The mathematical expression 4/25 x 10 represents the multiplication of the fraction 4/25 by the integer 10. This calculation can be easily performed using the basic principles of multiplication and fractions.

To solve 4/25 x 10, we can first convert the fraction 4/25 to its decimal equivalent. Divide 4 by 25: 4 ÷ 25 = 0.16. Then, multiply 0.16 by 10: 0.16 x 10 = 1.6. Therefore, the final result of 4/25 x 10 is 1.6.

This result can be further simplified by converting it back to a fraction. 1.6 can be written as 16/10. We can then simplify the fraction by dividing both the numerator and denominator by 2, which gives us 8/5. Hence, 4/25 x 10 is equivalent to 8/5.

## Simplifying the Fraction

The fraction 4/25 can be further simplified by finding its greatest common divisor (GCD), which is the largest number that divides both the numerator and denominator without leaving a remainder. In this case, the GCD of 4 and 25 is 1. Since the GCD is 1, the fraction 4/25 is already in its simplest form.

However, if the fraction were not in its simplest form, we could divide both the numerator and denominator by their GCD to simplify it. For example, if the fraction were 6/12, the GCD would be 6. Dividing both the numerator and denominator by 6 would give us the simplified fraction 1/2.

## Converting Fractions to Decimals

Fractions can be converted to decimals by dividing the numerator by the denominator. For example, to convert the fraction 4/25 to a decimal, we divide 4 by 25: 4 ÷ 25 = 0.16. The decimal equivalent of 4/25 is therefore 0.16.

Another method for converting fractions to decimals is to use long division. To do this, we set up the fraction as a long division problem, with the numerator as the dividend and the denominator as the divisor. We then perform the division as usual.

## Multiplying Fractions by Integers

To multiply a fraction by an integer, we simply multiply the numerator of the fraction by the integer and leave the denominator unchanged. For example, to multiply the fraction 4/25 by the integer 10, we multiply 4 by 10, which gives us 40. The answer is 40/25.

We can then simplify the fraction 40/25 by dividing both the numerator and denominator by their GCD, which is 5. This gives us the final answer of 8/5.

## Multiplying Decimals by Integers

To multiply a decimal by an integer, we simply multiply the decimal by the integer. For example, to multiply the decimal 0.16 by the integer 10, we simply multiply 0.16 by 10, which gives us 1.6.

It is important to note that when multiplying decimals, we multiply the digits to the right of the decimal point and then add the decimal point to the answer. For example, to multiply 0.16 by 10, we multiply 6 by 10, which gives us 60. We then add the decimal point to the answer, which gives us 1.6.

## Solving Word Problems

Word problems that involve multiplying fractions or decimals by integers can be solved using the same principles as outlined above. The key is to understand the problem and identify the appropriate mathematical operations to use.

For example, a word problem might ask us to find the total cost of a certain number of items. To solve this problem, we would multiply the cost of each item by the number of items.

## Applications of Multiplication

The concept of multiplication has numerous applications in real-world situations. For example, multiplication is used in:

- Calculating the area of a rectangle
- Finding the volume of a cube
- Converting units of measurement
- Scaling recipes
- Calculating percentages

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