Question

Find each quantity. \(\frac{1}{4}\) of 0.4

Short answer

0.1

Step-by-step solution

- Understand the Problem

Determine the quantity we are looking for, which is \(\frac{1}{4}\) of 0.4. This means we need to find one-fourth of the given number 0.4.

- Set up the Multiplication

To find \(\frac{1}{4}\) of 0.4, we need to multiply 0.4 by \(\frac{1}{4}\). Write the expression as \(0.4 \times \frac{1}{4}\).

- Perform the Multiplication

Calculate the multiplication: \(0.4 \times \frac{1}{4} = 0.4 \times 0.25\).

- Calculate the Product

Perform the multiplication to get the result: \(0.4 \times 0.25 = 0.1\).

- State the Final Answer

The result, or \(\frac{1}{4}\) of 0.4, is 0.1.

Key concepts

multiplication of fractions

One of the core concepts in algebra is the multiplication of fractions. To multiply fractions, you simply multiply their numerators (top numbers) together and their denominators (bottom numbers) together.
For example, multiplying \( \frac{1}{4} \) and \( \frac{1}{2} \) would look like this: \(\frac{1 \times 1}{4 \times 2} = \frac{1}{8} \).
When multiplying a fraction by a whole number, simply convert the whole number into a fraction by putting it over 1. For instance, multiplying \(3 \) by \( \frac{1}{4} \) becomes: \(\frac{3}{1} \times \frac{1}{4} = \frac{3 \times 1}{1 \times 4} = \frac{3}{4} \).
The key is to remember that multiplying fractions involves direct multiplication of numerators and denominators, without any need to find a common denominator.

decimal multiplication

Multiplying decimal numbers might seem tricky, but it's straightforward once you understand the process. Place the numbers vertically and multiply them as if they were whole numbers.
Ignore the decimal points temporarily. After performing the multiplication, count the total number of decimal places in both numbers.
In this problem, we multiplied 0.4 by \( \frac{1}{4} \), which is the same as multiplying 0.4 by 0.25.
Before multiplying, count the decimal places. After multiplying, the number of decimal places in the product should match the count from both original numbers.
For instance, 0.4 has one decimal place, and 0.25 has two. Thus, the product 0.1 has three decimal places, confirming it's accurate.

basic arithmetic operations

Having a strong understanding of basic arithmetic operations is essential. These operations include addition, subtraction, multiplication, and division.
Each operation has a specific set of rules and properties. Multiplication is repeated addition and is commutative, meaning that \( a \times b = b \times a \).
This means the order in which you multiply numbers does not change the result. Multiplication also distributes over addition. For example, in the expression \( a \times (b + c) = a \times b + a \times c \).
When dealing with decimals and fractions, these arithmetic rules still apply but knowing the correct approach ensures accuracy.
For instance, multiplying a decimal by a fraction involves converting the fraction to decimal form or vice versa. Then, perform the multiplication just like any other multiplication problem, mindful of decimal placement.