In this lesson, we're going to learn changing decimals to fraction. Changing decimal to fraction is quite easy because I shown the special fraction 1/10, 1/100, 1/1000 etc so it's easy when you're using these special fractions.
For example, "Change the following decimals to fractions, simplify if is necessary."
(a) 0.5 (b) 0.47 (c) 0.234 (d) 6.7 (e) 0.089
In question (a), 0.5 has only one decimal point, so 0.5 equals to 5/10.
Then we simplify and the answer is 1/2.
Question (b) has two decimal point, so we place 47 over 100 and it's 47/100.
This time we don't need to simplify it because there's no same number to divide by.
Question (c) has three decimal points, so we place 234 over 1000.
Then we simplify by the same number which is 2,
therefore the answer is 117/500.
Question (d) has one decimal point but there is 1 figure after the decimal point.
Therefore is 6 7/10.
Lastly, question (e), it has 3 decimal point, therefore we write 89 over 1000.
Therefore our answer is 89/1000.
* When there's 1 figure in front of the decimal point, place the number over 10.
When there's 2 figure in front of the decimal point, place the number over 100.
When there's 3 figure in front of the decimal point, place the number over 1000.
Monday, September 20, 2010
Sunday, September 19, 2010
Placing the decimal orders
In this lesson we're going to learn placing the each decimal ascending order or descending order. Placing the decimals into descending order or ascending order shows us which decimal is bigger or smaller.
Example 1 is "Order the following numbers in descending order."
77.4 77.04 77 77.44
Now, 77.4. 77.4 equals to 77 + 4/10,
77.04 equals to 77 + 4/100,
there's no decimal on 77,
and lastly 77.44 equals to 77 + 44/100.
Therefore the answer is 77.44, 77.4, 77.04, 77.
Second example is "Five hamsters ran in the 1m hamster marathon and recorded their time of finish in seconds. Order the following times in ascending order.
31.07, 34.67, 31.37, 21.79, 56.45
Now we do the same thing as we did it in the example 1.
31.07 equals to 31 + 7/100,
34.67 = 34 + 67/100,
31.37 = 31 + 37/100,
21.79 = 21 + 79/100,
56.45 = 56 + 45/100.
Therefore the answer is: 21.79, 31.07, 31.37, 34.67, 56.45.
Example 1 is "Order the following numbers in descending order."
77.4 77.04 77 77.44
Now, 77.4. 77.4 equals to 77 + 4/10,
77.04 equals to 77 + 4/100,
there's no decimal on 77,
and lastly 77.44 equals to 77 + 44/100.
Therefore the answer is 77.44, 77.4, 77.04, 77.
Second example is "Five hamsters ran in the 1m hamster marathon and recorded their time of finish in seconds. Order the following times in ascending order.
31.07, 34.67, 31.37, 21.79, 56.45
Now we do the same thing as we did it in the example 1.
31.07 equals to 31 + 7/100,
34.67 = 34 + 67/100,
31.37 = 31 + 37/100,
21.79 = 21 + 79/100,
56.45 = 56 + 45/100.
Therefore the answer is: 21.79, 31.07, 31.37, 34.67, 56.45.
Saturday, September 18, 2010
Decimal introduction and place value
In this lesson, we're doing a new topic. The new topic is decimal. Previously we learned about the fraction, now we're going to change the fractions into decimals and decimals into fraction, then we're going to learn about place value in decimal.
Firstly, changing decimal into fraction. Changing decimal into fraction is like this. Decimals are different from the the fraction but they're special fraction which the denominators are 10, 100, 1000, etc.
So for example, 1 and 59/100 is 1.59.
Secondly I want to talk about is place value in decimal.
Decimal place value is similar as the whole number place value.
The only difference is there is a tenth, hundredth, thousandth, etc.
Tenth is 1/10 in fraction, hundredth is 1/100 in fraction and in goes on 1000, 10000, 100000 etc.
For example 345.123.
We all know now that 3 is 300, 4 is 40, 5 just 5, and now,
1 is 1/10 because 1 is in tenth place,
2 is 1/100 because 2 is in hundredth place,
and 3 is 1/3000 because 3 is in thousandth place.
Second example is "write 34.56 in expanded form."
Expanded form is another way to show how much number are in each digits
that represents.
Therefore (3 x 10) + ( 4 x 1) + (5 x 1/10) + (6 x 1/100).
Third and last example is "What is the place value of 5 in 123.475?"
The answer is thousandth. Reason is 5 in the thousandth place,
the place value of 5 is 5 x 1/1000 = 5/1000.
Firstly, changing decimal into fraction. Changing decimal into fraction is like this. Decimals are different from the the fraction but they're special fraction which the denominators are 10, 100, 1000, etc.
So for example, 1 and 59/100 is 1.59.
Secondly I want to talk about is place value in decimal.
Decimal place value is similar as the whole number place value.
The only difference is there is a tenth, hundredth, thousandth, etc.
Tenth is 1/10 in fraction, hundredth is 1/100 in fraction and in goes on 1000, 10000, 100000 etc.
For example 345.123.
We all know now that 3 is 300, 4 is 40, 5 just 5, and now,
1 is 1/10 because 1 is in tenth place,
2 is 1/100 because 2 is in hundredth place,
and 3 is 1/3000 because 3 is in thousandth place.
Second example is "write 34.56 in expanded form."
Expanded form is another way to show how much number are in each digits
that represents.
Therefore (3 x 10) + ( 4 x 1) + (5 x 1/10) + (6 x 1/100).
Third and last example is "What is the place value of 5 in 123.475?"
The answer is thousandth. Reason is 5 in the thousandth place,
the place value of 5 is 5 x 1/1000 = 5/1000.
Friday, September 17, 2010
Changing one quantity as a fraction of another amount
In this lesson, we're going learn rates in fraction. Rates in fraction is like this, finding a part in the whole part.
Also each fractions needs to be expressed in the same units and it needs to be tat the smaller part goes the above.
First example is "What fraction is 30 minutes in 2 hours?"
Now we need to make the unit same so 1 hour equals 60 minutes, 2 hours equals 120 minutes.
Therefore 30 minutes/120 minutes equals 1/4.
This cancels down to 1/4.
Second example is "What example is 40 cents of $5?"
In this example 1 dollar is 100 cent,m so$5 is 500 cent.
Therefore, 40/500 equals 2/25.
Third and last example is "What fraction is 24cm of 1m?"
Same as the other examples, we need to make the units same so 1m equals to 100cm,
so 24/100 equals to 6/25.
Also each fractions needs to be expressed in the same units and it needs to be tat the smaller part goes the above.
First example is "What fraction is 30 minutes in 2 hours?"
Now we need to make the unit same so 1 hour equals 60 minutes, 2 hours equals 120 minutes.
Therefore 30 minutes/120 minutes equals 1/4.
This cancels down to 1/4.
Second example is "What example is 40 cents of $5?"
In this example 1 dollar is 100 cent,m so$5 is 500 cent.
Therefore, 40/500 equals 2/25.
Third and last example is "What fraction is 24cm of 1m?"
Same as the other examples, we need to make the units same so 1m equals to 100cm,
so 24/100 equals to 6/25.
Finding a fraction of amount.
In this lesson we're going to learn find an amount when multiplying the fraction. On few of the previous lesson, we had a calculation like this fraction times by the whole number. So we're going to learn further this time on this.
Now for example if the whole number is the quantity and the fraction is the amount that we need to find from the total amount we just multiply it.
The example 1 is "Find 5/6 of 85 ipods."
Now we do it like I showed you on previous lessons. In fraction any whole number is whole number over 1, so 85 is 85/1 in fraction, and the working out is 5 x 85 = 425 and 6 x 1 = 6.
Therefore the answer is 425/6, and if we simplify it, is 70.83333333... and we're going to round it off to the nearest rounds and is 71 ipods.
Second example is "Find 8/9 of $72."
We do the same as the previous example.72 is 72/1 and 72 x 8 = 576 and 9 x 1 = 9.
Therefore 576/9 is 64, therefore is $64.
Third and last example is "Find 8/40 of 100 Meters."
So as the last one, we do the same thing.
First is 100 is 100/1,
second is 8 x 100 = 800, 40 x 1 = 40.
Therefore our answer is 800/40 and if we simplify, the exact answer is 20, therefore is 20 meters.
* If you finished your calculation and doing the next question, double check later.
Reason is most of the questions have metric systems such as kilometers, meters, centimeters, etc.
Don't forget to write them!
Now for example if the whole number is the quantity and the fraction is the amount that we need to find from the total amount we just multiply it.
The example 1 is "Find 5/6 of 85 ipods."
Now we do it like I showed you on previous lessons. In fraction any whole number is whole number over 1, so 85 is 85/1 in fraction, and the working out is 5 x 85 = 425 and 6 x 1 = 6.
Therefore the answer is 425/6, and if we simplify it, is 70.83333333... and we're going to round it off to the nearest rounds and is 71 ipods.
Second example is "Find 8/9 of $72."
We do the same as the previous example.72 is 72/1 and 72 x 8 = 576 and 9 x 1 = 9.
Therefore 576/9 is 64, therefore is $64.
Third and last example is "Find 8/40 of 100 Meters."
So as the last one, we do the same thing.
First is 100 is 100/1,
second is 8 x 100 = 800, 40 x 1 = 40.
Therefore our answer is 800/40 and if we simplify, the exact answer is 20, therefore is 20 meters.
* If you finished your calculation and doing the next question, double check later.
Reason is most of the questions have metric systems such as kilometers, meters, centimeters, etc.
Don't forget to write them!
Dividing fractions
In this lesson, we're going learn dividing fractions. Dividing fraction is bit difficult to understand in the starter but if you find the way to solve it, it will be easy.
Now if you're dividing fractions, leave the first and make the second fraction a reciprocal, a reciprocal is flipping over, for example 3/4, if we do reciprocal, 3/4 turns into 4/3.
Example 1 is 6/8/ 4/5.
Now, we leave 6/8 and make 4/5, 5/4.
Then the working out is 6/8 x 5/4, 6 x 5 = 30 , 8 x 4 = 32.
Therefore the answer is 30/32 and we simplify by the common number that it can be divided equally, and is 15/16.
Second example is 6 / 3/6.
This time we make 6, 6 over 1 and flip 3/6.
Therefore 6/1 x 6/3 = 36/3.
Then we simplify by 3 because 3 can only divided by 3 or 1 in this case 36 needs to be divided by 3 because 36 and 3's common number is 3 so therefore the answer is 12.
Third and last example is Divide 9 1/3 by 4/7.
Now the easiest way to do it is change 9 1/3 to improper fraction and is 28/3.
Then we flip 4/7 and is 7/4.
Therefore is 28/3 x 7/4.
Finally our answer is 196/12, but we forgot the one last thing to do, we simplify by the same number.
Then our answer is 16.333333333... but we're going to round it off to the nearest whole number.
* If there's a question which it has a mixed fraction, the easiest to it is change the mixed fraction to the improper fraction.
Now if you're dividing fractions, leave the first and make the second fraction a reciprocal, a reciprocal is flipping over, for example 3/4, if we do reciprocal, 3/4 turns into 4/3.
Example 1 is 6/8/ 4/5.
Now, we leave 6/8 and make 4/5, 5/4.
Then the working out is 6/8 x 5/4, 6 x 5 = 30 , 8 x 4 = 32.
Therefore the answer is 30/32 and we simplify by the common number that it can be divided equally, and is 15/16.
Second example is 6 / 3/6.
This time we make 6, 6 over 1 and flip 3/6.
Therefore 6/1 x 6/3 = 36/3.
Then we simplify by 3 because 3 can only divided by 3 or 1 in this case 36 needs to be divided by 3 because 36 and 3's common number is 3 so therefore the answer is 12.
Third and last example is Divide 9 1/3 by 4/7.
Now the easiest way to do it is change 9 1/3 to improper fraction and is 28/3.
Then we flip 4/7 and is 7/4.
Therefore is 28/3 x 7/4.
Finally our answer is 196/12, but we forgot the one last thing to do, we simplify by the same number.
Then our answer is 16.333333333... but we're going to round it off to the nearest whole number.
* If there's a question which it has a mixed fraction, the easiest to it is change the mixed fraction to the improper fraction.
Tuesday, September 14, 2010
Multiplying fractions
In this lesson, we're learning multiplying fractions. Multiplying fraction is different to the adding and subtracting the fractions. When you're multiplying fractions you multiply numerators with numerators, denominators with denominators. Also when you're multiplying the whole number, write whole number over 1.
Our first example is 3/5 x 1/5.
We multiply out numerator times numerator, denominator times denominator.
Therefore, 3 x 1 = 3, 5 x 5 = 25, and the answer is 3/25.
Second example is 4/5 x 3/6.
We multiply numerator by numerator, denominator by denominator. That equals 4 x 3 = 12, 5 x 6 = 30.
Therefore our answer is 12/30, and if we simplify by 2,3 or 6, the answer will be 2/5.
Third example is 15 x 2/3.
Like I said numerator by numerator, denominator by denominator.
In this case, there's a whole number so we write 15 like this, 15/1.
Then we do the normal step, multiplying. 15 x 2 = 30, 1 x 3 = 3.
Therefore the answer is 30/3 but if we simplify, the exact answer is 10.
Forth and last example is 8 1/4 x 2 4/8.
Now this time, we have to change it to the mixed fractions so 8 1/4 turns into 33/4, 2 4/8 turns into 20/8.
33 x 20 = 660, 4 x 8 =32.
660/32 = 165/8.
then we change it to the mixed fraction, is 20 5/8.
Therefore our answer is 20 5/8.
Our first example is 3/5 x 1/5.
We multiply out numerator times numerator, denominator times denominator.
Therefore, 3 x 1 = 3, 5 x 5 = 25, and the answer is 3/25.
Second example is 4/5 x 3/6.
We multiply numerator by numerator, denominator by denominator. That equals 4 x 3 = 12, 5 x 6 = 30.
Therefore our answer is 12/30, and if we simplify by 2,3 or 6, the answer will be 2/5.
Third example is 15 x 2/3.
Like I said numerator by numerator, denominator by denominator.
In this case, there's a whole number so we write 15 like this, 15/1.
Then we do the normal step, multiplying. 15 x 2 = 30, 1 x 3 = 3.
Therefore the answer is 30/3 but if we simplify, the exact answer is 10.
Forth and last example is 8 1/4 x 2 4/8.
Now this time, we have to change it to the mixed fractions so 8 1/4 turns into 33/4, 2 4/8 turns into 20/8.
33 x 20 = 660, 4 x 8 =32.
660/32 = 165/8.
then we change it to the mixed fraction, is 20 5/8.
Therefore our answer is 20 5/8.
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