How Much Pizza is Left for Tyler and His Friends?
Imagine the scenario where Tyler shares one whole pizza with his friends. He gives one friend 1/3 of the pizza and another friend 1/6 of the pizza. How can we determine how much pizza Tyler has left for himself?
Understanding the Problem
To find out how much pizza Tyler has left for himself, we need to subtract the portions he gave to his friends from the whole pizza. Let's break down the problem step by step.
Subtracting Fractions with Different Denominators
The fractions given are 1/3 and 1/6. To add or subtract fractions, we need a common denominator. The least common multiple (LCM) of 3 and 6 is 6. converting the fractions to have the same denominator allows us to perform the subtraction.
Conversion to a Common Denominator
Convert 1/3 to sixths:1/3 2/6
Add the fractions together:2/6 1/6 3/6
Simplify the fraction:3/6 1/2
This means Tyler has given away 1/2 of the pizza to his friends.
Calculating the Remaining Pizza
To find out how much pizza Tyler has left, we subtract the given portions from the whole pizza (1).
Subtract the fractions from the whole:1 - 1/2 1/2
Therefore, Tyler has 1/2 of the pizza left for himself.
Verification and Explanation
Let's verify this calculation using the given premises and steps.
Confirming the Solution
TYler shares a whole pizza and divides it as follows:
Gives 1/3 to the first friend:1/3 2/6 of the pizza
Gives 1/6 to the second friend:1 - 2/6 - 1/6 1 - 3/6 1/2 of the pizza
Another way to express this is by converting to decimal form:
Total pizza - 1/3 - 1/6 1 - 0.333 - 0.167 0.5 or 1/2 leftover.Giving Tyler 1/3 of the pizza to the first friend and 1/6 to the second friend leaves 1/2 of the pizza for him to enjoy.
Conclusion
In conclusion, by solving the fractions step by step, we verify that Tyler has 1/2 of the pizza left for himself after sharing portions with his friends. Understanding how to subtract fractions with different denominators is a crucial skill in mathematical problem-solving.
Remember, practice and familiarity with fraction operations can make problem-solving more intuitive and efficient.