Decimals and fractions are very closely related. They are both part of the whole. Any decimal can be converted into an equal fraction, and any fraction can be converted into an equal decimal. For example 1/4 is equal to .75.
Sometimes you might see fractions like 5/9 which is the same as 5
Multiplying, Dividing, Subtracting and Adding Fractions
To multiply Fractions its pretty easy. Look below to see how.
1 5 > multiply these 2 numbers together, the answer would be 5
65 X 9 - > multiply these 2 numbers together the answer would be 585
Now you would want to simplify it, to simplify it, find a number that goes into both of the numbers. For example 5 goes into 5, and 5 goes into 585. 5 goes into 5 once, so you turn the five into a 1. 5 into 585 is 117. So 5
585 simplified is 1
To divide fractions you turn the second fraction (the second
fraction meaning if the problem was 2/16 ÷ 1/5 the second fraction would be 1/5) into its own reciprocal. Then you want to multiply the number that you didnt turn into its reciprocal.
Adding decimals is sometimes easy and sometimes not. If the problem is 3/9 + 4/9 then you would add the 2 numerators together, and when the 2 denominators are the same you keep them the same in your answer. So the answer would be 8/9. If it was 3/4 +2/4 then you would get 5/4, and 5/4 is an improper fraction. So you need to turn it into a proper fraction by dividing the denominator into the numerator. Now the answer is 1 and 1/4. Now if the answer ends up being something like 1 2/4 then you would want to reduce it to 1 and 1/2. If you can reduce a fraction then you want to reduce it.
If the problem is 5/9 + 3/7 then its a little more tricky. First you need to find the LCD of the 2 denominators. The LCD stands for the least common denominator. Put that number in this case 63, on the side of your problem so your problem should look like this. Follow the below steps. The Italic Font is the 1st step. You do the Regular Font 2nd, and do the Bold Font last.
Take the number you got below which is the 9, and multiply it by 5 the denominator 5which is 5, so 5x9= 45
9 multiplied by __= 63 9 multiplied by 7 = 63
+ add these 2 new fractions together
3 Take the 7 and times it by the denominator which is 3, so 3x7= 21
7 multiplied by __= 63 7 multiplied by 9 = 63
answer: = 63
Turn this answer into a proper fraction 1and 3/63 which = 1 and1/23, I reduced it even more. I think you understand how to add fractions if you still dont understand get some help at the tutoring page.
Subtracting fractions is a lot like adding fractions, if you have 5/9 and you want to subtract 3/9 you would only subtract the numerators from each other because the denominators are the same. So the answer would be 2/9. But if you have a problem like 5/9 2/18 its harder. Sometimes when you simplify the problems you can solve them easier like the 1 here. If you simplify 2/18 to 1/9 then you can just do 5/9- 1/9 which equals 4/9. You can also have problems that dont do that, like 7/8-2/9. An order to solve this problem, you first need to find the LCD, which is the Lowest Common Denominator. In this case it would be 72. Put youre LCD on the side of your problem so that your problem should look like the problem shown below. Do the steps below to figure the problem out. Do the Italics first, regular font next, and Bold last.
7 Take the number you got below 9 and multiply it by the numerator 7 you should get 63
8 multiplied by __ =72, 8 multiplied by 9= 72
- Subtract these 2 new fractions
2 Take the number you got below 8 and multiply it by the numerator 2 you should get 16
9 multiplied by __ = 72, 9 multiplied by 8 = 72
If you get an answer that can be simplified then you should simplify it. On this problem though you dont have to simplify it more because it cant be simplified.
If you have 2 fractions that you are subtracting, like 1 and 4/6 and you want to subtract 5/6, it doesnt work very well, so you have to borrow from the 1. So you would make 1 and 4/6 into 10/6, I know its an improper fraction, but now you can subtract. If you need to borrow from the a whole number then you add youre your denominator to your numerator, but keep your denominator the same. If you dont understand what Im talking about then you can get some help at the tutoring page.
Converting Decimals into Fractions and Fractions into Decimals
You can turn fractions into decimals and decimals into fractions.
If you have easy fractions it will be much easier. Lets say you have 1/4 and you want to convert it to a decimal. You want to divide the bottom number into the top number or the denominator into the numerator. That would be 1÷4. That sounds impossible, but with decimals it isnt.
Step 1. When you divide 4 into 1, add zeros to the 1 to make it divisible. Make sure that when you put more zeros on the 1 that you put a decimal on the right side of the 1. Then you can add the zeros. When you divide, put the decimal point right above where it is right now.
Step 2. Keep on adding zeros until it comes out equal or you can stop at the hundredths. Look at below to see where the hundredths are. If the problem says to go to the thousandths then go to the thousandths. Usually they want you to round to the nearest hundredths. Which is pretty easy. If the number is .785, then you would round it to .79. Always remember the decimal point. It is very important!
.0 is Tenths .00 is Hundredths .000 is Thousandths .0000 Ten Thousands and on and on and on.........
To convert decimals into fractions you listen to the sound of the fraction. If its .506 when you say that you say 506 thousandths so you put 1000 on the bottom of .506. You need top get rid of the decimal point though. If its .2 its called 2 tenths, so you get rid of the decimal and put a ten on the bottom. I think you can see the pattern.
Multiplying, Subtracting, Dividing and Adding Decimals
To multiply decimals its almost like multiplying regular whole numbers. In fact its exactly like multiplying whole numbers except that when you get your answer, count on the problem how many places their are on the right of the decimal. Make sure that you count both of the numbers decimals places. Then you count starting from the right of your answer the number of decimal places that you had already counted, now put a decimal point there.
To add decimals is the same as adding whole numbers except keep your decimals lined up. Ill show you what I mean (Look Below)
To subtract decimals is the same as adding whole numbers except you keep the decimals point lined up in your answer and when you subtract.
You already learned how to divide decimals when you were converting fractions them into decimals. The other way is, say you have .23 and you want to divide it into .7865. You have to move the decimal on the divisor so that its a whole number. In this case you would move it so that its 23., whatever you do to the divisor you have to do to the dividend. So you would change. .7865 to 78.65. Then you would divide and make sure you line the decimal point up. If the problem is .23 into 700, you might get confused on where to move the decimal on the 700. You would change .23 to 23., and 700 to 70000. I added 2 zeros because I moved the decimal, which is like adding zeros. If you still dont understand anything that I was talking about you can contact someone to help you at the tutoring page.