Complete the equivalent fraction by filling in the box.
$\begin{array}{l}
19 \quad 76 \\
7 \quad \square
\end{array}$
Answer (2)
To find the missing value in the equivalent fraction, we set up the proportion 7 19 = x 76 . By cross-multiplying and solving, we find that x = 28 . Thus, the equivalent fraction is 28 76 .
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Set up the proportion: 7 19 = x 76 .
Cross-multiply: 19 x = 7 ⋅ 76 .
Solve for x : x = 19 7 ⋅ 76 .
Simplify to find the missing number: x = 28 .
Explanation
Understanding the Problem We are given two fractions, 7 19 and □ 76 , and we need to find the number that goes in the box to make the two fractions equivalent. In other words, we are looking for a number that maintains the same ratio between the numerator and the denominator.
Setting up the Proportion Let's call the missing number x . The problem can be written as an equation: 7 19 = x 76 To solve for x , we can use cross-multiplication.
Cross-Multiplication Cross-multiplication involves multiplying the numerator of the first fraction by the denominator of the second fraction, and setting it equal to the product of the denominator of the first fraction and the numerator of the second fraction: 19 ⋅ x = 7 ⋅ 76
Isolating x Now, we need to isolate x by dividing both sides of the equation by 19: x = 19 7 ⋅ 76
Simplifying the Fraction We can simplify the fraction by noticing that 76 is a multiple of 19 ( 76 = 4 ⋅ 19 ): x = 19 7 ⋅ ( 4 ⋅ 19 ) Now, we can cancel the common factor of 19 from the numerator and the denominator: x = 7 ⋅ 4
Calculating the Final Value Finally, we multiply 7 by 4 to find the value of x : x = 28 So, the missing number in the equivalent fraction is 28.
Final Answer Therefore, the equivalent fraction is: 7 19 = 28 76
Examples
Understanding equivalent fractions is essential in many real-life situations. For instance, when scaling a recipe, you need to maintain the correct ratios of ingredients. If a recipe calls for 2 1 cup of flour and you want to double the recipe, you need to find the equivalent fraction with a denominator that reflects the doubled quantity. Similarly, when working with maps, understanding scale ratios (e.g., 1 inch represents 10 miles) requires using equivalent fractions to determine actual distances. These concepts are also crucial in financial calculations, such as converting currencies or calculating proportions of investments.
