Calculate The Following Expressions:1. $ \frac{1}{2} \cdot \frac{1}{2} = $2. $ 0.4 \times 6 = $3. $ 24 \div 672 = $4. $ \frac{1}{9} + \frac{1}{3} = $

Introduction

Mathematics is a fundamental subject that plays a crucial role in our daily lives. It is used in various fields such as science, technology, engineering, and mathematics (STEM), finance, economics, and many more. Mathematical expressions are a way of representing mathematical operations in a concise and precise manner. In this article, we will focus on calculating four different mathematical expressions, covering various operations such as multiplication, division, and addition.

Expression 1: Multiplication of Fractions

The first expression we will calculate is the multiplication of two fractions: $\frac{1}{2} \cdot \frac{1}{2}$. To solve this expression, we need to follow the rules of fraction multiplication.

Step 1: Multiply the Numerators

The numerator of the first fraction is 1, and the numerator of the second fraction is also 1. When we multiply these two numerators, we get:

1 × 1 = 1

Step 2: Multiply the Denominators

The denominator of the first fraction is 2, and the denominator of the second fraction is also 2. When we multiply these two denominators, we get:

2 × 2 = 4

Step 3: Write the Result as a Fraction

Now that we have multiplied the numerators and denominators, we can write the result as a fraction:

$\frac{1}{4}$

Therefore, the value of the expression $\frac{1}{2} \cdot \frac{1}{2}$ is $\frac{1}{4}$.

Expression 2: Multiplication of Decimal Numbers

The second expression we will calculate is the multiplication of two decimal numbers: $0.4 \times 6$. To solve this expression, we need to follow the rules of decimal multiplication.

Step 1: Multiply the Decimal Numbers

When we multiply 0.4 and 6, we get:

0.4 × 6 = 2.4

Therefore, the value of the expression $0.4 \times 6$ is 2.4.

Expression 3: Division of Whole Numbers

The third expression we will calculate is the division of two whole numbers: $24 \div 672$. To solve this expression, we need to follow the rules of division.

Step 1: Divide the Dividend by the Divisor

When we divide 24 by 672, we get:

24 ÷ 672 = 0.0357 (rounded to four decimal places)

Therefore, the value of the expression $24 \div 672$ is approximately 0.0357.

Expression 4: Addition of Fractions

The fourth expression we will calculate is the addition of two fractions: $\frac{1}{9} + \frac{1}{3}$. To solve this expression, we need to follow the rules of fraction addition.

Step 1: Find a Common Denominator

The denominators of the two fractions are 9 and 3. To add these fractions, we need to find a common denominator, which is 9.

Step 2: Convert the Second Fraction to Have the Common Denominator

The second fraction is $\frac{1}{3}$. To convert this fraction to have a denominator of 9, we multiply the numerator and denominator by 3:

$\frac{1}{3} \times \frac{3}{3} = \frac{3}{9}$

Step 3: Add the Fractions

Now that we have both fractions with the same denominator, we can add them:

$\frac{1}{9} + \frac{3}{9} = \frac{4}{9}$

Therefore, the value of the expression $\frac{1}{9} + \frac{1}{3}$ is $\frac{4}{9}$.

Conclusion

Introduction

Mathematical expressions are a fundamental concept in mathematics, and understanding how to solve them is crucial for success in various fields. In this article, we will address some of the most frequently asked questions related to mathematical expressions, covering topics such as multiplication, division, and addition.

Q: What is the order of operations in mathematical expressions?

A: The order of operations in mathematical expressions is a set of rules that dictate the order in which operations should be performed. The acronym PEMDAS is commonly used to remember the order of operations:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I multiply fractions?

A: To multiply fractions, you simply multiply the numerators together and multiply the denominators together. For example, to multiply $\frac{1}{2}$ and $\frac{3}{4}$, you would multiply the numerators (1 and 3) to get 3, and multiply the denominators (2 and 4) to get 8. The result is $\frac{3}{8}$.

Q: How do I divide fractions?

A: To divide fractions, you invert the second fraction (i.e., flip the numerator and denominator) and then multiply the fractions. For example, to divide $\frac{1}{2}$ by $\frac{3}{4}$, you would invert the second fraction to get $\frac{4}{3}$, and then multiply the fractions to get $\frac{1}{2} \times \frac{4}{3} = \frac{4}{6} = \frac{2}{3}$.

Q: How do I add fractions with different denominators?

A: To add fractions with different denominators, you need to find a common denominator. The common denominator is the least common multiple (LCM) of the two denominators. Once you have found the common denominator, you can convert both fractions to have that denominator, and then add them. For example, to add $\frac{1}{4}$ and $\frac{1}{6}$, you would find the LCM of 4 and 6, which is 12. You would then convert both fractions to have a denominator of 12, and add them to get $\frac{3}{12} + \frac{2}{12} = \frac{5}{12}$.

Q: How do I subtract fractions?

A: To subtract fractions, you need to find a common denominator, just like when adding fractions. Once you have found the common denominator, you can convert both fractions to have that denominator, and then subtract them. For example, to subtract $\frac{1}{4}$ from $\frac{3}{4}$, you would find the LCM of 4 and 4, which is 4. You would then convert both fractions to have a denominator of 4, and subtract them to get $\frac{3}{4} - \frac{1}{4} = \frac{2}{4} = \frac{1}{2}$.

Q: What is the difference between a fraction and a decimal?

A: A fraction is a way of representing a part of a whole as a ratio of two numbers. A decimal is a way of representing a fraction as a number with a point separating the whole number part from the fractional part. For example, the fraction $\frac{1}{2}$ is equivalent to the decimal 0.5.

Conclusion

In this article, we have addressed some of the most frequently asked questions related to mathematical expressions. We have covered topics such as the order of operations, multiplying and dividing fractions, adding and subtracting fractions, and the difference between fractions and decimals. By understanding these concepts, you will be better equipped to solve mathematical expressions and become more confident in your mathematical abilities.