If a kilo of beef costs $9.57, ho much would 5 kilograms cost?
$9.57 This question's structure is finding the quantity, so is multiplication.
x 5 after the calculation is finished, you need to put the decimal point
2 figures to the right.
$47.85
3. A reward money of $ 6325.90 has to be shared equally between 5 people.
How much does each person receive?
1265.18
5 6325.90 Shared equally means divide $6325.90 by 5.
60
32
30
25
25
9
5
40
Therefore the answer is $1265.18.
Saturday, September 25, 2010
Decimals in money
In this lesson we're going to learn about decimals in money. The reason why I'm calling this lesson "Decimals in money is because when you're writing the currency (money), you write the cents in tenth and hundredth place.
Also the 4 operations are applying to the decimals because it applies in exactly the same way to money problems that we're dealing everyday.
Before I show you examples, I want to tell you how to write the currencies in numbers.
For example twenty three dollars and thirty seven cents.
$23.37 We write $23 in the whole number column and we write thirty cents in tenths and we just write 3 in there and 7 cents in hundredth.
1. Our first example is $539 + $78.26.
1
$539.00 0 + 6 = 6, we just write 6 under, 0 + 2 = 2 we just write 2 under,
+ $78.26 9 + 8 = 17 we write 7 and write 1 above 3, 3 + 7 = 10 and we add 1
= $617.26 that makes 11, so we write 1 and write another 1 above 5.
Lastly we add 1 to 5 and that makes 6 therefore the answer is $617.26.
2. Second example is 183.74 - 54.26.
$183.74 We can't do 4 - 6 so we borrow 1 from 7 and that makes us 14 - 6 = 8,
- $54.26 7 becomes 6. 6 - 2 = 4, we borrow 1 from 8, 13 - 4 = 9,
8 becomes 7, 7 - 5 = 2, there's nothing do with 1 so we just write 1.
= $129.48
Therefore the answer is $129.48.
3. Third example is $4.73 x 8.
2
$4.73 Firstly, 3 x 8 = 24, we write 4 under 8 and write 2 above 7,
x 8 7 x 8 =56 56 + 2 = 58 we write 8 behind 4, write 5 above the 4.
Lastly, 4 x 8 = 32, 32 + 5 = 37.
$37.84
Therefore our answer is $37.84.
4. Forth and last example is $76.82/2.
38.41
2 76.82 6 is close to 7 and is smaller so 2 x 3 = 6, 7 - 6 = 1,1 comes down so as 6,
6 it makes 16, 2 x 8 = 16, 16 -16 = 0, then 2 x 4 =8 equals to 8, 8 - 8 =0,
16 2 x 1 = 2 therefore we subtract 2 - 2 equals 2
16
8
8
2
2
0
Therefore the answer is $38.41.
Also the 4 operations are applying to the decimals because it applies in exactly the same way to money problems that we're dealing everyday.
Before I show you examples, I want to tell you how to write the currencies in numbers.
For example twenty three dollars and thirty seven cents.
$23.37 We write $23 in the whole number column and we write thirty cents in tenths and we just write 3 in there and 7 cents in hundredth.
1. Our first example is $539 + $78.26.
1
$539.00 0 + 6 = 6, we just write 6 under, 0 + 2 = 2 we just write 2 under,
+ $78.26 9 + 8 = 17 we write 7 and write 1 above 3, 3 + 7 = 10 and we add 1
= $617.26 that makes 11, so we write 1 and write another 1 above 5.
Lastly we add 1 to 5 and that makes 6 therefore the answer is $617.26.
2. Second example is 183.74 - 54.26.
$183.74 We can't do 4 - 6 so we borrow 1 from 7 and that makes us 14 - 6 = 8,
- $54.26 7 becomes 6. 6 - 2 = 4, we borrow 1 from 8, 13 - 4 = 9,
8 becomes 7, 7 - 5 = 2, there's nothing do with 1 so we just write 1.
= $129.48
Therefore the answer is $129.48.
3. Third example is $4.73 x 8.
2
$4.73 Firstly, 3 x 8 = 24, we write 4 under 8 and write 2 above 7,
x 8 7 x 8 =56 56 + 2 = 58 we write 8 behind 4, write 5 above the 4.
Lastly, 4 x 8 = 32, 32 + 5 = 37.
$37.84
Therefore our answer is $37.84.
4. Forth and last example is $76.82/2.
38.41
2 76.82 6 is close to 7 and is smaller so 2 x 3 = 6, 7 - 6 = 1,1 comes down so as 6,
6 it makes 16, 2 x 8 = 16, 16 -16 = 0, then 2 x 4 =8 equals to 8, 8 - 8 =0,
16 2 x 1 = 2 therefore we subtract 2 - 2 equals 2
16
8
8
2
2
0
Therefore the answer is $38.41.
Friday, September 24, 2010
Multiplying and dividing decimals by powers of 10.
In this lesson we're going to learn about multiplying and dividing decimals by powers of 10.
Sometimes when you're multiplying or dividing decimals, you have to multiply or divide by 10, 100, or 1000 etc,
so today we're going to learn how to multiply or divide the decimals just using the decimal point.
When multiplying a decimal by 10, 100 or 1000, move the decimal point 1,2 or 3 places to the right.
When dividing decimal by 10, 100 or 1000, move the decimal point 1,2 or 3 places to the right.
Our first example is 76.23 x 10.
We need to move the decimal point to the right just once.
Reason is we're moving the decimal point by the number of the zeroes.
Therefore our answer is 762.3.
Second example is 8.745 x 100.
Now we do the same but the position of the decimal point.
There are two zeroes at this time, so we move the decimal point to the right twice.
Therefore 8.745 x 100 = 874.5.
Third example is "Convert 2.7 meters to centimeters.
1m = 100cm, the working out should be like this, 2.7 x 100.
Then we move the decimal point to the right twice.
Therefore our answer is 270cm.
Forth and last example on multiplication is 2.967 x 1000.
This time there are 3 zeroes so we move the decimal point to the right three times.
Therefore the answer is 2967.
In dividing decimals, you move the decimal point to the left.
First example is 76.7/10.
There's only one zero so we move the decimal point to the left once.
Therefore the answer is 7.67.
Second example is 984.5/100.
There are two zeroes so we move the decimal point to left twice.
Therefore the answer is 9.845.
Third and last example is 85.9/1000.
There are three zeroes so we move the decimal point to the left three times.
Therefore the answer is 0.0859.
Sometimes when you're multiplying or dividing decimals, you have to multiply or divide by 10, 100, or 1000 etc,
so today we're going to learn how to multiply or divide the decimals just using the decimal point.
When multiplying a decimal by 10, 100 or 1000, move the decimal point 1,2 or 3 places to the right.
When dividing decimal by 10, 100 or 1000, move the decimal point 1,2 or 3 places to the right.
Our first example is 76.23 x 10.
We need to move the decimal point to the right just once.
Reason is we're moving the decimal point by the number of the zeroes.
Therefore our answer is 762.3.
Second example is 8.745 x 100.
Now we do the same but the position of the decimal point.
There are two zeroes at this time, so we move the decimal point to the right twice.
Therefore 8.745 x 100 = 874.5.
Third example is "Convert 2.7 meters to centimeters.
1m = 100cm, the working out should be like this, 2.7 x 100.
Then we move the decimal point to the right twice.
Therefore our answer is 270cm.
Forth and last example on multiplication is 2.967 x 1000.
This time there are 3 zeroes so we move the decimal point to the right three times.
Therefore the answer is 2967.
In dividing decimals, you move the decimal point to the left.
First example is 76.7/10.
There's only one zero so we move the decimal point to the left once.
Therefore the answer is 7.67.
Second example is 984.5/100.
There are two zeroes so we move the decimal point to left twice.
Therefore the answer is 9.845.
Third and last example is 85.9/1000.
There are three zeroes so we move the decimal point to the left three times.
Therefore the answer is 0.0859.
Thursday, September 23, 2010
Multiplying and dividing decimals.
In this lesson we're going to learn multiplying and dividing decimals. Difficulty of multiplying and dividing decimals are same as adding and subtracting decimals. Also the steps are similar as multiplying and dividing the whole number.
When you're multiplying decimal, if you're confused with the decimal point,
erase the decimal point for a while then put the decimal point when the calculation is done.
After you finished your calculation of multiplying decimals, add how many places did decimal point moved on each decimal and add all the positions.
Our first example is "Find 1.63 x 4.2."
Like we did on adding and subtracting decimals, we do it in easy way.
a
163
x 42
326
+ 652
6846
After the calculation is over, we put the decimal points.
When you're putting the decimal point, you need to make sure that the answer has the same number of decimal places as the question.
Therefore, 2 in 1.63 and 1 in 4.2, the total is 3 therefore our answer is 6.846.
Second example is " Find 0.4 of $5.60."
There are two way s to work out this question. You either go directly 0.4 times 5.60, or change the unit of $5.60 into 560 cents. The answer is same on which method you use.
Method 1 is 0.4
x 5.60
Therefore our answer is $2.24.
Method 2 is $5.60 is 560 cents, so 0.4 equals to 4/10
4/10 x 560 equals to 224, in dollar, is $2.24.
In Dividing decimal, we do the same thing as we did it in multiplying decimal but the working out is different.
Example 1 is " Evaluate 6.47/5."
1.294
5 6.47
5
1.4
1.0
47
45
20
Therefore our answer is 1.294.
Second example is "Find 52.16/0.4."
Firstly, we need to make 0.4 to whole number, and is 4.
Also we need to make sure that 52.16 turns into 521.6.
Reason is 0.4 moved to right to make a whole number, therefore the other decimal point must be moved to right.
130.4
4 521.6
4
12
12
1.6
1.6
0
Therefore our answer is 130.4.
When you're multiplying decimal, if you're confused with the decimal point,
erase the decimal point for a while then put the decimal point when the calculation is done.
After you finished your calculation of multiplying decimals, add how many places did decimal point moved on each decimal and add all the positions.
Our first example is "Find 1.63 x 4.2."
Like we did on adding and subtracting decimals, we do it in easy way.
a
163
x 42
326
+ 652
6846
After the calculation is over, we put the decimal points.
When you're putting the decimal point, you need to make sure that the answer has the same number of decimal places as the question.
Therefore, 2 in 1.63 and 1 in 4.2, the total is 3 therefore our answer is 6.846.
Second example is " Find 0.4 of $5.60."
There are two way s to work out this question. You either go directly 0.4 times 5.60, or change the unit of $5.60 into 560 cents. The answer is same on which method you use.
Method 1 is 0.4
x 5.60
Therefore our answer is $2.24.
Method 2 is $5.60 is 560 cents, so 0.4 equals to 4/10
4/10 x 560 equals to 224, in dollar, is $2.24.
In Dividing decimal, we do the same thing as we did it in multiplying decimal but the working out is different.
Example 1 is " Evaluate 6.47/5."
1.294
5 6.47
5
1.4
1.0
47
45
20
Therefore our answer is 1.294.
Second example is "Find 52.16/0.4."
Firstly, we need to make 0.4 to whole number, and is 4.
Also we need to make sure that 52.16 turns into 521.6.
Reason is 0.4 moved to right to make a whole number, therefore the other decimal point must be moved to right.
130.4
4 521.6
4
12
12
1.6
1.6
0
Therefore our answer is 130.4.
Wednesday, September 22, 2010
Addition and subtraction in decimals.
In this lesson we're going learn adding and subtracting decimals. Adding and subtracting decimals are different from adding and subtracting the whole number.
Reason is there's a decimal point and we need to put the decimal point in the right position.
On adding decimals, you have to make the decimal point directly under each other.
On subtracting decimals you make the decimal point directly under each other, and borrow 1 if necessary.
Our first example is 3.42 + 23.56 + 5.09 + 34.23.
Now we do it in the easy way.
3.42 All you need to remember is the order of operation and
23.56 and make all the decimal point directly under each other.
5.09
+ 34.23
66.3
Second example is 89.76 - 34.23.
89.76
- 34.23
55.53
Therefore our answer is 55.53.
Third and last example is," On Monday I spend $25.45 on entertainment, $12.56 for transport, and $4.00 on drink. How much have I left over from $60.00?
This question want s you to find the amount spend then subtract from $60.00
The total is $25.45 + $12.56 + $4.00 = $42.01
Then we subtract from $60.00.
Therefore $60.00 - $42.01 = $17.99,
and the answer would be $17.99 left.
* Don't forget to place all the decimal points directly under each other.
Reason is there's a decimal point and we need to put the decimal point in the right position.
On adding decimals, you have to make the decimal point directly under each other.
On subtracting decimals you make the decimal point directly under each other, and borrow 1 if necessary.
Our first example is 3.42 + 23.56 + 5.09 + 34.23.
Now we do it in the easy way.
3.42 All you need to remember is the order of operation and
23.56 and make all the decimal point directly under each other.
5.09
+ 34.23
66.3
Second example is 89.76 - 34.23.
89.76
- 34.23
55.53
Therefore our answer is 55.53.
Third and last example is," On Monday I spend $25.45 on entertainment, $12.56 for transport, and $4.00 on drink. How much have I left over from $60.00?
This question want s you to find the amount spend then subtract from $60.00
The total is $25.45 + $12.56 + $4.00 = $42.01
Then we subtract from $60.00.
Therefore $60.00 - $42.01 = $17.99,
and the answer would be $17.99 left.
* Don't forget to place all the decimal points directly under each other.
Converting difficult fractions to decimals.
In this lesson, we're going learn more on converting fractions to decimals.
Now, previously, we understand the special fraction and what special fraction is, but sometimes when you have a fraction that's not an equivalent, the special fractions won't work.
It happens most of the time wen you're converting fractions into decimals.
This is what you have to do. The method is very simple, only thing you have to do is divide the denominator from the numerator.
Our first example is "Convert 7/9 into decimal."
Like I said, we need to divide the denominator from the numerator.
So 7 divide from 9 and the answer is 0.777777778.
Second example is " Convert 5/21 into decimal."
Same as this, 5 divided by 21, and the answer is 0.238095238.
* In some of the fraction, you will notice that numbers tenths and hundredths are repeating.
In this case, you put a dot above the number on tenths and hundredth, it depends which number on which place is repeating and if the number on tenth is repeating, you put the dot above the number on tenth.
Now, previously, we understand the special fraction and what special fraction is, but sometimes when you have a fraction that's not an equivalent, the special fractions won't work.
It happens most of the time wen you're converting fractions into decimals.
This is what you have to do. The method is very simple, only thing you have to do is divide the denominator from the numerator.
Our first example is "Convert 7/9 into decimal."
Like I said, we need to divide the denominator from the numerator.
So 7 divide from 9 and the answer is 0.777777778.
Second example is " Convert 5/21 into decimal."
Same as this, 5 divided by 21, and the answer is 0.238095238.
* In some of the fraction, you will notice that numbers tenths and hundredths are repeating.
In this case, you put a dot above the number on tenths and hundredth, it depends which number on which place is repeating and if the number on tenth is repeating, you put the dot above the number on tenth.
Tuesday, September 21, 2010
Fractions to decimals
Previously, we learned converting decimal to fraction. In this lesson, we're going to learn converting fraction to decimal. Changing fraction to decimal is easy, if you know the special fraction.
Now, to change the fraction to decimal, you need to make the denominator into 10, 100 or 1000 or etc depends on the denominator which it has tens, hundreds or thousands. Also if you're converting fraction to decimal, first thing you have to do is, figure out which number is going to make the product of 10, 100, 1000, etc.
Our first example is " Convert 1/5 into decimal.
To convert fraction into decimal, we need to multiply something with 5 to make the denominator 10.
Reason is 5 is close to 10, so we're going to times 2 to make the denominator 10.
Therefore, 5 got times by 2 and the answer is 10, and don't forget to times 2 to 1 because it needs to be equal.
Then our answer is 2/10 and in decimal is 0.2.
Our second example is "Convert 7/25 into decimal."
In this example, you need to figure out which number needs to be multiply and make the product 100.
Now, 100 divided by 4 is 25 so then we need to do 7 times by 4, then our answer is 28.
Therefore our answer is 28/100 and in decimal, is 0.28.
Third and last example is " Convert 5/8 into decimal."
Now, 8 multiplied by 125 is 1000, and we do the same thing to the numerator.
5 multiplied by 125 is 625, therefore our answer is 625/1000
and in decimal is 0.625.
Now, to change the fraction to decimal, you need to make the denominator into 10, 100 or 1000 or etc depends on the denominator which it has tens, hundreds or thousands. Also if you're converting fraction to decimal, first thing you have to do is, figure out which number is going to make the product of 10, 100, 1000, etc.
Our first example is " Convert 1/5 into decimal.
To convert fraction into decimal, we need to multiply something with 5 to make the denominator 10.
Reason is 5 is close to 10, so we're going to times 2 to make the denominator 10.
Therefore, 5 got times by 2 and the answer is 10, and don't forget to times 2 to 1 because it needs to be equal.
Then our answer is 2/10 and in decimal is 0.2.
Our second example is "Convert 7/25 into decimal."
In this example, you need to figure out which number needs to be multiply and make the product 100.
Now, 100 divided by 4 is 25 so then we need to do 7 times by 4, then our answer is 28.
Therefore our answer is 28/100 and in decimal, is 0.28.
Third and last example is " Convert 5/8 into decimal."
Now, 8 multiplied by 125 is 1000, and we do the same thing to the numerator.
5 multiplied by 125 is 625, therefore our answer is 625/1000
and in decimal is 0.625.
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