Evaluate.
$\frac{7}{9}+\frac{1}{6} \div \frac{3}{7}$
Write your answer in simplest form.
Answer (1)
Perform the division first: 6 1 ÷ 7 3 = 18 7 .
Find a common denominator to add the fractions: 9 7 = 18 14 .
Add the fractions: 18 14 + 18 7 = 18 21 .
Simplify the fraction: 18 21 = 6 7 .
Explanation
Understanding the Problem We need to evaluate the expression 9 7 + 6 1 ÷ 7 3 and write the answer in simplest form. Remember that we need to perform the division before the addition.
Performing the Division First, let's perform the division. To divide fractions, we multiply by the reciprocal of the second fraction: 6 1 ÷ 7 3 = 6 1 × 3 7 = 6 × 3 1 × 7 = 18 7 .
Finding a Common Denominator Now, we add the result to 9 7 : 9 7 + 18 7 . To add these fractions, we need a common denominator. The least common multiple of 9 and 18 is 18. So we rewrite 9 7 with the denominator 18: 9 7 = 9 × 2 7 × 2 = 18 14 .
Adding the Fractions Now we can add the two fractions: 18 14 + 18 7 = 18 14 + 7 = 18 21 .
Simplifying the Fraction Finally, we simplify the fraction. Both the numerator and denominator are divisible by 3: 18 21 = 18 ÷ 3 21 ÷ 3 = 6 7 . So, the simplified fraction is 6 7 .
Final Answer Therefore, the final answer is 6 7 .
Examples
Fractions are used in everyday life, such as when cooking, measuring ingredients, or splitting a bill with friends. Understanding how to add, subtract, multiply, and divide fractions is essential for accurate calculations in these situations. For example, if you need to double a recipe that calls for 3 1 cup of flour, you would need to multiply 3 1 by 2, resulting in 3 2 cup of flour. Similarly, if you are splitting a pizza with 8 slices among 6 people, each person gets 6 8 or 3 4 slices, which is 1 and 3 1 slices each.
