Work out $5 \frac{1}{2}+\frac{3}{4}$. Give your answer in its simplest form.
Answer (1)
Convert the mixed number to an improper fraction: 5 2 1 = 2 11 .
Find a common denominator: 2 11 = 4 22 .
Add the fractions: 4 22 + 4 3 = 4 25 .
Convert the improper fraction to a mixed number: 4 25 = 6 4 1 .
6 4 1
Explanation
Understanding the Problem We need to calculate the sum of a mixed number and a fraction: 5 2 1 + 4 3 . The answer should be given in its simplest form.
Converting to Improper Fraction First, let's convert the mixed number 5 2 1 into an improper fraction. To do this, we multiply the whole number part (5) by the denominator (2) and add the numerator (1):
5 2 1 = 2 ( 5 × 2 ) + 1 = 2 10 + 1 = 2 11
Finding a Common Denominator Now we have the expression: 2 11 + 4 3 . To add these fractions, we need to find a common denominator. The least common multiple of 2 and 4 is 4. So, we convert 2 11 to an equivalent fraction with a denominator of 4:
2 11 = 2 × 2 11 × 2 = 4 22
Adding the Fractions Now we can add the two fractions:
4 22 + 4 3 = 4 22 + 3 = 4 25
Converting Back to Mixed Number The fraction 4 25 is an improper fraction, so let's convert it back to a mixed number. We divide 25 by 4:
25 ÷ 4 = 6 with a remainder of 1.
So, 4 25 = 6 4 1
Final Answer The sum 5 2 1 + 4 3 in its simplest form is 6 4 1 .
Examples
Understanding fractions and mixed numbers is crucial in everyday situations, such as cooking and baking. For instance, if a recipe calls for 5 2 1 cups of flour and you want to add an extra 4 3 cup, you need to calculate the total amount of flour required. Knowing how to add these quantities ensures your recipe turns out perfectly. This skill is also useful in measuring ingredients, calculating distances, and managing time.
