Multiplying a Fraction and a Decimal

Oct 13, 2025 by magicalceylontours.com 57 views

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

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

Answer Key

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