Hey guys! Are you struggling with DAV Class 7 Maths Chapter 2 Worksheet 1? Don't worry, you're not alone! This worksheet can be tricky, but with the right guidance, you can ace it. This guide will walk you through each question, providing detailed explanations and solutions. Let's dive in!

Question 1: Understanding the Basics

The first question usually covers the fundamental concepts of the chapter. This includes understanding different types of numbers, such as integers, fractions, and decimals. It also tests your knowledge of basic operations like addition, subtraction, multiplication, and division involving these numbers. Make sure you have a solid grasp of these concepts before moving on.

Detailed Explanation

To tackle this question effectively, start by reviewing the definitions and properties of different number types. For instance, integers include all positive and negative whole numbers and zero, while fractions represent parts of a whole. Decimals, on the other hand, are numbers expressed in base 10, often used to represent non-integer values.

When dealing with operations, remember the order of operations (PEMDAS/BODMAS): Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). Applying this order consistently will help you avoid common mistakes. Also, pay close attention to the signs of the numbers involved. Adding a negative number is the same as subtracting a positive number, and vice versa. Similarly, multiplying or dividing two numbers with the same sign results in a positive number, while different signs yield a negative number.

For example, if the question involves adding fractions, ensure they have a common denominator before adding the numerators. If it involves multiplying decimals, multiply as you would with whole numbers and then place the decimal point in the correct position based on the total number of decimal places in the original numbers. Practicing these basics will not only help you solve Question 1 but also build a strong foundation for more complex problems later on.

Tips and Tricks

• Review Definitions: Ensure you know the definitions of integers, fractions, and decimals.
• PEMDAS/BODMAS: Always follow the order of operations.
• Sign Conventions: Pay attention to the signs of numbers.
• Practice: Solve similar problems to reinforce your understanding.

Question 2: Addition and Subtraction of Integers

This question typically involves adding and subtracting integers, including positive and negative numbers. Understanding the rules for these operations is crucial. A common mistake is not handling negative signs correctly, so pay close attention!

Detailed Explanation

When adding integers, remember that adding two positive integers results in a positive integer, and adding two negative integers results in a negative integer. The tricky part comes when you add a positive and a negative integer. In this case, you subtract the smaller absolute value from the larger absolute value and use the sign of the number with the larger absolute value.

For example, if you're adding -7 and +4, you subtract 4 from 7 to get 3, and since -7 has a larger absolute value, the result is -3. Similarly, when subtracting integers, you can think of it as adding the opposite. For example, 5 - (-3) is the same as 5 + 3, which equals 8. This approach helps simplify the process and reduces the chance of making errors.

Also, be mindful of the properties of addition and subtraction, such as the commutative property (a + b = b + a) and the associative property (a + (b + c) = (a + b) + c). These properties can be useful in simplifying expressions and making calculations easier. Practicing a variety of problems with different combinations of positive and negative integers will help you master this skill and confidently tackle Question 2.

For instance, consider the problem -12 + 5 - (-3). First, rewrite the subtraction as addition: -12 + 5 + 3. Then, add the numbers from left to right: -12 + 5 = -7, and -7 + 3 = -4. Thus, the final answer is -4. Consistent practice and attention to detail are key to success.

Tips and Tricks

• Adding Same Signs: Add the numbers and keep the sign.
• Adding Different Signs: Subtract the smaller absolute value from the larger and use the sign of the larger.
• Subtraction as Addition: Rewrite subtraction as adding the opposite.
• Practice: Solve a variety of problems to build confidence.

Question 3: Multiplication and Division of Fractions

Fractions can be intimidating, but multiplying and dividing them is actually quite straightforward. This question tests your ability to perform these operations accurately. Remember to simplify fractions whenever possible!

Detailed Explanation

To multiply fractions, you simply multiply the numerators together and the denominators together. For example, if you want to multiply 2/3 by 3/4, you multiply 2 * 3 to get 6, and 3 * 4 to get 12. So, the result is 6/12, which can be simplified to 1/2. Always remember to simplify the resulting fraction to its lowest terms by dividing both the numerator and denominator by their greatest common divisor (GCD).

Dividing fractions involves a little trick: you flip the second fraction (the divisor) and then multiply. This is often referred to as