Multiplying Mixed Numbers

Multiplying Mixed Numbers

In mathematics, multiplying mixed numbers involves applying multiplication rules to both the whole number part and the fractional part of the given numbers. This process can be a bit more complex compared to multiplying integers since it involves working with fractions. Let's explore how to do this step by step.

To multiply two mixed numbers together, you need to know how to:

1. Multiply a whole number by another whole number.
2. Multiply two fractions.
3. Add or subtract any common factors between them.

Let's dive into each step further.

Step 1: Multiplying Integers

Just like we learned in arithmetic, when multiplying a whole number by another whole number, we simply multiply their digits according to the rules of multiplication. For instance, if we have (3 × 4) + (6 × 9), where 3 and 9 represent multiples of 10 and 6 represents a single digit, we would follow these steps:

  3 ✕ 4 = 12
+ 6 ✕ 9 = 54
----
   12 + 54 = 66

Step 2: Multiplying Fractions

Multiplying fractions requires some careful work. To find the product of two fractions, you need to multiple the numerators and also the denominators separately. Then, simplify the result if possible. Here's how you can do this:

2/3 × 5/8 = (2 × 5)/(3 × 8) = 10/24

This is how you handle multiple fractions and get the final answer:

2/3 × 5/8 = 10/32

Step 3: Handling Common Factors

If there are common factors between the two mixed numbers you want to multiply, such as their common denominator or numerator, you need to reduce those shared factors out before calculating the product. Let's consider the following example: (2 5/6) × (3 4/6).

Here, the common factor is 6. Since we already have two halves of 6 in our mixed numbers, we can simplify them by dividing only one of them by 6:

(2 5/6) → (2 5/6 ÷ 6) = (2 5/36)

Now, our new mixed numbers are (2 5/36) × (3 4/6). By cross-multiplying, which means changing the order of the terms being multiplied, we get:

25 \* 36 = 900
4 \* 5 = 20

Then, adding the results gives us:

900 + 20 = 920

Thus, the result of multiplying (2 5/6) and (3 4/6) is (2 5/36) × (3 4/6) = 920.