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Chapter 3: Problem 21

Convert to fraction notation. $$ 12 \frac{3}{4} $$

Short Answer

Expert verified
\(\frac{51}{4}\)

Step by step solution

01

Understand the Mixed Number

A mixed number like \(12 \frac{3}{4}\) consists of a whole number part (12) and a fractional part (\(\frac{3}{4}\)).
02

Convert the Whole Number to a Fraction

The whole number 12 can be written as a fraction by placing it over 1: \(12 = \frac{12}{1}\).
03

Convert the Mixed Number to an Improper Fraction

To combine them into an improper fraction, multiply the denominator of the fractional part by the whole number and add the numerator: \[12 \frac{3}{4} = \frac{12 \times 4 + 3}{4}\]
04

Simplify the Fraction if Needed

Performing the calculation in Step 3, we get: \[\frac{12 \times 4 + 3}{4} = \frac{48 + 3}{4} = \frac{51}{4}\]

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Key Concepts

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

mixed number
A mixed number combines both a whole number and a fraction. For example, in the mixed number $$12 \frac{3}{4}$$, 12 is the whole number, and \( \frac{3}{4} \) is the fractional part. Understanding mixed numbers is essential for converting them into improper fractions. Mixed numbers are often found in everyday situations, like when measuring ingredients for a recipe or recording time.
improper fraction
An improper fraction has a numerator larger than or equal to its denominator. For example, \( \frac{51}{4} \) is an improper fraction because 51 is greater than 4. Improper fractions are helpful in calculations because they skip the step of converting back and forth between whole numbers and fractions. Converting mixed numbers to improper fractions simplifies mathematical operations like addition, subtraction, multiplication, and division.
fraction conversion
Conversion between mixed numbers and improper fractions is a common task in mathematics. To convert a mixed number to an improper fraction:
1. Multiply the denominator of the fractional part by the whole number.
2. Add the product to the numerator of the fractional part.
3. Place the sum over the original denominator.
For example, \( 12 \frac{3}{4} \) converts to \( \frac{12 \times 4 + 3}{4} = \frac{51}{4} \).
mathematics education
Learning to convert mixed numbers to improper fractions is a key skill in mathematics education. It enhances understanding of how fractions work and improves problem-solving abilities. Teachers often use visual aids and practical examples to help students grasp these concepts. Practicing conversions regularly with exercises and real-life examples can make the mathematical process second nature to students.

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Most popular questions from this chapter

Janine took \(\frac{1}{5} \mathrm{~g}\) of ibuprofen before lunch and \(\frac{1}{2} \mathrm{~g}\) after lunch. How much did she take altogether?

Add and simplify. $$ \frac{3}{8}+\frac{1}{8}+\frac{2}{8} $$

Simplify. $$ \frac{\frac{3}{8}}{\frac{11}{8}} $$

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 . $$ 43 \frac{16}{17} \div 11 \frac{2}{13} $$

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 . $$ 96 \frac{2}{13} \div 5 \frac{19}{20}+3 \frac{1}{7} \cdot 5 \frac{18}{21} $$
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