Understanding the Basics of Fractions and Mixed Numbers

Oct 13, 2025 by miodeya.com 67 views

In mathematics, the product of two or more numbers is the result obtained by multiplying them together. In this article, we will explore the product of each of the given expressions, which involve fractions and mixed numbers.

Understanding the Basics of Fractions and Mixed Numbers

Before we dive into the product of each expression, let's quickly review the basics of fractions and mixed numbers.

A fraction is a way of expressing a part of a whole. It consists of a numerator (the top number) and a denominator (the bottom number). For example, 1/2 is a fraction where 1 is the numerator and 2 is the denominator.
A mixed number is a combination of a whole number and a fraction. For example, 2 1/2 is a mixed number where 2 is the whole number and 1/2 is the fraction.

Expression 1: Product of a Mixed Number

The first expression is 1 1/4. To find the product of this expression, we need to multiply the whole number part (1) by the fraction part (1/4).

1 1/4 = 1 × 1/4 = 1/4

So, the product of the expression 1 1/4 is 1/4.

Expression 2: Product of a Negative Fraction

The second expression is -2/3. To find the product of this expression, we simply need to multiply the fraction by 1, which is the multiplicative identity.

-2/3 × 1 = -2/3

So, the product of the expression -2/3 is -2/3.

Expression 3: Product of Two Negative Fractions

The third expression is -5/6 × (-3/2). To find the product of this expression, we need to multiply the numerators together and the denominators together.

-5/6 × (-3/2) = (-5 × -3) / (6 × 2) = 15/12

We can simplify the fraction 15/12 by dividing both the numerator and the denominator by their greatest common divisor, which is 3.

15/12 = 5/4

So, the product of the expression -5/6 × (-3/2) is 5/4.

Expression 4: Product of Two Fractions with Opposite Signs

The fourth expression is -2/5 × 5/3. To find the product of this expression, we need to multiply the numerators together and the denominators together.

-2/5 × 5/3 = (-2 × 5) / (5 × 3) = -10/15

We can simplify the fraction -10/15 by dividing both the numerator and the denominator by their greatest common divisor, which is 5.

-10/15 = -2/3

So, the product of the expression -2/5 × 5/3 is -2/3.

Conclusion

$In this article, we have explored the product of each of the given expressions, which involve fractions and mixed numbers. We have seen that the product of a mixed number is obtained by multiplying the whole number part by the fraction part, the product of a negative fraction is the same as the fraction itself, the product of two negative fractions is a positive fraction, and the product of two fractions with opposite signs is a negative fraction.<br/> **Frequently Asked Questions (FAQs) About the Product of Expressions**$

In this article, we will address some of the most frequently asked questions about the product of expressions, which involve fractions and mixed numbers.

Q: What is the product of two fractions with the same sign?

A: The product of two fractions with the same sign is a positive fraction. For example, 1/2 × 1/3 = 1/6.

Q: What is the product of two fractions with opposite signs?

A: The product of two fractions with opposite signs is a negative fraction. For example, 1/2 × -1/3 = -1/6.

Q: How do I multiply a fraction by a whole number?

A: To multiply a fraction by a whole number, you simply multiply the numerator by the whole number and keep the denominator the same. For example, 1/2 × 3 = 3/2.

Q: How do I multiply a fraction by a mixed number?

A: To multiply a fraction by a mixed number, you first convert the mixed number to an improper fraction, then multiply the numerators together and the denominators together. For example, 1/2 × 2 1/2 = 1/2 × 5/2 = 5/4.

Q: Can I multiply a fraction by a decimal?

A: Yes, you can multiply a fraction by a decimal. To do this, you first convert the decimal to a fraction, then multiply the numerators together and the denominators together. For example, 1/2 × 0.5 = 1/2 × 1/2 = 1/4.

Q: What is the product of a fraction and a negative number?

A: The product of a fraction and a negative number is a negative fraction. For example, 1/2 × -1 = -1/2.

Q: Can I multiply a fraction by a variable?

A: Yes, you can multiply a fraction by a variable. To do this, you simply multiply the numerator by the variable and keep the denominator the same. For example, 1/2 × x = x/2.

Q: How do I simplify a product of fractions?

A: To simplify a product of fractions, you can cancel out any common factors between the numerators and denominators. For example, 2/4 × 3/6 = 1/2 × 1/2 = 1/4.

Q: Can I multiply a fraction by a fraction with a different denominator?

A: Yes, you can multiply a fraction by a fraction with a different denominator. To do this, you multiply the numerators together and the denominators together, then simplify the resulting fraction. For example, 1/2 × 3/4 = (1 × 3) / (2 × 4) = 3/8.

Conclusion

In this article, we have addressed some of the most frequently asked questions about the product of expressions, which involve fractions and mixed numbers. We hope that this article has provided you with a better understanding of how to multiply fractions and mixed numbers, and how to simplify the resulting products.