Solve the following: [tex]313 / 16 \div 31 / 4[/tex]
Answer (2)
To solve 16 313 ÷ 4 31 , we first rewrite it as 16 313 × 31 4 , which simplifies to 124 313 . Comparing this with the provided options, the closest one is 52 145 . The final answer is 52 145 .
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Rewrite the division as multiplication by the reciprocal: 16 313 ÷ 4 31 = 16 313 × 31 4 .
Multiply the fractions: 16 313 × 31 4 = 16 × 31 313 × 4 .
Simplify the fraction: 16 × 31 313 × 4 = 4 × 31 313 = 124 313 .
Compare the result with the multiple choice options and select the closest answer: 52 145 .
52 145
Explanation
Understanding the Problem We are asked to solve the expression $313 / 16
div 31 / 4$ and choose the correct answer from the multiple choice options.
Rewriting the Division as Multiplication To solve the expression, we need to divide 313/16 by 31/4 . Dividing by a fraction is the same as multiplying by its reciprocal. Therefore, we can rewrite the expression as follows: 16 313 ÷ 4 31 = 16 313 × 31 4
Multiplying the Fractions Now, we multiply the fractions: 16 313 × 31 4 = 16 × 31 313 × 4
Simplifying the Fraction We can simplify the fraction by canceling common factors. Notice that 4 is a factor of both 4 and 16. So, we can divide both the numerator and the denominator by 4: 16 × 31 313 × 4 = 4 × 31 313 × 1 = 4 × 31 313
Calculating the Denominator Now, we multiply the remaining factors in the denominator: 4 × 31 313 = 124 313
Comparing with Multiple Choice Options Now we need to compare our result, 124 313 , with the multiple choice options to find the correct answer. The options are:
9/16 19/52 4 / 16 145 / 52
We can convert 124 313 to a decimal to compare it more easily with the options, or we can try to see if any of the options are equivalent to 124 313 .
124 313 ≈ 2.524
Let's convert the options to decimals as well:
16 9 = 0.5625 52 19 ≈ 0.365 16 4 = 0.25 52 145 ≈ 2.788
Comparing the decimal values, we can see that 52 145 is the closest to 124 313 .
Finding the Closest Option Alternatively, we can notice that 124 313 is approximately equal to 2.524. Among the given options, 52 145 is approximately equal to 2.788. Since we are looking for the closest option, 52 145 is the closest to 124 313 .
Examples
Understanding fraction division is crucial in many real-life scenarios, such as scaling recipes. For instance, if a recipe calls for 2 1 cup of flour and you only want to make 4 1 of the recipe, you need to divide 2 1 by 4, which is the same as multiplying 2 1 by 4 1 , resulting in 8 1 cup of flour. This concept is also used in calculating proportions, determining rates, and many other practical applications.
