$6 \frac{1}{4} + \frac{2}{3} =$
Answer (1)
Convert the mixed number to an improper fraction: 6 4 1 = 4 25 .
Find a common denominator for the fractions: The least common multiple of 4 and 3 is 12.
Convert the fractions to have the common denominator: 4 25 = 12 75 and 3 2 = 12 8 .
Add the fractions and convert back to a mixed number: 12 75 + 12 8 = 12 83 = 6 12 11 .
6 12 11
Explanation
Problem Analysis We need to add a mixed number and a fraction. The mixed number is 6 4 1 and the fraction is 3 2 .
Converting Mixed Number to Improper Fraction First, let's convert the mixed number 6 4 1 into an improper fraction. To do this, we multiply the whole number part (6) by the denominator (4) and add the numerator (1). This gives us 6 × 4 + 1 = 24 + 1 = 25 . So, 6 4 1 = 4 25 .
Finding a Common Denominator Now we need to add the two fractions: 4 25 + 3 2 . To add fractions, we need a common denominator. The least common multiple of 4 and 3 is 12. So, we convert both fractions to have a denominator of 12.
Converting Fractions to Common Denominator To convert 4 25 to a fraction with a denominator of 12, we multiply both the numerator and the denominator by 3: 4 × 3 25 × 3 = 12 75 . To convert 3 2 to a fraction with a denominator of 12, we multiply both the numerator and the denominator by 4: 3 × 4 2 × 4 = 12 8 .
Adding the Fractions Now we can add the two fractions: 12 75 + 12 8 = 12 75 + 8 = 12 83 .
Converting Improper Fraction to Mixed Number The result is an improper fraction, so let's convert it back to a mixed number. We divide 83 by 12. 83 ÷ 12 = 6 with a remainder of 11. So, 12 83 = 6 12 11 .
Final Answer Therefore, 6 4 1 + 3 2 = 6 12 11 .
Examples
When baking, you might need to combine different amounts of ingredients. For example, if a recipe calls for 6 4 1 cups of flour and you want to add an extra 3 2 cup, you need to calculate the total amount of flour needed. Adding these fractions helps you determine the correct amount of flour to use, ensuring your baked goods turn out perfectly. This skill is also useful in other real-life situations, such as measuring liquids for mixing solutions or calculating distances when combining segments of a journey.
