Write $\frac{3 t+4}{7}+\frac{10 t}{7}$ as a single fraction in its simplest form.
Answer (2)
Combine the fractions since they have a common denominator: 7 3 t + 4 + 7 10 t = 7 ( 3 t + 4 ) + 10 t .
Simplify the numerator by combining like terms: 3 t + 10 t = 13 t .
The expression simplifies to 7 13 t + 4 .
The final simplified expression is 7 13 t + 4 .
Explanation
Understanding the problem We are given the expression 7 3 t + 4 + 7 10 t and we want to simplify it into a single fraction.
Combining the fractions Since both fractions have the same denominator, we can combine them by adding their numerators: 7 3 t + 4 + 7 10 t = 7 ( 3 t + 4 ) + 10 t
Simplifying the numerator Now, we simplify the numerator by combining like terms. We have 3 t and 10 t , which add up to 13 t . So the expression becomes: 7 3 t + 4 + 10 t = 7 13 t + 4
Final simplification The expression 7 13 t + 4 is now in its simplest form because there are no common factors between the numerator ( 13 t + 4 ) and the denominator ( 7 ).
Examples
Imagine you are sharing a pizza with friends. One person eats 7 3 t + 4 of the pizza, and another eats 7 10 t of the pizza. To find the total fraction of the pizza eaten, you would add these two fractions together, just like we did in the problem. Simplifying the expression helps you understand the total amount of pizza consumed in a clear and concise way. This concept is useful in many real-life situations where you need to combine or simplify fractions to understand quantities or proportions.
To combine the fractions 7 3 t + 4 + 7 10 t , we add the numerators since they share a common denominator. This results in 7 13 t + 4 , which is the simplified expression. The final answer is 7 13 t + 4 .
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