$5 \frac{2}{7}+4 \frac{2}{3}$
Answer (1)
Convert the mixed numbers to improper fractions: 5 7 2 = 7 37 and 4 3 2 = 3 14 .
Find a common denominator and add the fractions: 7 37 + 3 14 = 21 111 + 21 98 = 21 209 .
Convert the result back to a mixed number: 21 209 = 9 21 20 .
The final answer is: 9 21 20 .
Explanation
Understanding the problem We are asked to evaluate the expression 5 7 2 + 4 3 2 . This involves adding two mixed numbers. A mixed number is a whole number and a proper fraction combined. To add them, we can convert them to improper fractions, add the improper fractions, and then convert back to a mixed number.
Converting to improper fractions First, we convert the mixed numbers to improper fractions. To convert a mixed number to an improper fraction, we multiply the whole number by the denominator and add the numerator. This result becomes the new numerator, and we keep the same denominator.
For 5 7 2 , we have 5 × 7 + 2 = 35 + 2 = 37 . So, 5 7 2 = 7 37 .
For 4 3 2 , we have 4 × 3 + 2 = 12 + 2 = 14 . So, 4 3 2 = 3 14 .
Adding the improper fractions Now we add the two improper fractions: 7 37 + 3 14 . To add fractions, we need a common denominator. The least common multiple of 7 and 3 is 21. So we convert both fractions to have a denominator of 21.
7 37 = 7 × 3 37 × 3 = 21 111 .
3 14 = 3 × 7 14 × 7 = 21 98 .
Now we can add them: 21 111 + 21 98 = 21 111 + 98 = 21 209 .
Converting back to a mixed number Finally, we convert the improper fraction 21 209 back to a mixed number. To do this, we divide 209 by 21. The quotient is the whole number part, and the remainder is the numerator of the fractional part. The denominator stays the same.
209 ÷ 21 = 9 with a remainder of 20 . So, 21 209 = 9 21 20 .
Final Answer Therefore, 5 7 2 + 4 3 2 = 9 21 20 .
Examples
Mixed number arithmetic is useful in everyday situations such as cooking and construction. For example, if a recipe calls for 2 2 1 cups of flour and you want to double the recipe, you need to calculate 2 2 1 + 2 2 1 . Similarly, if you are building a bookshelf and need to cut a piece of wood to a length of 3 4 3 feet, you need to be comfortable working with mixed numbers. Understanding how to add and subtract mixed numbers allows for accurate measurements and adjustments in these practical scenarios.
