/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 2 Write as a mixed number. $$ ... [FREE SOLUTION] | 91影视

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Chapter 1: Problem 2

Write as a mixed number. $$ 15.4 $$

Short Answer

Expert verified
15.4 as a mixed number is \( 15\frac{2}{5} \).

Step by step solution

01

Separate Whole Number and Decimal

Identify the whole number and the decimal part of 15.4. The whole number is 15, and the decimal part is 0.4.
02

Convert Decimal to Fraction

Convert the decimal part, 0.4, into a fraction. Since 0.4 means 4 tenths, it can be written as \( \frac{4}{10} \).
03

Simplify the Fraction

Simplify \( \frac{4}{10} \) by dividing both the numerator and the denominator by their greatest common divisor, which is 2. This results in \( \frac{2}{5} \).
04

Combine Whole Number and Fraction

Combine the whole number 15 with the simplified fraction \( \frac{2}{5} \) to write 15.4 as a mixed number. This gives us \( 15 \frac{2}{5} \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Decimal to Fraction Conversion
When converting a decimal to a fraction, you are essentially expressing the decimal number using two integers - one as the numerator and the other as the denominator.
Let鈥檚 take the example of the decimal 0.4. The number 0.4 means 4 tenths, which can be written as the fraction \( \frac{4}{10} \).
Here鈥檚 a simple way to convert any decimal to a fraction:
  • Identify the place value of the last digit (For 0.4, the last digit '4' is in the tenths place).
  • Write the number without the decimal point as the numerator (here it is 4).
  • The denominator is 10 for the tenths place (0.1), 100 for the hundredths (0.01), and so on.
By following these easy steps, converting a decimal to a fraction becomes straightforward.
Simplifying Fractions
Simplifying fractions involves reducing them to their simplest form. This means finding the smallest numerator and denominator that still represent the same value.
In our example, the fraction \( \frac{4}{10} \) can be simplified.
To simplify, you need to find the GCD (Greatest Common Divisor) of the numerator and denominator:
  • Determine the GCD: For 4 and 10, the GCD is 2.
  • Divide both the numerator and denominator by the GCD (\( \frac{4 \div 2}{10 \div 2} \)).
  • You get a simplified fraction \( \frac{2}{5} \).
Simplifying fractions helps make them easier to understand and work with.
Whole Numbers
Whole numbers are numbers without fractions or decimals, simply complete entities starting from 0.
In the context of writing a decimal as a mixed number, a whole number is considered separate from the fractional part.
For 15.4, the whole number is 15.
  • This number establishes the starting point of a mixed number format.
  • Adding a fraction to a whole number allows expression between certain values (like in 15 \( \frac{2}{5} \)).
  • Whole numbers are utilized in several arithmetic operations and are fundamental to number theory.
Recognizing whole numbers within mixed numbers helps in properly identifying and performing mathematical expressions.

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