Problem Analysis:
The image shows two cakes, each divided into fractions. The task is to determine:
1.
How much of the cake has been eaten?
2.
How much of the cake is left?
Let's analyze each cake separately.
---
Cake 1:
- The cake is divided into
quarters (4 equal parts).
- Two quarters of the cake have been eaten.
- Each quarter represents \( \frac{1}{4} \) of the whole cake.
#### Step 1: Calculate the fraction of the cake that has been eaten.
The cake has two quarters eaten:
\[
\text{Fraction eaten} = \frac{1}{4} + \frac{1}{4} = \frac{2}{4} = \frac{1}{2}
\]
#### Step 2: Calculate the fraction of the cake that is left.
Since the whole cake is \( 1 \) (or \( \frac{4}{4} \)), and \( \frac{2}{4} \) has been eaten:
\[
\text{Fraction left} = 1 - \frac{2}{4} = \frac{4}{4} - \frac{2}{4} = \frac{2}{4} = \frac{1}{2}
\]
---
Cake 2:
- The cake is divided into
halves (2 equal parts).
- One half of the cake has been eaten.
- Each half represents \( \frac{1}{2} \) of the whole cake.
#### Step 1: Calculate the fraction of the cake that has been eaten.
The cake has one half eaten:
\[
\text{Fraction eaten} = \frac{1}{2}
\]
#### Step 2: Calculate the fraction of the cake that is left.
Since the whole cake is \( 1 \) (or \( \frac{2}{2} \)), and \( \frac{1}{2} \) has been eaten:
\[
\text{Fraction left} = 1 - \frac{1}{2} = \frac{2}{2} - \frac{1}{2} = \frac{1}{2}
\]
---
Final Answers:
For both cakes:
1.
How much of the cake has been eaten?
\[
\boxed{\frac{1}{2}}
\]
2.
How much of the cake is left?
\[
\boxed{\frac{1}{2}}
\]
---
Explanation:
- In both cases, the cakes are divided into equal parts, and the portions eaten are clearly marked.
- By adding the fractions of the eaten parts, we determine how much has been consumed.
- Subtracting the eaten portion from the whole cake gives the remaining portion.
- Both cakes result in the same fractions because the eaten portions are equivalent to \( \frac{1}{2} \) in both scenarios.
Parent Tip: Review the logic above to help your child master the concept of fraction vocabulary worksheet.
