This is a diagram of a vegetable garden. It shows the fraction of the garden planted with potatoes and cabbages. The remaining area is planted with carrots. What fraction of the garden is planted with carrots?
The pink rectangle represents the whole garden. If we subtract the amount of the garden where potatoes are planted or two-thirds and then subtract the amount of the garden where cabbages are planted which is one-quarter, that will tell us how much of the garden is planted with carrots.
Two-thirds and one-quarter both have different denominators. Before we can subtract, these fractions need to have the same denominator. So we need to find a number which is a multiple of three and four. 12 is a multiple of three and four. To change thirds into twelfths, we need to multiply the denominator by four. So we need to do the same to the numerator or the number on top. Two multiplied by four is eight. So two-thirds are equal to eight twelfths.
To get from four to 12, we have to multiply by three. So we need to do the same to the numerator or the number on top. One multiplied by three is three. One-quarter is the same as three twelfths. Eight twelfths and three twelfths makes eleven twelfths. So now we can subtract eleven twelfths from one whole. We can write one whole as twelve twelfths. twelve twelfths take away eleven twelfths equals one twelfth. So the fraction of the garden planted with carrots is one twelfth.
We realised that we had to calculate one whole take away two-thirds take away a quarter. But because these fractions have different denominators, we found a common denominator. We added together the amount of the garden where potatoes and cabbages are planted, eight twelfths plus three twelfths, then we took eleven twelfths away from twelve twelfths, which is the same as a whole, to give us the answer one twelfth. The fraction of the garden planted with carrots is one twelfth.