Complete the equivalent fraction by filling in the box.
$\frac{19}{7}=\frac{76}{\square}$
Answer (2)
Let x be the missing number: 7 19 = x 76 .
Cross-multiply: 19 x = 7 × 76 .
Divide by 19: x = 19 7 × 76 .
Simplify to find the missing number: x = 28 , so the equivalent fraction is 7 19 = 28 76 .
The missing number is 28 .
Explanation
Understanding the Problem We are given the equation 7 19 = □ 76 and asked to find the number that goes in the box to make the fractions equivalent.
Setting up the Equation Let x be the number in the box. Then we have the equation 7 19 = x 76 .
Cross-Multiplication To solve for x , we can cross-multiply, which means multiplying both sides by 7 x . This gives us 19 x = 7 ⋅ 76 .
Isolating x Now, we divide both sides by 19 to isolate x : x = 19 7 ⋅ 76 .
Simplifying the Fraction We can simplify the fraction by noticing that 76 = 4 ⋅ 19 , so x = 19 7 ⋅ 4 ⋅ 19 .
Canceling Common Factors Now we cancel the 19s: x = 7 ⋅ 4 .
Calculating the Result Finally, we calculate x = 28 . Therefore, the missing number in the box is 28.
Examples
Understanding equivalent fractions is crucial in many real-life situations. For instance, when scaling a recipe, you might need to double or triple the ingredients while maintaining the correct proportions. If a recipe calls for 4 1 cup of sugar and you want to double the recipe, you need to find the equivalent fraction with a denominator that suits your measuring tools, such as 8 2 or 16 4 cup. This ensures the recipe tastes the same, just in a larger quantity. Similarly, when dealing with discounts or sales, understanding equivalent fractions helps you calculate the actual savings and make informed purchasing decisions.
The missing number in the equivalent fraction 7 19 = □ 76 is 28. This can be found by cross-multiplying and isolating the variable. Therefore, 28 76 is equivalent to 7 19 .
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