Solve for $w$ in the proportion.
$\frac{w}{7}=\frac{65}{455}$
Answer (2)
We have the proportion 7 w = 455 65 .
Multiply both sides by 7 to get w = 7 × 455 65 .
Simplify the fraction to get w = 7 × 7 1 .
Therefore, w = 1 .
Explanation
Understanding the Proportion We are given the proportion 7 w = 455 65 and we need to solve for w . This means we need to isolate w on one side of the equation.
Isolating w To isolate w , we can multiply both sides of the equation by 7: w = 7 × 455 65 Now we need to simplify the fraction 455 65 .
Simplifying the Fraction We can simplify the fraction by finding the greatest common divisor (GCD) of 65 and 455. Since 455 = 7 × 65 , the GCD is 65. So, we divide both the numerator and the denominator by 65: 455 65 = 455 ÷ 65 65 ÷ 65 = 7 1
Substituting Back Now we substitute the simplified fraction back into the equation for w :
w = 7 × 7 1
Calculating w Finally, we calculate the value of w :
w = 1
Examples
Proportions are useful in everyday life. For example, if you are baking a cake and the recipe calls for 2 cups of flour for every 1 cup of sugar, you can use a proportion to determine how much flour you need if you only want to use half a cup of sugar. In this case, the proportion would be 1 2 = 0.5 x , where x is the amount of flour needed. Solving for x , you would find that you need 1 cup of flour.
To find w in the proportion 7 w = 455 65 , multiply both sides by 7 and simplify the fraction. After calculation, we find that w = 1 . The solution is w = 1 .
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