Let's add unit fractions where the numerator is 1. Let's shade 1/2 + 1/3.
1/2 of the shape is three parts.
A third of the shape is one row or two parts.
Now let's see what 1/2 and 1/3 look like in terms of sixths. 1/2 is one of the two columns. That's three of the six parts. So 1/2 equals 36. 1/3 is one of the three rows which is two of the six parts. So 1/3 equ= 2 sixths. 36 + 26ths equals 56ths.
The shape has been divided into halves and/3 which gives us six equal parts.
Our sum 56s was in terms of sixths.
Let's try a different problem. Here we're adding 1/5 + 1/2. 1/5if of the shape is one of the five columns, which is two of the 10 parts. 1/2 of the shape is one of the two rows, which covers five of the 10 parts.
When we add 1/5 and 1/2, we're actually adding tenths. 1/5 covers two of the 10 parts. So 1/5 equals 2/10.
1/2 covers five of 10 parts, so it equals 510.
The grid is helpful for understanding, but we don't always need to draw it. We can find a common denominator by multiplying the two original denominators. Let's look at 1/3 + 1/4.
The denominators are 3 and 4.
Multiplying them gives us 12. So, our common denominator is 12. To change 1/3 into 12ths, we ask 3 * what = 12? The answer is 4. So, we multiply the numerator and denominator by 4. 1/3 becomes 4 12ths. For 1/4, we ask 4 * what equals 12? That's three. We multiply the numerator and denominator by 3. So 1/4 becomes 3 12ths. Now we can add 4 12ths and 3 12ths.
Let's do one more. What is 1/10th + 1/3? The common denominator is 10 * 3, which is 30. To convert 1/10th to 30ths, we multiply the numerator and denominator by 3, which gives us 330ths. To convert 1/3 to 30ths, we multiply the numerator and denominator by 10, giving us 10 30ths. The sum is 3/30ths + 10 30ths.
Multiplying the denominators is a reliable way to find a common denominator. This allows us to express both fractions in the same terms so we can add them together.
