$\frac{1}{5} \quad 18,4 \frac{1}{2} \div 2 \frac{1}{4}$
Answer (1)
Convert mixed numbers to improper fractions: 4 2 1 = 2 9 and 2 4 1 = 4 9 .
Perform the division: 2 9 ÷ 4 9 = 2 9 × 9 4 = 2 .
Multiply the remaining numbers: 5 1 × 18 × 2 = 5 36 .
Convert the improper fraction to a decimal: 5 36 = 7.2 . The final answer is 7.2 .
Explanation
Understanding the Expression We are given the expression 5 1 × 18 × 4 2 1 ÷ 2 4 1 . Our goal is to evaluate this expression step by step, following the order of operations. First, we need to convert the mixed numbers into improper fractions.
Converting Mixed Numbers Let's convert the mixed numbers to improper fractions: 4 2 1 = 2 4 × 2 + 1 = 2 9 2 4 1 = 4 2 × 4 + 1 = 4 9
Rewriting the Expression Now we can rewrite the expression as: 5 1 × 18 × 2 9 ÷ 4 9
Performing Division Next, we perform the division operation. Remember that dividing by a fraction is the same as multiplying by its reciprocal: 2 9 ÷ 4 9 = 2 9 × 9 4
Simplifying the Division Now, let's simplify the result of the division: 2 9 × 9 4 = 2 × 9 9 × 4 = 18 36 = 2
Substituting Back Now we substitute the result of the division back into the expression: 5 1 × 18 × 2
Multiplying the Numbers Now we multiply the numbers from left to right: 5 1 × 18 × 2 = 5 18 × 2 = 5 36
Final Result Finally, we can convert the improper fraction to a mixed number or a decimal: 5 36 = 7 5 1 = 7.2 So, the final answer is 7.2 .
Examples
Understanding how to evaluate expressions with fractions and mixed numbers is essential in many real-life situations. For example, if you are baking and need to adjust a recipe that calls for 4 2 1 cups of flour but you only want to make half the recipe, you need to divide 4 2 1 by 2. Similarly, if you are calculating distances on a map where the scale is given in fractions, you need to perform multiplication and division with fractions to find the actual distances. These skills are also crucial in financial calculations, such as calculating interest or dividing expenses among friends.
