4.2 as a mixed number

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30-03-2025

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The decimal 4.2 represents a number between 4 and 5. To convert it to a mixed number (a whole number and a fraction), we need to understand what the decimal part signifies. Let's break down the process.

Understanding Decimals and Fractions

Decimals and fractions both represent parts of a whole. The decimal 4.2 means 4 and 2 tenths. We can write this as 4 and 2/10. This is already a mixed number, but we can simplify it further.

Simplifying the Fraction

The fraction 2/10 can be simplified by finding the greatest common divisor (GCD) of the numerator (2) and the denominator (10). The GCD of 2 and 10 is 2. We divide both the numerator and the denominator by 2:

2 ÷ 2 = 1 10 ÷ 2 = 5

This simplifies the fraction to 1/5.

Putting it Together: The Mixed Number

Now we replace the simplified fraction back into our mixed number:

4 and 2/10 simplifies to 4 and 1/5.

Therefore, 4.2 expressed as a mixed number is 4 1/5.

Other Examples of Decimal to Mixed Number Conversion

Let's look at a few more examples to solidify your understanding:

• 6.75: This is 6 and 75 hundredths, or 6 and 75/100. Simplifying 75/100 by dividing both by 25 gives 3/4. Therefore, 6.75 as a mixed number is 6 3/4.

• 2.25: This is 2 and 25 hundredths, or 2 and 25/100. Simplifying 25/100 by dividing both by 25 gives 1/4. Therefore, 2.25 as a mixed number is 2 1/4.

• 1.5: This is 1 and 5 tenths, or 1 and 5/10. Simplifying 5/10 by dividing both by 5 gives 1/2. Therefore, 1.5 as a mixed number is 1 1/2.

Why is this conversion useful?

Converting decimals to mixed numbers is a valuable skill in various mathematical contexts. It's frequently used in:

• Everyday calculations: Sharing items, measuring ingredients in cooking, etc.
• Algebra: Simplifying expressions and solving equations.
• Geometry: Working with fractions of shapes and areas.
• Further mathematical studies: Fractions often provide a clearer understanding of numerical relationships.

By mastering this conversion, you strengthen your foundation in fractions and decimals, allowing you to approach mathematical problems with greater confidence and accuracy.