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Chapter 4: Problem 673

Convert the mixed number to an improper fraction. $$ 3 \frac{2}{7} $$

Short Answer

Expert verified
The improper fraction is \( \frac{23}{7} \).

Step by step solution

01

Understand the Mixed Number

A mixed number consists of a whole number and a fractional part. In this exercise, the mixed number is \( 3 \frac{2}{7} \).
02

Multiply Whole Number by Denominator

Multiply the whole number part (3) by the denominator of the fraction part (7). \( 3 \times 7 = 21 \)
03

Add Numerator to the Product

Add the numerator of the fraction part (2) to the product obtained in the previous step.\( 21 + 2 = 23 \)
04

Write as Improper Fraction

Combine the result from the previous step as the numerator and use the original denominator (7) to form the improper fraction.The improper fraction is \( \frac{23}{7} \).

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Key Concepts

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

Mixed Numbers
A mixed number is a combination of a whole number and a fraction. For example, in the mixed number \(3 \frac{2}{7}\), 3 is the whole number, and \( \frac{2}{7}\) is the fractional part. Mixed numbers are often easier to understand in daily life situations, like measuring ingredients in a recipe or describing distances. They provide a more intuitive feel for quantities greater than one.
Improper Fractions
An improper fraction is a fraction where the numerator (the top number) is greater than or equal to the denominator (the bottom number). This represents a value equal to or greater than one whole. For instance, \( \frac{23}{7} \) is an improper fraction because 23 is greater than 7. Improper fractions are useful in mathematical computations because they are easier to work with in algebraic expressions and equations.
Fraction Conversion
Converting a mixed number to an improper fraction involves a few simple steps:
First, multiply the whole number part by the denominator of the fraction part.
For example, with the mixed number \(3 \frac{2}{7}\), multiply 3 by 7 to get 21.
Next, add the numerator of the fraction part to this product. In our example, add 2 to 21 to get 23.
Finally, place this sum over the original denominator to form the improper fraction. Thus, \(3 \frac{2}{7} = \frac{23}{7}\).
Breaking it down, we have:
  • Multiply: 3 \times 7 = 21
  • Add: 21 + 2 = 23
  • Form the fraction: \frac{23}{7} \

Understanding these steps makes converting between mixed numbers and improper fractions straightforward and helps in solving various mathematical problems efficiently.

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Most popular questions from this chapter

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