Final answer:
To determine the number of pencils in the larger part of the ratio 1:2 from 102 pencils, first find the number of pencils per part by dividing 102 by 3, which gives 34. Then multiply by 2 for the larger part of the ratio, resulting in 68 pencils.
Step-by-step explanation:
The question asks to find out how many pencils are in the larger part when a collection of 102 pencils is divided in the ratio 1:2. To do this, first add the parts of the ratio together: 1 + 2 = 3. This tells us that there are 3 equal parts in total. Now, divide the total number of pencils, which is 102, by the total number of parts, which is 3, to find out the amount per part:
102 ÷ 3 = 34
Since the larger part of the ratio is 2 parts, we multiply the amount per part by 2:
34 × 2 = 68
Therefore, there are 68 pencils in the larger part of the ratio.