In the division problem 64.94 divided by 8.5, should the dividend and divisor be multiplied by 10 or 100 to make the divisor a whole number? explain.

10

The divisor is 8.5. When it is multiplied by 10, the digits are all shifted left one place relative to the decimal point. (The decimal point moves right one place relative to the digits.) This makes the number be 85, a whole number.

To make the dividend a whole number, you would multiply it by 100 to shift the decimal point 2 places to the right. However, that is not what is required in order to do long division.

Comment on scaling in division problems

Some of us grew up in an era when the tool of choice for multiplication and division was a slide rule. Using that tool, you need to keep track of the scaling of operands and answers, generally using scientific notation. Here, the problem is about the same as 65/8, so will have an answer that can be estimated to be about 7 or 8. Once we know that, we can do the division without worrying about the decimal point, and scale the result appropriately.

In scientific notation, we might work this problem as ...

... (6.494×10¹)/(0.85×10¹) = 6.494/0.85×10¹⁻¹ = 7.64×10⁰ = 7.64

We put the decimal point in different places in the numerator and denominator because we know that 6.494/8.5 will give a number less than 1, so will need to be rescaled. By choosing the denominator to be 0.85 instead, we do the scaling "up front" so we end up with a number in proper scientific notation after the division.

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions