[tex]\frac{5}{7} \times \frac{14}{35}=\frac{70}{245}[/tex]
Answer (2)
We simplified the left side of the equation, showing that 7 5 × 35 14 equals 245 70 . Upon rewriting, we found that the missing number x is 1, satisfying the equation. Thus, the final answer is 1 .
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Simplify the left side of the equation: 7 5 × 35 14 = 245 70 .
Rewrite the equation: 245 70 = 245 70 ÷ x .
Isolate x by multiplying both sides by x: 245 70 x = 245 70 .
Solve for x by dividing both sides by 245 70 : x = 1 . The missing number is 1 .
Explanation
Understanding the Problem We are given the equation 7 5 × 35 14 = 245 70 ÷ and we need to find the missing number to complete the equation.
Setting up the Equation Let x be the missing number. The equation is 7 5 × 35 14 = 245 70 ÷ x .
Simplifying the Left Side First, let's simplify the left side of the equation: 7 5 × 35 14 = 7 × 35 5 × 14 = 245 70
Rewriting the Equation Now we have: 245 70 = 245 70 ÷ x
Isolating x To solve for x , we can multiply both sides of the equation by x : 245 70 x = 245 70
Solving for x Now, divide both sides by 245 70 to isolate x : x = 245 70 245 70 = 1
Final Answer Therefore, the missing number is 1.
Examples
Imagine you are scaling a recipe. If you multiply the ingredients by a certain fraction on one side of the recipe, you need to divide by the same number on the other side to keep the recipe balanced. This problem illustrates the basic principle of maintaining equality in equations, which is crucial in many real-life situations, such as balancing chemical equations, calculating financial transactions, or designing engineering structures.
