Write 2.4 as a mixed number in simplest form

Write 2.4 as a mixed number in simplest form

The Correct Answer and Explanation is :

To convert the decimal 2.4 into a mixed number, we start by recognizing that a mixed number consists of a whole number and a proper fraction. Here’s a step-by-step breakdown of the conversion process:

Step 1: Identify the Whole Number

The number 2.4 can be separated into two parts: the whole number part and the decimal part. In this case, the whole number part is 2.

Step 2: Convert the Decimal to a Fraction

Next, we need to convert the decimal part, which is 0.4, into a fraction. The decimal 0.4 can be read as “four tenths,” which can be expressed as the fraction:

[
0.4 = \frac{4}{10}
]

Step 3: Simplify the Fraction

Now, we simplify the fraction (\frac{4}{10}). To do this, we find the greatest common divisor (GCD) of the numerator and denominator. The GCD of 4 and 10 is 2. We can divide both the numerator and denominator by their GCD:

[
\frac{4 \div 2}{10 \div 2} = \frac{2}{5}
]

Step 4: Combine the Whole Number and Fraction

Now that we have the whole number (2) and the simplified fraction ((\frac{2}{5})), we can combine them to form the mixed number. This gives us:

[
2.4 = 2 \frac{2}{5}
]

Final Answer

The mixed number representation of 2.4 in its simplest form is:

[
\boxed{2 \frac{2}{5}}
]

Explanation

The process of converting a decimal to a mixed number involves breaking down the decimal into its whole number and fractional components. Understanding fractions and their simplification is crucial in this conversion. By expressing decimals as fractions, we can further manipulate and simplify them to find their most reduced form. This skill is valuable in various mathematical applications, including measurements, ratios, and everyday calculations. Mixed numbers are particularly useful in contexts where whole quantities and parts of a whole need to be expressed together, such as in cooking, carpentry, and other practical scenarios.