Problem 60
Question
For exercises \(23-74\), evaluate. $$ \frac{1}{7}+\frac{5}{7} $$
Step-by-Step Solution
Verified Answer
\(\frac{6}{7}\)
1Step 1: Identify the Denominator
Notice that the denominators of both fractions are the same: 7. When adding fractions with the same denominator, the denominator remains unchanged.
2Step 2: Add the Numerators
Add the numerators of both fractions: 1 and 5. So we have: 1 + 5 = 6.
3Step 3: Combine the Sum
Combine the numerators over the common denominator: \[\frac{1}{7} + \frac{5}{7} = \frac{6}{7}\].
Key Concepts
Common DenominatorNumeratorStep-by-Step Solution
Common Denominator
When adding fractions, a crucial step is ensuring they have a common denominator. The denominator is the number at the bottom of the fraction, showing how many equal parts the whole is divided into. For instance, in the fraction \(\frac{1}{7}\), 7 is the denominator, indicating the whole is divided into 7 parts.
If fractions have different denominators, like \(\frac{1}{4}\) and \(\frac{3}{8}\), you can't directly add them. First, you must find a common denominator. The simplest way is to find a common multiple. For example, for 4 and 8, 8 is a common multiple.
Once we have a common denominator, it turns complex fraction addition into a straightforward process.
If fractions have different denominators, like \(\frac{1}{4}\) and \(\frac{3}{8}\), you can't directly add them. First, you must find a common denominator. The simplest way is to find a common multiple. For example, for 4 and 8, 8 is a common multiple.
Once we have a common denominator, it turns complex fraction addition into a straightforward process.
Numerator
The numerator is the top number in a fraction, representing how many parts of the whole are considered. For instance, in the fraction \(\frac{5}{7}\), 5 is the numerator. It tells us we have 5 out of 7 parts of a whole.
When adding fractions with a common denominator, the numerators are simply added together. For example, in \(\frac{1}{7} + \frac{5}{7}\), we add 1 and 5 to get 6.
This gives us the new numerator in our resulting fraction, making the addition process easier to grasp.
When adding fractions with a common denominator, the numerators are simply added together. For example, in \(\frac{1}{7} + \frac{5}{7}\), we add 1 and 5 to get 6.
This gives us the new numerator in our resulting fraction, making the addition process easier to grasp.
Step-by-Step Solution
For students, a step-by-step solution is the key to mastering fraction addition. Breaking it down helps you understand each part clearly.
Step 1: Check the Denominator Start by ensuring the denominators are the same. In our example, both fractions are \(\frac{1}{7}\) and \(\frac{5}{7}\), which have the same denominator, 7. So, we keep the denominator as 7.
Step 2: Add the Numerators Next, add the numerators: 1 and 5. This gives us 6.
Step 3: Combine and Simplify Finally, place the sum of the numerators over the common denominator. Hence, \(\frac{1}{7} + \frac{5}{7} = \frac{6}{7}\).
Understanding this clear, step-by-step approach ensures you can tackle any fraction addition problem confidently.
Step 1: Check the Denominator Start by ensuring the denominators are the same. In our example, both fractions are \(\frac{1}{7}\) and \(\frac{5}{7}\), which have the same denominator, 7. So, we keep the denominator as 7.
Step 2: Add the Numerators Next, add the numerators: 1 and 5. This gives us 6.
Step 3: Combine and Simplify Finally, place the sum of the numerators over the common denominator. Hence, \(\frac{1}{7} + \frac{5}{7} = \frac{6}{7}\).
Understanding this clear, step-by-step approach ensures you can tackle any fraction addition problem confidently.
Other exercises in this chapter
Problem 59
For exercises \(23-74\), evaluate. $$ \frac{1}{9}+\frac{4}{9} $$
View solution Problem 59
For exercises 1-80, evaluate. $$ [(60 \cdot 2 \div 6)-(13+1)]^{2} $$
View solution Problem 60
For exercises 1-80, evaluate. $$ [(40 \cdot 3 \div 5)-(14+2)]^{2} $$
View solution Problem 61
If 5 out of 20 shirts are T-shirts, find the percent of the shirts that are T-shirts.
View solution