Write and solve an equation for thius sentence: The quotient of a number and -14 is 7.?

Answer 1

x/(-14) = 7
x = -14 * 7
x = -98

Answer 2

Sum: result of an addition. The numbers that you are summing are called addends.

Difference: result of a subtraction. The number you are subtracting from is the minuend; the number being subtracted, the subtrahend. When you are asked for the difference of number u and number v, number u is usually the minuend; v, the subtrahend. This is also the way you enter the numbers into a calculator to do a subtraction: minuend, minus sign, subtrahend. The difference is written u - v. However, if you are asked to subtract v from u, the first number is the subtrahend. Getting the numbers in the right order is important with subtraction because interchanging the numbers (usually) gives a different result.

Product: the result of a multiplication. The top number is the multiplicand and the bottom number is the multiplier. Because the order makes no difference in the result of a multiplication, both are sometimes called multipliers or factors.

Quotient: the result of a division. The divisor is the number you are dividing by and the dividend is the number being divided into. If you are asked for "the quotient of u and v," the first number given is the dividend and the second is the divisor. When written as a fraction, the number on top is the dividend and the one on the bottom is the divisor. When doing a division on a calculator, you enter the dividend first, then the divide sign, then the divisor.

You can translate your sentence into math notation as follows:

"The quotient...": this is a division problem.

"...of a number...": the first number, which is the dividend, has not been given. Assign it a variable, which is often x unless you have a preference for another symbol. The expression thus far is therefore

x / ....

"...and -14...: This is the second number, which is the divisor. Expression now is

x / (-14)

The parentheses around the -14 are necessary in this case to prevent the sign on the number from being interpreted as a subtract.

"...is..." translates in this context into "equals". What was formerly just a mathematical expression has now become part of a mathematical sentence, with the equals sign being the verb. This makes it into an equation - an incomplete one because we don't know what x / 14 "is" yet. The incomplete equation can now be written as

x / (-14) = ...

"...7," which is the quotient and the number that belongs on the other side of the equals sign.

x / (-14) = 7.

In algebra, to solve an equation, you ultimately try to get your unknown variable by itself on one side of the equals sign and everything everything else on the other side. Conventionally, the left side is chosen as the side to put the variable, but some equations are more easily solved by putting the variable on the right. This, however, isn't one of them.

You undo divisions by multiplying both sides of the equation by the divisor. Therefore, we undo the divide by -14 on the left by multiplying both sides by -14, giving

x / (-14) * (-14) = 7 * (-14)

Actually, the multiply sign (*) on the right is often omitted. Some might also omit the multiply sign on the left too. This is a convention that has become so strongly established that the multiply is often omitted from the spoken description of an expression as well. The expression "2x," for example, is often read as "two-ex" rather than "two times ex," which means the same thing. Similarly, "xy" is usually read "ex wye," but it could also be read as "ex times wye."

But enough digression; back to the problem at hand. Because the divide by -14 and the multiply by -14 undo each other, we are left with x on the left side, for

x = 7 * (-14).

We have now isolated the variable on the left. To find out what x is, we must now perform the arithmetic on the right, to give

x = 98.

Answer 3

quotient means division

let x be the number

x / -14 = 7

mulitply -14 for both side
x = -98

Answer 4

x/-14=7
Solve by multiplying both sides by -14.
x=-98

Answer 5

x/-14=7
x = -98
OR
-14/x = 7
x= -2