Expressions - SAT Math

Since both fractions in the expression have a common denominator of , we can combine like terms into a single numerator over the denominator:

Since both rational terms in the expression have the common denominator , combine the numerators and simplify like terms:

Since both terms in the expression have the common denominator , combine the fractions and simplify the numerators:

To add rational expressions, first find the least common denominator. Because the denominator of the first fraction factors to 2(x+2), it is clear that this is the common denominator. Therefore, multiply the numerator and denominator of the second fraction by 2.

This is the most simplified version of the rational expression.

To simplify the following, a common denominator must be achieved. In this case, the first term must be multiplied by (x+2) in both the numerator and denominator and likewise with the second term with (x-3).

We will need to simplify the expression . We can think of this as a large fraction with a numerator of and a denominator of .

In order to simplify the numerator, we will need to combine the two fractions. When adding or subtracting fractions, we must have a common denominator. has a denominator of , and has a denominator of . The least common denominator that these two fractions have in common is . Thus, we are going to write equivalent fractions with denominators of .

In order to convert the fraction to a denominator with , we will need to multiply the top and bottom by .

Similarly, we will multiply the top and bottom of by .

We can now rewrite as follows:

=

Let's go back to the original fraction . We will now rewrite the numerator:

=

To simplify this further, we can think of as the same as . When we divide a fraction by another quantity, this is the same as multiplying the fraction by the reciprocal of that quantity. In other words, .

=

Lastly, we will use the property of exponents which states that, in general, .

The answer is .

If we plug in _a_2 for b in the radical expression, we get √(_a_3) = 8. This can be rewritten as a_3/2 = 8. Thus, log_a 8 = 3/2. Plugging in the answer choices gives 4 as the correct answer.

To solve this, we need to set a proportion.

Cross Multiply

So it will take Jill to walk

Factor first. The numerators will not factor, but the first denominator factors to (x – 2)(x + 2) and the second denomintaor factors to x(x – 2). Multiplying fractions does not require common denominators, so now look for common factors to divide out. There is a factor of x and a factor of (x + 2) that both divide out, leaving 4 in the numerator and two factors of (x – 2) in the denominator.

6/8 X 20/3 first step is to reduce 6/8 -> 3/4 (Divide top and bottom by 2)

3/4 X 20/3 (cross-cancel the threes and the 20 reduces to 5 and the 4 reduces to 1)

1/1 X 5/1 = 5

The procedure for multplying together two rational expressions is the same as multiplying together any two fractions: find the product of the numerators and the product of the denominators separately, and then simplify the resulting quotient as far as possible, as shown:

The "is" in the question means "equal," so whatever comes before "is" must be equal to whatever comes after. We will find an expression for the information before "is" and an expression for the information after "is," and then we will set these two expressions equal.

Twenty percent of a number can be represented as 0.2n, because 20% expressed as a decimal is 0.2, and because twenty percent "of" a number means the product of that number and twenty percent.

Four greater than the product of a number and six means that we must first find the product of that number and six, and then increase this value by 4.

The product of a number and six means that we must multiply this number by six, which can be represented by 6n. Increasing 6n by 4 can be modeled by the expression 6n + 4, or 4 + 6n (because of the commutative property of addition).

Setting the two expressions equal gives us 0.2n = 4 + 6n .

There are B+G total students in the elementary school class, so G out of B+G are girls.

There are a few ways to do this problem, but we will focus on the total number of votes method as follows. First, let Clinton = C, Gore = G, Paul = P, and Johnson = J. We know C + G + P + J = 150 million. We also know that C = 3J. Paul received 30% of the vote which is 150,000,000 * .3 = 45 million votes. Gore received 30 million votes. We can now create an equation with individual totals and substitute 3J for Clinton's vote total:

3J + 30 million + 45 million + J = 150 million

4J = 75 million

J = 18.75 million

Then C = 3J = 56.25 million. So Clinton received 56.25 million votes, Paul received 45 million votes, Gore received 30 million votes, and Johnson received 18.75 million votes. The correct answer is Hillary Clinton.

The easiest way to solve this problem is to guess-and-check the answer choices. The equation that can be used to match the table will be correct.

We can see that the values in the table match the equation for each given value. Thus, this must be our answer.

We can also determine certain characteristics from the table itself. For example, as x increases, y(x) decreases. This tells us that there is likely a negative coefficient, which can help narrow down the answer options.

Find how many free throws Justin made: 84 x 0.619 = 51.99. Since the problem talks free throws, we round to 52 shots went in. To calculate shots missed:

84 – 52 = 32.

Combine like terms by subtracting 6 from both sides so: 5x + 24 = –7x. Then subtract 5x from both sides: 24 = –12x. Divide both sides by –12 and x = –2.