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Answer :
- Calculate the total weight gained: $4
\times \frac{2}{10} = \frac{8}{10}$.
- Convert the initial weight to an improper fraction: $5 \frac{3}{5} = \frac{28}{5}$.
- Find a common denominator and add the fractions: $\frac{28}{5} + \frac{8}{10} = \frac{56}{10} + \frac{8}{10} = \frac{64}{10}$.
- Simplify and convert to a mixed number: $\frac{64}{10} = 6 \frac{2}{5}$. The puppy's final weight is $\boxed{6 \frac{2}{5}}$.
### Explanation
1. Understanding the Problem
We want to find the puppy's weight after 4 weeks, given its initial weight and weekly weight gain.
2. Calculating Total Weight Gain
First, we need to find the total weight gained over the 4 weeks. The puppy gains $\frac{2}{10}$ pounds each week, so over 4 weeks, it gains $4 \times \frac{2}{10}$ pounds.
3. Multiplying to Find Total Gain
$4 \times \frac{2}{10} = \frac{4 \times 2}{10} = \frac{8}{10}$ pounds.
4. Converting Initial Weight to Improper Fraction
Next, we need to add the total weight gain to the puppy's initial weight. The initial weight is $5 \frac{3}{5}$ pounds, which can be written as an improper fraction: $5 \frac{3}{5} = \frac{5 \times 5 + 3}{5} = \frac{28}{5}$ pounds.
5. Finding a Common Denominator
Now we add the initial weight and the total weight gain: $\frac{28}{5} + \frac{8}{10}$. To add these fractions, we need a common denominator. The least common multiple of 5 and 10 is 10, so we convert $\frac{28}{5}$ to a fraction with a denominator of 10: $\frac{28}{5} = \frac{28 \times 2}{5 \times 2} = \frac{56}{10}$.
6. Adding the Fractions
Now we can add the fractions: $\frac{56}{10} + \frac{8}{10} = \frac{56 + 8}{10} = \frac{64}{10}$ pounds.
7. Simplifying and Converting to Mixed Number
Finally, we simplify the fraction and convert it to a mixed number: $\frac{64}{10} = \frac{32}{5} = 6 \frac{2}{5}$ pounds.
8. Final Answer
The puppy weighed $6 \frac{2}{5}$ pounds at the end of the fourth week.
### Examples
Understanding how a puppy's weight changes over time helps pet owners adjust their feeding schedule and ensure their pet is growing at a healthy rate. This is similar to tracking a child's growth or monitoring the progress of a plant as it grows. By using fractions and mixed numbers, we can accurately calculate changes and make informed decisions about care and nutrition.
\times \frac{2}{10} = \frac{8}{10}$.
- Convert the initial weight to an improper fraction: $5 \frac{3}{5} = \frac{28}{5}$.
- Find a common denominator and add the fractions: $\frac{28}{5} + \frac{8}{10} = \frac{56}{10} + \frac{8}{10} = \frac{64}{10}$.
- Simplify and convert to a mixed number: $\frac{64}{10} = 6 \frac{2}{5}$. The puppy's final weight is $\boxed{6 \frac{2}{5}}$.
### Explanation
1. Understanding the Problem
We want to find the puppy's weight after 4 weeks, given its initial weight and weekly weight gain.
2. Calculating Total Weight Gain
First, we need to find the total weight gained over the 4 weeks. The puppy gains $\frac{2}{10}$ pounds each week, so over 4 weeks, it gains $4 \times \frac{2}{10}$ pounds.
3. Multiplying to Find Total Gain
$4 \times \frac{2}{10} = \frac{4 \times 2}{10} = \frac{8}{10}$ pounds.
4. Converting Initial Weight to Improper Fraction
Next, we need to add the total weight gain to the puppy's initial weight. The initial weight is $5 \frac{3}{5}$ pounds, which can be written as an improper fraction: $5 \frac{3}{5} = \frac{5 \times 5 + 3}{5} = \frac{28}{5}$ pounds.
5. Finding a Common Denominator
Now we add the initial weight and the total weight gain: $\frac{28}{5} + \frac{8}{10}$. To add these fractions, we need a common denominator. The least common multiple of 5 and 10 is 10, so we convert $\frac{28}{5}$ to a fraction with a denominator of 10: $\frac{28}{5} = \frac{28 \times 2}{5 \times 2} = \frac{56}{10}$.
6. Adding the Fractions
Now we can add the fractions: $\frac{56}{10} + \frac{8}{10} = \frac{56 + 8}{10} = \frac{64}{10}$ pounds.
7. Simplifying and Converting to Mixed Number
Finally, we simplify the fraction and convert it to a mixed number: $\frac{64}{10} = \frac{32}{5} = 6 \frac{2}{5}$ pounds.
8. Final Answer
The puppy weighed $6 \frac{2}{5}$ pounds at the end of the fourth week.
### Examples
Understanding how a puppy's weight changes over time helps pet owners adjust their feeding schedule and ensure their pet is growing at a healthy rate. This is similar to tracking a child's growth or monitoring the progress of a plant as it grows. By using fractions and mixed numbers, we can accurately calculate changes and make informed decisions about care and nutrition.
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