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Decimal multiplication involves multiplying numbers with decimal points. To multiply decimals, you can ignore the decimals initially and multiply them as whole numbers. Once you have your product, count the total number of decimal places from the numbers you are multiplying. Place the same number of decimal places in the product. For example, in Step 2, we multiplied \(\frac{5}{6}\) by 0.0765. First, we calculate \[ \frac{5}{6} \times 765 \] as if there's no decimal. After getting the product, reintroduce the decimal point to get 0.06375 (since 0.0765 has four decimal places). Similarly, multiplying \(\frac{5}{4}\) by 0.1124 has a similar approach, resulting in 0.1405. Understanding these principles ensures accuracy when multiplying decimals.

Adding fractions involves combining fractions with a common denominator. If the denominators differ, first find a common denominator by identifying their least common multiple (LCM). In our exercise, we added the final decimal results directly. However, if we had fractions, like \[ \frac{1}{2} + \frac{1}{3} \], we would convert them to \[ \frac{3}{6} + \frac{2}{6} = \frac{5}{6} \]. After converting, sum the numerators while keeping the denominator the same. This method of finding a common denominator and then adding the fractions helps in achieving accurate results when dealing with multiple fractions.

Basic arithmetic operations include addition, subtraction, multiplication, and division. For our exercise, we focused on multiplication and addition. Multiplication combines numbers to get a product. After multiplication, perform addition to combine our results from Step 2 and Step 3. Arithmetic operations are foundational skills in math and are essential for solving more complex problems. Understanding how to correctly perform these operations ensures your calculations are precise and efficient.