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Chapter 4: Problem 73

Convert the improper fraction to a mixed number. $$\frac{133}{11}$$

Short Answer

Expert verified
12 \, \frac{1}{11}

Step by step solution

01

Divide the Numerator by the Denominator

Divide 133 by 11 to find out how many whole numbers are there. \[ 133 \, 梅 \, 11 \, = \, 12 \, R \, 1 \] So, the quotient is 12 and the remainder is 1.
02

Write Down the Whole Number

The quotient from the division is the whole number part of the mixed number. So, write down 12 as the whole number.
03

Form the Mixed Number

The remainder from the division (1) becomes the numerator of the fraction part, and the denominator remains 11. So the mixed number is: \[ 12 \, \frac{1}{11} \]

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Key Concepts

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

improper fractions
Understanding improper fractions is the first step in many math exercises. An improper fraction is when the numerator (the top number) is greater than or equal to the denominator (the bottom number). For instance, in the fraction \(\frac{133}{11}\), the numerator 133 is much larger than the denominator 11. Improper fractions usually represent a value greater than one whole unit. These types of fractions can often be converted into mixed numbers for easier comprehension.
mixed numbers
Mixed numbers make it simpler to visualize portions greater than one whole unit. A mixed number combines a whole number with a fraction. For example, consider the improper fraction \(\frac{133}{11}\). When we divide the numerator by the denominator, we get the quotient 12 (whole number) and a remainder of 1 (fraction). Thus, our mixed number would be: \((12 \frac{1}{11}})\). This form is often easier to grasp as it separates the whole part from the fractional part.
division of fractions
Dividing fractions is an essential part of converting improper fractions to mixed numbers. In the process, you divide the numerator by the denominator. For \(\frac{133}{11}\), you perform the division: 133 梅 11. The result of this operation is 12 with a remainder of 1. This indicates that 133 divided by 11 goes 12 times with 1 left over. This step helps to break down the fraction into more manageable parts: a whole number and a fractional remainder.
numerator and denominator
To understand fractions deeply, knowing the terms numerator and denominator is crucial. The numerator is the top number of a fraction, representing how many parts we have. The denominator is the bottom number, indicating into how many equal parts the whole is divided. In \(\frac{133}{11}\), 133 is the numerator, and 11 is the denominator. When converting to a mixed number, the whole number part is obtained by dividing the numerator by the denominator. The remainder forms the new numerator, with the original denominator staying the same.

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Most popular questions from this chapter

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