If $j = h$ and $k = m$, then which expression represents the value of g?
$g=\frac{f}{2}$
$g =2 f$
$g=\frac{j}{h}$
Answer (1)
Given j = h , we want to find an expression for g .
Consider the expression g = h j .
Substitute j with h to get g = h h .
Simplify to find g = 1 , so the answer is g = h j .
Explanation
Understanding the Problem We are given that j = h and we need to determine which expression represents the value of g from the given options: g = 2 f , g = 2 f , and g = h j .
Substitution Let's analyze the expression g = h j . Since we know that j = h , we can substitute h for j in the expression.
Performing the Substitution Substituting h for j in the expression g = h j , we get g = h h .
Simplifying the Expression Now, we simplify the expression g = h h . Since any non-zero number divided by itself is 1, we have g = 1 .
Determining the Correct Expression Comparing g = 1 with the given options, g = 2 f and g = 2 f , we see that g = h j simplifies to g = 1 , which is a constant value and does not depend on f . Therefore, the correct expression is g = h j .
Final Answer Therefore, the expression that represents the value of g is g = h j .
Examples
Imagine you are baking a cake and the recipe calls for a certain ratio of flour to sugar. If you know that you have the same amount of flour and sugar (j = h), then the ratio of flour to sugar (g = j/h) is simply 1. This means you have a balanced mix of flour and sugar. This concept of ratios and substitutions is fundamental in many real-life situations, from cooking to engineering, where maintaining the correct proportions is crucial for success.
