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Chapter 4: Problem 47

For Exercises 47鈥�58, convert the mixed number to an improper fraction. $$1 \frac{3}{4}$$

Short Answer

Expert verified
\( 1 \frac{3}{4} \) as an improper fraction is \( \frac{7}{4} \).

Step by step solution

01

- Identify the mixed number

The given mixed number is 1 \( \frac{3}{4} \). It consists of a whole number part (1) and a fractional part (\( \frac{3}{4} \)).
02

- Multiply the whole number by the denominator

Multiply the whole number (1) by the denominator of the fraction (4). \[ 1 \times 4 = 4 \]
03

- Add the result to the numerator

Add the result from Step 2 (4) to the numerator of the fraction (3): \[ 4 + 3 = 7 \]
04

- Place the result over the original denominator

The new fraction will have the sum obtained in Step 3 as the numerator and the original denominator (4) as the denominator. Thus, the improper fraction is: \[ \frac{7}{4} \]

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Key Concepts

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

mixed numbers
In mathematics, a mixed number combines a whole number and a fraction. For example, in the mixed number 1 \( \frac{3}{4} \), the 1 is the whole number, and \( \frac{3}{4} \) is the fractional part.
Mixed numbers are commonly used to represent quantities that are greater than a whole but not a full integer.
For example, you might use a mixed number to represent someone who ran 1 full mile and an additional \( \frac{3}{4} \) of a mile.
improper fractions
An improper fraction is a fraction where the numerator is greater than or equal to the denominator. For instance, \( \frac{7}{4} \) is an improper fraction because 7 (the numerator) is larger than 4 (the denominator).
Improper fractions make calculations easier, especially when multiplying or dividing fractions.
Often, improper fractions are converted back to mixed numbers for ease of understanding, but during operations, improper fractions are more practical.
fraction conversion
Converting a mixed number to an improper fraction involves a few straightforward steps. Here's how to do it:
  • Step 1: Identify the whole number and the fractional part of the mixed number.
  • Step 2: Multiply the whole number by the denominator of the fraction. This converts the whole number into an equivalent fraction.
  • Step 3: Add the result to the numerator of the fraction. This combines the whole and fractional parts.
  • Step 4: Place this sum over the original denominator to get the improper fraction.
These steps ensure that your fraction is correctly converted and represents the same value as the original mixed number.
basic arithmetic
Basic arithmetic operations such as addition, subtraction, multiplication, and division are fundamental in converting mixed numbers to improper fractions.

In our example of converting 1 \( \frac{3}{4} \) to an improper fraction:
  • Multiply (1) by 4 (denominator): 1 脳 4 = 4.
  • Add this product (4) to the numerator (3): 4 + 3 = 7.
  • Place this result (7) over the original denominator (4): \( \frac{7}{4} \).
The steps involve simple multiplications and additions, both crucial operations in basic arithmetic.
Understanding these basic arithmetic concepts assures accuracy and efficiency in conversions and calculations.

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Most popular questions from this chapter

Convert the improper fraction to a mixed number. $$-\frac{27}{10}$$

Convert the mixed number to an improper fraction. $$11 \frac{5}{12}$$

Plot the fraction on the number line. $$-\frac{5}{6}$$

Which expressions are equivalent to \(\frac{-4}{1} ?\) a. \(\frac{4}{-1} \quad\) b. \(-4 \quad\) c. \(-\frac{4}{1} \quad\) d. \(\frac{1}{-4}\)

Label the fraction as proper or improper. $$\frac{3}{3}$$
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