Problem 1
Question
Find the reciprocal of each number. \(\frac{5}{6}\)
Step-by-Step Solution
Verified Answer
\( \frac{6}{5} \)
1Step 1 - Understanding Reciprocals
To find the reciprocal of a fraction, you simply switch the numerator (the top number) and the denominator (the bottom number). If you have a whole number, you can think of it as a fraction with a denominator of 1.
2Step 2 - Identify Numerator and Denominator
The given fraction is \(\frac{5}{6}\). Here, 5 is the numerator and 6 is the denominator.
3Step 3 - Switch Numerator and Denominator
To find the reciprocal, switch the numerator and denominator. So, the reciprocal of \(\frac{5}{6}\) becomes \(\frac{6}{5}\).
Key Concepts
Finding ReciprocalsNumerator and DenominatorFraction Operations
Finding Reciprocals
Finding the reciprocal of a number is a fundamental concept in math, especially when working with fractions. To find the reciprocal, you simply switch the numerator (top number) and the denominator (bottom number) of the fraction.
For example, if you have a fraction like \(\frac{5}{6}\), its reciprocal would be \(\frac{6}{5}\).
Remember, the process involves three simple steps:
For example, if you have a fraction like \(\frac{5}{6}\), its reciprocal would be \(\frac{6}{5}\).
Remember, the process involves three simple steps:
- Identify the numerator and denominator.
- Swap their places.
- Write the new fraction.
Numerator and Denominator
Understanding the terms 'numerator' and 'denominator' is crucial when dealing with fractions. The numerator is the number above the horizontal line in a fraction. It represents how many parts of a whole we have.
In the fraction \(\frac{5}{6}\), 5 is the numerator.
The denominator is the number below the horizontal line. It shows into how many equal parts the whole is divided.
In the fraction \(\frac{5}{6}\), 6 is the denominator.
By swapping the numerator and the denominator, we change the fraction's relationship to the whole. This is how we find its reciprocal, which is \(\frac{6}{5}\).
In the fraction \(\frac{5}{6}\), 5 is the numerator.
The denominator is the number below the horizontal line. It shows into how many equal parts the whole is divided.
In the fraction \(\frac{5}{6}\), 6 is the denominator.
By swapping the numerator and the denominator, we change the fraction's relationship to the whole. This is how we find its reciprocal, which is \(\frac{6}{5}\).
Fraction Operations
Handling fractions involves understanding basic operations like addition, subtraction, multiplication, and division. One of the key operations is finding the reciprocal, which is essential for dividing fractions.
When you divide by a fraction, you actually multiply by its reciprocal. For instance, dividing by \(\frac{5}{6}\) is the same as multiplying by \(\frac{6}{5}\).
Here are some basic guidelines:
When you divide by a fraction, you actually multiply by its reciprocal. For instance, dividing by \(\frac{5}{6}\) is the same as multiplying by \(\frac{6}{5}\).
Here are some basic guidelines:
- To add or subtract fractions, they need a common denominator.
- To multiply fractions, simply multiply the numerators and the denominators.
- To divide fractions, multiply by the reciprocal of the divisor.
Other exercises in this chapter
Problem 1
Multiply and simplify. $$ \frac{2}{3} \cdot \frac{1}{2} $$
View solution Problem 1
For Exercises \(1-16,\) answer yes or no and give a reason based on the tests for divisibility. Determine whether 84 is divisible by \(3 .\)
View solution Problem 2
Determine whether the second number is a factor of the first. $$ 52 ; 13 $$
View solution Problem 2
Identify the numerator and the denominator. $$ \frac{9}{10} $$
View solution