Problem 75
Question
For exercises \(75-80\), rewrite the fraction as an equivalent fraction with the given denominator. $$ \frac{4}{5} ; 100 $$
Step-by-Step Solution
Verified Answer
\frac{80}{100}
1Step 1 - Understand the Problem
Given the fraction \(\frac{4}{5}\) and the task is to rewrite it as an equivalent fraction with a denominator of 100.
2Step 2 - Find the Multiplicative Factor
To convert \(\frac{4}{5}\) to an equivalent fraction with a denominator of 100, find the number that you need to multiply 5 by to get 100. \[\frac{4}{5} \times \frac{n}{n} = \frac{4 \times n}{5 \times n}\] We need \[5 \times n = 100.\] Solving for \(n\), we get \[n = 20.\]
3Step 3 - Multiply Numerator and Denominator
Multiply both the numerator and the denominator of \(\frac{4}{5}\) by 20. \[\frac{4}{5} \times \frac{20}{20} = \frac{4 \times 20}{5 \times 20} = \frac{80}{100}\]
4Step 4 - Write the Equivalent Fraction
The equivalent fraction of \(\frac{4}{5}\) with a denominator of 100 is \(\frac{80}{100}\).
Key Concepts
FractionsDenominatorNumerator
Fractions
A fraction represents a part of a whole. It consists of two numbers separated by a line: the numerator (on top) and the denominator (on the bottom).
Fractions indicate how many parts of a certain size there are, compared to a whole that is split into equal parts. For example, in \(\frac{1}{2}\), the whole is divided into 2 parts, and we are talking about 1 of those parts.
Fractions can be used in various mathematical operations, and understanding fractions is key to mastering topics like addition, subtraction, multiplication, and division of fractions.
Fractions indicate how many parts of a certain size there are, compared to a whole that is split into equal parts. For example, in \(\frac{1}{2}\), the whole is divided into 2 parts, and we are talking about 1 of those parts.
Fractions can be used in various mathematical operations, and understanding fractions is key to mastering topics like addition, subtraction, multiplication, and division of fractions.
Denominator
The denominator is the bottom number in a fraction. It shows into how many equal parts the whole is divided. For example, in the fraction \(\frac{4}{5}\), the denominator is 5, indicating that the whole is divided into 5 equal parts.
When solving problems involving fractions, one common task is to rewrite a fraction with a different denominator. This often involves finding an equivalent fraction.
To rewrite \(\frac{4}{5}\) with a denominator of 100, we must multiply both the numerator and the denominator by the same number. This number (called the multiplicative factor) makes the new denominator the desired value. In this case:
\[5 \times n = 100\] Solving for \(n\), we get \[n = 20\]
When solving problems involving fractions, one common task is to rewrite a fraction with a different denominator. This often involves finding an equivalent fraction.
To rewrite \(\frac{4}{5}\) with a denominator of 100, we must multiply both the numerator and the denominator by the same number. This number (called the multiplicative factor) makes the new denominator the desired value. In this case:
\[5 \times n = 100\] Solving for \(n\), we get \[n = 20\]
Numerator
The numerator is the top number in a fraction. It represents the number of parts we have. Using the same example, in \(\frac{4}{5}\), the numerator is 4, meaning we have 4 parts out of the 5 equal parts that make up the whole.
When rewriting a fraction to have a new denominator, like changing \(\frac{4}{5}\) to have a denominator of 100, it is important to adjust the numerator by the same multiplicative factor. This ensures that the new fraction is equivalent to the original. So, we multiply both the numerator and denominator by 20 to get:
\[ \frac {4 \times 20}{5 \times 20} = \frac {80}{100} \]
This way, the fraction \(\frac{4}{5}\) becomes \(\frac{80}{100}\), which is equivalent to \(\frac{4}{5}\) but with a different denominator.
When rewriting a fraction to have a new denominator, like changing \(\frac{4}{5}\) to have a denominator of 100, it is important to adjust the numerator by the same multiplicative factor. This ensures that the new fraction is equivalent to the original. So, we multiply both the numerator and denominator by 20 to get:
\[ \frac {4 \times 20}{5 \times 20} = \frac {80}{100} \]
This way, the fraction \(\frac{4}{5}\) becomes \(\frac{80}{100}\), which is equivalent to \(\frac{4}{5}\) but with a different denominator.
Other exercises in this chapter
Problem 74
For exercises 1-80, evaluate. $$ [9(17-12)-2]-(9-4)^{2} $$
View solution Problem 75
$$ \text { Find } 32 \% \text { of } 50 \text {. } $$
View solution Problem 75
For exercises 15-100, evaluate. $$ (4-9)^{2}-3(-1) $$
View solution Problem 75
For exercises 1-80, evaluate. $$ \left(\frac{6+5 \cdot 0}{6}\right)^{2} $$
View solution