double the sum of a double the number and quotient of five and two. write as an algebraic expression.
double the sum ... 2(? + ?)
double the number ... 2x
quotient of five and two ... 5/2
So,
2(2x + 5/2) = 4x+5
To write the expression, let's break it down step by step:
Step 1: Start with a number.
Let's call this number "x".
Step 2: Double the number.
To double the number, we multiply it by 2.
The expression so far: 2x
Step 3: Find the quotient of five and two.
To find the quotient, we divide five by two.
The expression so far: 2x + 5/2
Step 4: Multiply the result from step 3 by double the number.
To do this, we multiply the result from step 3 by 2.
The expression becomes: 2x + 2(5/2)
Simplifying further: 2x + 10/2
Final expression: 2x + 5
To write the given problem as an algebraic expression, let's break it down step by step:
Step 1: "Double the number"
Let's represent the number as 'x'. To double it, we multiply it by 2, so the expression becomes 2x.
Step 2: "Quotient of five and two"
Dividing 5 by 2 gives us 2.5. Since we need to represent it as an algebraic expression, we can write it as 5/2 or (1/2) * 5.
Step 3: "Sum of 2x and (5/2)"
To find the sum of two expressions, you simply add them together. So the sum of 2x and (5/2) is expressed as 2x + (5/2).
Step 4: "Double the sum"
To double an expression, multiply it by 2. Therefore, the double of 2x + (5/2) is 2 * (2x + (5/2)).
Putting it all together, the algebraic expression is:
2 * (2x + (5/2))
Simplifying this expression further would involve distributing the 2 across the parentheses if desired.