Gil's Aunt Cut His Birthday Cake Into 32 Equal Pieces. Eighteen Pieces Were Eaten At His Birthday Party. What Fraction Of The Cake Was Left?A. 7 16 \frac{7}{16} 16 7 ​ B. 9 16 \frac{9}{16} 16 9 ​ C. 7 12 \frac{7}{12} 12 7 ​ D. 9 14 \frac{9}{14} 14 9 ​

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Gil's Birthday Cake: A Math Problem

Gil's birthday cake was cut into 32 equal pieces, and 18 of them were eaten at the party. The remaining pieces of cake are a fraction of the total cake. In this article, we will calculate the fraction of the cake that was left.

To solve this problem, we need to understand the concept of fractions and how to calculate them. A fraction is a way to represent a part of a whole. It consists of a numerator (the number on top) and a denominator (the number on the bottom). The numerator tells us how many equal parts we have, and the denominator tells us how many equal parts the whole is divided into.

Let's start by identifying the information given in the problem:

  • The cake was cut into 32 equal pieces.
  • 18 pieces were eaten at the party.

To find the fraction of the cake that was left, we need to subtract the number of pieces eaten from the total number of pieces.

Step 1: Subtract the Number of Pieces Eaten from the Total Number of Pieces

total_pieces = 32
pieces_eaten = 18
pieces_left = total_pieces - pieces_eaten

Step 2: Calculate the Fraction of Cake Left

Now that we know the number of pieces left, we can calculate the fraction of the cake that was left. To do this, we need to divide the number of pieces left by the total number of pieces.

fraction_left = pieces_left / total_pieces

The fraction we calculated may not be in its simplest form. To simplify the fraction, we need to find the greatest common divisor (GCD) of the numerator and the denominator and divide both numbers by the GCD.

Step 1: Find the GCD of the Numerator and the Denominator

import math
gcd = math.gcd(pieces_left, total_pieces)

Step 2: Simplify the Fraction

Now that we know the GCD, we can simplify the fraction by dividing both the numerator and the denominator by the GCD.

simplified_fraction = (pieces_left // gcd) / (total_pieces // gcd)

In conclusion, we calculated the fraction of the cake that was left by subtracting the number of pieces eaten from the total number of pieces and then simplifying the resulting fraction. The fraction of the cake that was left is 716\boxed{\frac{7}{16}}.

The correct answer is A. 716\frac{7}{16}.

This problem is a great example of how math can be applied to real-life situations. It requires the student to understand the concept of fractions and how to calculate them. The student must also be able to simplify the fraction to its simplest form.

  • Make sure to read the problem carefully and understand what is being asked.
  • Use a calculator or a computer program to help with the calculations.
  • Simplify the fraction to its simplest form to make it easier to understand.
  • If 24 pieces of cake were eaten at the party, what fraction of the cake was left?
  • If the cake was cut into 40 equal pieces, and 20 pieces were eaten at the party, what fraction of the cake was left?

In our previous article, we solved the problem of Gil's birthday cake, which was cut into 32 equal pieces, and 18 of them were eaten at the party. We calculated the fraction of the cake that was left and found that it was 716\frac{7}{16}. In this article, we will answer some frequently asked questions related to this problem.

Q: What is the total number of pieces of cake that were cut? A: The total number of pieces of cake that were cut is 32.

Q: How many pieces of cake were eaten at the party? A: 18 pieces of cake were eaten at the party.

Q: What is the fraction of the cake that was left? A: The fraction of the cake that was left is 716\frac{7}{16}.

Q: How do I calculate the fraction of the cake that was left? A: To calculate the fraction of the cake that was left, you need to subtract the number of pieces eaten from the total number of pieces and then simplify the resulting fraction.

Q: What is the greatest common divisor (GCD) of two numbers? A: The greatest common divisor (GCD) of two numbers is the largest number that divides both numbers without leaving a remainder.

Q: How do I simplify a fraction? A: To simplify a fraction, you need to find the GCD of the numerator and the denominator and divide both numbers by the GCD.

Q: What is the difference between a numerator and a denominator? A: The numerator is the number on top of a fraction, and the denominator is the number on the bottom.

Q: Can I use a calculator to help with the calculations? A: Yes, you can use a calculator to help with the calculations.

Q: What if the cake was cut into a different number of pieces? A: If the cake was cut into a different number of pieces, you would need to adjust the calculations accordingly.

Q: Can I use this problem to practice my math skills? A: Yes, you can use this problem to practice your math skills, such as calculating fractions and simplifying them.

In conclusion, we answered some frequently asked questions related to Gil's birthday cake problem. We hope that this article has been helpful in understanding the concept of fractions and how to calculate them.

  • Make sure to read the problem carefully and understand what is being asked.
  • Use a calculator or a computer program to help with the calculations.
  • Simplify the fraction to its simplest form to make it easier to understand.
  • If 24 pieces of cake were eaten at the party, what fraction of the cake was left?
  • If the cake was cut into 40 equal pieces, and 20 pieces were eaten at the party, what fraction of the cake was left?
  • Numerator: The number on top of a fraction.
  • Denominator: The number on the bottom of a fraction.
  • Greatest Common Divisor (GCD): The largest number that divides both numbers without leaving a remainder.
  • Fraction: A way to represent a part of a whole.
  • Simplifying a fraction: Finding the GCD of the numerator and the denominator and dividing both numbers by the GCD.