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Answer :
- Convert the mixed number to an improper fraction: $2 \frac{14}{15} = \frac{44}{15}$.
- Multiply 30 by the improper fraction: $30 \times \frac{44}{15}$.
- Simplify the expression: $\frac{30 \times 44}{15} = 2 \times 44$.
- Calculate the final result: $2 \times 44 = 88$. The answer is $\boxed{88}$.
### Explanation
1. Problem Analysis
We are asked to multiply a whole number, 30, by a mixed number, $2 \frac{14}{15}$. To do this, we first convert the mixed number to an improper fraction.
2. Converting to Improper Fraction
To convert the mixed number $2 \frac{14}{15}$ to an improper fraction, we multiply the whole number part (2) by the denominator (15) and add the numerator (14). This gives us $2 \times 15 + 14 = 30 + 14 = 44$. So, the improper fraction is $\frac{44}{15}$.
3. Multiplying
Now, we multiply 30 by the improper fraction $\frac{44}{15}$: $$30 \times \frac{44}{15} = \frac{30 \times 44}{15}$$
4. Simplifying
We can simplify this by dividing 30 by 15, which gives us 2. So, we have: $$\frac{30 \times 44}{15} = 2 \times 44 = 88$$
5. Final Answer
Therefore, $30 \times 2 \frac{14}{15} = 88$.
### Examples
Understanding multiplication of mixed numbers is crucial in everyday situations, such as calculating the total cost of buying multiple items at a store. For instance, if you want to buy 30 items that cost $2 \frac{14}{15}$ each, you would need to perform this calculation to determine the total amount you need to pay. This skill is also useful in cooking, where you might need to scale up a recipe by multiplying the ingredients by a certain factor.
- Multiply 30 by the improper fraction: $30 \times \frac{44}{15}$.
- Simplify the expression: $\frac{30 \times 44}{15} = 2 \times 44$.
- Calculate the final result: $2 \times 44 = 88$. The answer is $\boxed{88}$.
### Explanation
1. Problem Analysis
We are asked to multiply a whole number, 30, by a mixed number, $2 \frac{14}{15}$. To do this, we first convert the mixed number to an improper fraction.
2. Converting to Improper Fraction
To convert the mixed number $2 \frac{14}{15}$ to an improper fraction, we multiply the whole number part (2) by the denominator (15) and add the numerator (14). This gives us $2 \times 15 + 14 = 30 + 14 = 44$. So, the improper fraction is $\frac{44}{15}$.
3. Multiplying
Now, we multiply 30 by the improper fraction $\frac{44}{15}$: $$30 \times \frac{44}{15} = \frac{30 \times 44}{15}$$
4. Simplifying
We can simplify this by dividing 30 by 15, which gives us 2. So, we have: $$\frac{30 \times 44}{15} = 2 \times 44 = 88$$
5. Final Answer
Therefore, $30 \times 2 \frac{14}{15} = 88$.
### Examples
Understanding multiplication of mixed numbers is crucial in everyday situations, such as calculating the total cost of buying multiple items at a store. For instance, if you want to buy 30 items that cost $2 \frac{14}{15}$ each, you would need to perform this calculation to determine the total amount you need to pay. This skill is also useful in cooking, where you might need to scale up a recipe by multiplying the ingredients by a certain factor.
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