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Chapter 4: Problem 63

Express 11 as an equivalent fraction having denominator \(4 \mathrm{~m}\).

Short Answer

Expert verified
11 can be expressed as \(\frac{44m}{4m}\) with the denominator of \(4m\).

Step by step solution

01

Understand the Problem

We need to express the whole number 11 as a fraction with the denominator changed to \(4m\). This involves writing 11 as a fraction \(\frac{a}{b}\) and then adjusting it to the desired denominator.
02

Write 11 as a Fraction

Any whole number can be expressed as a fraction by placing it over 1. Thus, 11 can be written as \(\frac{11}{1}\).
03

Adjust the Denominator

The goal is to have a denominator of \(4m\). To achieve this, we need to multiply both the numerator and the denominator of \(\frac{11}{1}\) by \(4m\).
04

Perform the Multiplication

Multiply the numerator and the denominator by \(4m\):\[\frac{11}{1} = \frac{11 \times 4m}{1 \times 4m} = \frac{44m}{4m}\]Thus, the fraction \(\frac{11}{1}\) with a new denominator \(4m\) becomes \(\frac{44m}{4m}\).

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Key Concepts

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

Whole Numbers
Whole numbers are fundamental in mathematics. They include all the non-negative numbers like 0, 1, 2, 3, and so on. They do not include fractions, decimals, or negative numbers. When we see a whole number, it's a complete entity, like 11 in our exercise. It isn鈥檛 divided into parts.

Expressing whole numbers as fractions can make them more flexible in mathematics. Simply put, when you convert a whole number to a fraction form, you place it over 1. For instance, 11 is expressed as the fraction \( \frac{11}{1} \).
  • Whole numbers simplify arithmetic operations.
  • They are the building blocks for other number systems.
Understanding the role of whole numbers is crucial because they lay the foundation for more complex operations, like creating equivalent fractions.
Denominators
In any fraction, the denominator is the number below the line. It signifies how many equal parts the whole is divided into. For example, in the fraction \( \frac{1}{4} \), the denominator 4 means the whole is divided into four equal parts.

Changing the denominator in a fraction involves multiplying or dividing both the top and bottom of the fraction by the same number. This concept is central when adjusting the fraction to have a new specific denominator, like transforming \( \frac{11}{1} \) to have a denominator of \( 4m \).
  • The denominator determines the size of each part.
  • A larger denominator means smaller parts.
  • A smaller denominator indicates larger parts.
Thus, manipulating the denominator allows us to express numbers in new forms, equivalent but distinct from the original.
Equivalent Fractions
Equivalent fractions are different fractions that represent the same portion of a whole. While the numerators and denominators may vary, the overall value does not change.

To understand equivalent fractions, consider the exercise where 11 is rewritten. We start with \( \frac{11}{1} \) and multiply both numerator and denominator by \( 4m \) to obtain \( \frac{44m}{4m} \). Both fractions equal the same value.
  • Multiplying the top and bottom by the same value keeps the fraction balanced.
  • Equivalent fractions are useful for adding, subtracting, or comparing fractions.
Recognizing equivalent fractions helps simplify and solve problems more effectively, making mathematics that involve fractions more manageable.

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Most popular questions from this chapter

Divide the fractions, and simplify your result. $$\frac{-x}{12 y^{4}} \div \frac{-23 x^{3}}{16 y^{3}}$$

Reduce the given fraction to lowest terms. $$\frac{26 x^{2}}{32 x^{6}}$$

Multiply the fractions, and simplify your result. $$\frac{-16 y^{6}}{15} \cdot \frac{-21}{13 y^{4}}$$

Multiply the numbers and express your answer as a mixed fraction. $$\left(-3 \frac{1}{2}\right)\left(3 \frac{1}{3}\right)$$

A trapezoid has bases measuring \(3 \frac{3}{8}\) and \(5 \frac{1}{2}\) feet, respectively. The height of the trapezoid is 7 feet. Find the area of the trapezoid.
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