Is it always necessary to have a common denominator to add and subtract fractions? Why? What about multiplication and division with fractions?
yes it is...can't explain it but that's how it's always been. It's a rule.
For the multiplication and division of fractions it is not necessary.
Just cross multiply.
I'm not good at explaining but here goes.
Yes, because you need to have the right proportion. Lets say you have 1/2 + 1/3. You have half a cake plus a third of a cake. If you added them togther, you will not know how much you have left over or if you have too much (in numbers that is)
But if you added them to a common demominator, you will get 3/6 + 2/6, so you know you will have 1/6 of the cake left.
Muliplication you dont
1/2 x 1/3 = 1/6
It all works out. One third of one half is one sixth. Try it out.
Dividing fractions, all you do is flip the fraction around.
1/2 (divide) 1/3 is 1/2 x 3
This is the reason, using 1/2 + 1/3 as example:
the denominator means the number of equal parts you divide the whole thing into.
1/2 means you divide the whole thing into 2 equal parts and you take one part.
1/3 means you divide the same whole thing into 3 equal parts and you take one part.
in both cases, you take one part, but the size of each part is different, that's the reason you can add or subtract, they are not of the same size.
we can add 1/4 to 2/4 because each part is of the same size.
Wow Qun is good, I sooooo got that explanation!
hi
When adding or subtracting fractions, it is necessary to have a common denominator. This is because the fractions must have the same denominator in order to be combined.
To find the common denominator, you need to identify the least common multiple (LCM) of the denominators. The LCM is the smallest number that both denominators can divide evenly into. Once you have the common denominator, you can then add or subtract the fractions by adding or subtracting the numerators while keeping the common denominator.
For example, let's say we have the fractions 1/4 and 1/3. The denominators are 4 and 3 respectively, and the LCM of 4 and 3 is 12. To find the equivalent fractions with the common denominator of 12, we need to multiply the numerator and denominator of each fraction by the appropriate multiplier. In this case, we need to multiply 1/4 by 3/3 (which is equivalent to 1) and 1/3 by 4/4 (which is also equivalent to 1). This gives us the fractions 3/12 and 4/12, which can now be added or subtracted.
On the other hand, when multiplying fractions, you do not necessarily need a common denominator. To multiply fractions, you simply multiply the numerators together and the denominators together. The resulting fraction may or may not be in simplest form, so it is often necessary to simplify.
For example, if we have the fractions 2/3 and 4/5, we can multiply them by multiplying the numerators (2 * 4 = 8) and multiplying the denominators (3 * 5 = 15). So the product is 8/15.
Division with fractions is similar to multiplication. To divide fractions, you can multiply the first fraction by the reciprocal (or multiplicative inverse) of the second fraction. The reciprocal of a fraction is obtained by swapping the numerator and denominator.
For example, if we have the fractions 2/3 and 3/4, we can divide them by multiplying the first fraction by the reciprocal of the second fraction: (2/3) * (4/3). This gives us (2 * 4) / (3 * 3) = 8/9.
In summary, a common denominator is necessary when adding or subtracting fractions, but not when multiplying or dividing.