Algebraic Expressions

The statement is true because product, sum, difference, and quotient are all mathematical operations that involve performing calculations on numbers. In order to clearly indicate the expression that needs to be calculated, it is common practice to put parentheses around it. Therefore, the answer is true as all these operations require the use of parentheses.

The given expression "5+y" represents the phrase "five more than a number". It implies that we are adding 5 to a certain number y, resulting in the sum of 5 and y. The expression does not simplify further as it is already in its simplest form.

The expression "20-y" represents the phrase "twenty less a number." The variable "y" represents the unknown number that is being subtracted from 20. Therefore, the expression "20-y" correctly represents the given phrase.

The given expression represents the product of 8 and a number, which can be represented as 8y. The variable "y" represents the unknown number being multiplied by 8. Therefore, the correct answer is 8y.

The expression "4x + 5x" represents 4 times a variable (x) plus 5 times the same variable. By combining like terms, we simplify the expression to 9x, indicating the total value obtained by adding 4x and 5x together. This demonstrates the distributive property of multiplication over addition and simplifies the expression to its simplest form.

The given expression "8/y" represents the division of the number 8 by another number, denoted as "y". The answer is "eight divided by a number" because it describes the operation of dividing 8 by an unknown value, which is represented by the variable "y".

The given expression, 7+1/3x, represents the sum of 7 and one third of a number x. This can be understood by breaking down the expression: 1/3x represents one third of the number x, and when we add 7 to it, we get the result of 7 more than one third of the number x.

The given expression "y+6" represents the phrase "six more than a number". This means that a certain number, represented by "y", is being added to 6. So, the expression "y+6" correctly represents the phrase "six more than a number".

The given expression represents the sum of 20 and a number x, divided by 5. This can be simplified as (20+y)/5.

The given question states "a+b" and describes it as "A number increased by a number." This implies that the expression "a+b" represents the sum of two numbers, where one number is added to another number. Therefore, the correct answer is "A number increased by a number."

The given expression (y-10) represents the difference between a number and ten. It subtracts 10 from the variable y, indicating that the value of y is being reduced by 10. This expression can be used to find the numerical difference between any number and ten by substituting the desired value for y.