Danny sold $2 \frac{3}{6}$ cakes and Ariel sold $8 \frac{2}{3}$ cakes. How many more cakes did Ariel sell than Danny? Give your answer as a mixed number in its simplest form.
Answer (1)
Convert the mixed numbers to improper fractions: Danny sold 6 15 cakes, and Ariel sold 3 26 cakes.
Find a common denominator to subtract the fractions: 3 26 = 6 52 .
Subtract the fractions: 6 52 − 6 15 = 6 37 .
Convert the improper fraction back to a mixed number: 6 37 = 6 6 1 .
Ariel sold 6 6 1 more cakes than Danny.
Explanation
Understanding the Problem We are given that Danny sold 2 6 3 cakes and Ariel sold 8 3 2 cakes. We need to find how many more cakes Ariel sold than Danny. This means we need to subtract the number of cakes Danny sold from the number of cakes Ariel sold.
Converting to Improper Fractions First, let's convert the mixed numbers to improper fractions. Danny: 2 6 3 = 6 2 × 6 + 3 = 6 12 + 3 = 6 15 Ariel: 8 3 2 = 3 8 × 3 + 2 = 3 24 + 2 = 3 26
Subtracting the Fractions Now, subtract the number of cakes Danny sold from the number of cakes Ariel sold: 3 26 − 6 15
Finding a Common Denominator and Subtracting To subtract the fractions, we need a common denominator. The least common multiple of 3 and 6 is 6. So, we convert 3 26 to a fraction with a denominator of 6: 3 26 = 3 × 2 26 × 2 = 6 52 Now we can subtract: 6 52 − 6 15 = 6 52 − 15 = 6 37
Converting Back to a Mixed Number Now, convert the improper fraction 6 37 back to a mixed number. 6 37 = 6 6 1
Final Answer The mixed number 6 6 1 is already in its simplest form. Therefore, Ariel sold 6 6 1 more cakes than Danny.
Examples
Understanding fractions and mixed numbers is essential in everyday situations, such as cooking and baking. For instance, if a recipe calls for 2 2 1 cups of flour and you want to double the recipe, you need to multiply the mixed number by 2. This involves converting the mixed number to an improper fraction, performing the multiplication, and then converting back to a mixed number to easily measure the required amount. This skill ensures accurate measurements and successful culinary outcomes.
