Final answer:
The part to whole simplified ratio of six pennies to the total coins in the coin holder, when including four nickels, is 3:5 after simplifying the original ratio of 6:10 by dividing both parts by 2.
Step-by-step explanation:
To find the part to whole simplified ratio of six pennies to the total number of coins in the coin holder, which includes both pennies and nickels, we first count the total number of coins.
The part-to-whole ratio can be determined by dividing the number of pennies by the total number of coins. In this case, there are six pennies and four nickels, so the part-to-whole ratio of pennies is 6 divided by 10 (6 pennies + 4 nickels) which simplifies to 3/5. Therefore, the simplified part-to-whole ratio of pennies to total coins is 3:5.
There are six pennies and four nickels, making a total of ten coins. The ratio of pennies to the total number of coins is therefore 6:10. To simplify this ratio, we divide both numbers by the greatest common divisor, which in this case is 2, giving us the simplified ratio of 3:5. This ratio means that for every three pennies, there are five coins in total (pennies and nickels) in the coin holder.