Determine The Product Of 14 4 \frac{14}{4} 4 14 ​ And -1.6.Enter The Exact Value Of The Product In The Box. You May Enter Your Answer As A Simplified Fraction, A Mixed Number, Or As A Decimal.

Understanding the Problem

In this problem, we are tasked with finding the product of two numbers: $\frac{14}{4}$ and -1.6. To solve this problem, we need to understand how to multiply fractions and decimals.

Multiplying Fractions

Fractions are numbers that represent a part of a whole. They are written in the form $\frac{a}{b}$, where $a$ is the numerator and $b$ is the denominator. To multiply fractions, we simply multiply the numerators together and the denominators together.

Example: Multiplying Two Fractions

Let's consider the example of multiplying two fractions: $\frac{2}{3}$ and $\frac{3}{4}$. To find the product, we multiply the numerators together and the denominators together:

$$\frac{2}{3} \times \frac{3}{4} = \frac{2 \times 3}{3 \times 4} = \frac{6}{12}$$

Simplifying the Fraction

We can simplify the fraction $\frac{6}{12}$ by dividing both the numerator and the denominator by their greatest common divisor, which is 6. This gives us:

$$\frac{6}{12} = \frac{1}{2}$$

Multiplying Decimals

Decimals are numbers that have a decimal point. They can be written in the form $a.b$, where $a$ is the whole number part and $b$ is the decimal part. To multiply decimals, we can multiply them as if they were whole numbers and then round the result to the correct number of decimal places.

Example: Multiplying Two Decimals

Let's consider the example of multiplying two decimals: 2.5 and 3.2. To find the product, we multiply the numbers together:

$$2.5 \times 3.2 = 8.0$$

Multiplying a Fraction and a Decimal

Now that we have understood how to multiply fractions and decimals, let's consider the problem at hand: finding the product of $\frac{14}{4}$ and -1.6.

Step 1: Convert the Fraction to a Decimal

To multiply a fraction and a decimal, we need to convert the fraction to a decimal. We can do this by dividing the numerator by the denominator:

$$\frac{14}{4} = 3.5$$

Step 2: Multiply the Decimal by the Fraction

Now that we have converted the fraction to a decimal, we can multiply it by the decimal -1.6:

$$3.5 \times -1.6 = -5.6$$

Conclusion

In this problem, we were tasked with finding the product of $\frac{14}{4}$ and -1.6. To solve this problem, we first converted the fraction to a decimal and then multiplied the decimal by the fraction. The result is -5.6.

Key Takeaways

• To multiply fractions, we multiply the numerators together and the denominators together.
• To multiply decimals, we can multiply them as if they were whole numbers and then round the result to the correct number of decimal places.
• To multiply a fraction and a decimal, we need to convert the fraction to a decimal and then multiply the decimal by the fraction.

Practice Problems

1. Multiply the fractions $\frac{2}{3}$ and $\frac{3}{4}$.
2. Multiply the decimals 2.5 and 3.2.
3. Multiply the fraction $\frac{14}{4}$ and the decimal 2.5.

Answer Key

1. $\frac{6}{12} = \frac{1}{2}$
2. 8.0
3. 8.75