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Chapter 3: Problem 33

Convert to a mixed numeral. $$ \frac{18}{5} $$

Short Answer

Expert verified
3 \(\frac{3}{5}\)

Step by step solution

01

Understand the Problem

The given problem asks to convert the improper fraction \(\frac{18}{5}\) into a mixed numeral. A mixed numeral consists of an integer part and a fractional part.
02

Perform the Division

Divide the numerator (18) by the denominator (5). The quotient will be the integer part, and the remainder will form the new numerator for the fractional part.\[18 \, \text{divided by} \, 5 = 3 \, \text{with a remainder of} \, 3\]
03

Convert to Mixed Numeral

From the division, the quotient is 3, and the remainder is 3. The denominator remains the same (5). Write the mixed numeral as:\[3 \frac{3}{5}\]

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Key Concepts

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

Improper Fractions
An improper fraction is a type of fraction where the numerator (the top number) is greater than or equal to the denominator (the bottom number). This means that the fraction represents a value greater than or equal to one whole.
For example, in the fraction \(\frac{18}{5}\), 18 is greater than 5, making it an improper fraction.
Understanding improper fractions is essential as it leads us to convert these into mixed numerals, which are easier to interpret in practical situations like measurements and everyday math.
  • Numerator > Denominator: Improper fraction
  • Numerator < Denominator: Proper fraction
Fractions Conversion
Converting improper fractions to mixed numerals is a fundamental skill in arithmetic. A mixed numeral combines both an integer and a fraction part, making it simpler to understand.
To convert an improper fraction like \(\frac{18}{5}\) to a mixed numeral, follow these steps:
  • Step 1: Divide the numerator by the denominator (e.g., 18 梅 5).
  • Step 2: The quotient (3) becomes the integer part of the mixed numeral.
  • Step 3: The remainder (3) forms the numerator of the fractional part.
  • Step 4: The denominator remains the same (5).
So, \(\frac{18}{5}\) converts to the mixed numeral \(\text{3} \frac{3}{5} \). This process can be summarized as:
1. Division for integer.
2. Remainder as new numerator.
3. Same denominator.
Basic Arithmetic
Basic arithmetic skills are crucial for converting between fractions and mixed numerals. One needs to be comfortable with division, remainders, and understanding fractions.
Step-by-step division:
When dividing 18 by 5:
  • Think how many times 5 fits into 18 (3 times, since 5 * 3 = 15).
  • The quotient (3) represents the integer part.
  • The remainder (18 - 15 = 3) becomes the numerator.
Hence, \(\frac{18}{5}\) is converted to the mixed numeral 3 \(\frac{3}{5}\).
This example illustrates basic arithmetic to convert and grasp the idea of mixed numerals. Success in arithmetic sets a solid foundation for tackling more complex mathematical problems in the future.

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Most popular questions from this chapter

Simplify. $$ \left(\frac{2}{3}\right)^{2}-\frac{1}{3} \cdot 1 \frac{1}{4} $$

Estimate each of the following by estimating each mixed numeral as a whole number or as a mixed numeral where the fraction part is \(\frac{1}{2}\) and by estimating each fraction as \(0, \frac{1}{2},\) or 1 . $$ 12 \frac{5}{6} $$

Add and simplify. $$ \frac{1}{18}+\frac{7}{12} $$

Estimate each of the following as \(0, \frac{1}{2},\) or 1 . $$ \frac{5}{9} $$

Simplify. $$ (10+3 \cdot 4 \div 6)^{2}-11 \cdot 2^{2} \quad[1.9 \mathrm{c}] $$
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