how do i solve this?
3 1/3-2 2/5=
3 1/3 - 2 2/5
First thing you want to do is turn each complex fraction into improper fraction. So you get:
10/3 - 12/5
since the denominators are different, you want to find the least common denominator (LCM). In this case, it is 15. So, you need to turn the denominators into 15, by multiplying a number to the denominator and multiplying the same number to the numerator.
So, for the first fraction, you see that you can turn 3 into 15 by multiplying 5 to the denominator. That same number (5) should then be multiplied to the numerator as well. Therefore, 10/3 becomes 50/15. When you apply the same thought to the second fraction, you see that you can turn 5 into 15 by multiplying it with 3. So, the second fraction (12/5) becomes 36/15.
Now you can carry out the subtraction:
50/15 - 36/15
Subtract the numerators from one another. You get 50 - 36, which is 14.
So, the answer will be 14/15.
I hope this helps.
The key to this is taking complex fractions (whole number plus a simple fraction) and turning them into simple fractions.
Original complex fraction: 3 1/3
Add the product of the denominator and whole number to the numerator: 3x3+1=10
This becomes your new numerator: 10/3
You do the same steps for the second number.
Original complex fraction: 2 2/5
Add the product of the denominator and whole number to the numerator: 2x5+2=12
This becomes your new numerator: 12/5
Now you're have this equation: 10/3 + 12/5. You cannot add two fractions that have different denominators, so you will need to find a common multiple and use that to transform both fractions.
equation: 10/3 + 12/5 =
multiply denominators to find common multiple: 3x5=15
transform first number by multiplying numerator and denominator by 5: (10x5)/(3x5) = 50/15
transform second number by multiplying numerator and denominator by 3: (12x3)/(5x3) = 36/15
Now that we've transformed both fractions so they have the same denominator, it's pretty simple; just subtract the numerators and leave the denominator alone.
Subtract: 50/15 - 36/15 = 14/15
Change 3 1/3 to 10/3 by multiplying 3x3=9 then 9+1=10, hence 10/3.
Same for 2 2/5 to 12/5 by multiplying 2x5=10 then 10+2=12, hence 12/5
Now solve 10/3 - 12/5 like any other fraction. The least common multiple of 3 and 5 is 15.
Therefore our new fractions are 50/15 - 36/15, sice the denominator is the same we do 50 - 36= 14.
So, the answer is 14/15.