Decimal and Fraction Calculations: Order of Operations

This page introduces the fundamental concepts of adding and subtracting decimals worksheets PDF. It explains the proper techniques for aligning decimal points and digits when performing these operations.

For addition of decimals, the guide emphasizes the importance of lining up decimal points and digits correctly. This ensures accurate calculation, especially when dealing with numbers that have different numbers of decimal places.

Example: When adding 48.26 and 3.2, the correct alignment would be: 48.26

• 03.20 51.46

The same principle applies to subtraction of decimals. The document stresses the need for proper alignment to avoid errors in calculation.

Example: For subtracting 12.7 from 56.91: 56.91

• 12.70 44.21

The page also covers multiplication of decimals, introducing a method where you multiply the numbers as if they were whole numbers and then place the decimal point in the final answer based on the total number of decimal places in the original factors.

Highlight: When multiplying decimals, count the total number of decimal places in the factors and ensure the answer has the same number of decimal places.

For division of decimals, the guide presents a technique of multiplying both the dividend and divisor by powers of 10 until the divisor becomes a whole number. This transforms the problem into a simpler integer division.

Example: To divide 12.4 by 0.8, multiply both by 10: (12.4 × 10) ÷ (0.8 × 10) = 124 ÷ 8

This approach simplifies decimal division by converting it to whole number division, making the calculation more straightforward for students.

Order of Operations with Fractions

This page delves into the intricacies of multiplying and dividing fractions worksheets, focusing on the order of operations when working with fractions. It provides a step-by-step guide for addition, subtraction, multiplication, and division of fractions.

For addition and subtraction of fractions, the document emphasizes the importance of finding a common denominator. It explains that before performing these operations, any mixed numbers should be converted to improper fractions.

Definition: An improper fraction, also known as a top-heavy fraction, is a fraction where the numerator is greater than or equal to the denominator.

The guide then walks through the process of finding the least common multiple (LCM) of the denominators to create equivalent fractions with the same denominator. This step is crucial for accurately adding or subtracting fractions.

Example: To add 2/3 and 1/4, first find the LCM of 3 and 4, which is 12. Then convert each fraction: (2/3 × 4/4) + (1/4 × 3/3) = 8/12 + 3/12 = 11/12

For multiplication of fractions, the document explains that you simply multiply the numerators together and the denominators together, then simplify the result if possible.

Highlight: When multiplying fractions, there's no need to find a common denominator. Simply multiply numerators and denominators separately.

The page also touches on the concept of simplifying fractions after multiplication, which is an important skill for students to master in fraction calculations.