Basic Addition, Subtraction, Multiplication and Division - SSAT Upper Level Quantitative

First, convert $\frac{1}{4}$ into a decimal. We are left with

.24+2.5+.25

Now add the three numbers, being careful to line the decimal points up exactly. From right to left we will add:

1. 4 and 5 = 9

2. 5, 2, and 2 = 9

3. 2 is alone = 2

This leaves us with 2.99 for the final answer.

Use order of operations, so you would first complete the operation in the parentheses, which would give you .

Then you do exponenets, so .

Then you do division which is .

Then you do addition from left to right, so .

Last, you add to , which is .

You add the percentages and you get 142 percent. To convert a percent to a decimal, you divide by 100, so the answer is 1.42.

Supplementary angles add up to 180 degrees. Given that , the correct answer is 135.

Do the expression in the parantheses and you get . Then you do and you get . Then you do and you get . Then you add .

You add all three values and you get .

To find the greatest possible value of , add the greatest possible value of to the greatest possible value of . This happens when is equal to the greatest prime between 35 and 45, which is 43, and when is equal to the greatest prime between 85 and 95, which is 89. Add the two numbers:

can be equal to any of the prime numbers between 45 and 55, of which there are two - 47 or 53.

can be equal to any of the prime numbers between 15 and 25, of which there are three - 17, 19, and 23.

Their sum can be any of the following:

This makes five possible sums.

Since this reasoning is valid regardless of the actual scores, suppose Quinn scored 100. Then Ned scored 19 more than Quinn, or 119, and Melanie scored 12 more than Ned, or 131. Phyllis scored 45 more than Ned, or 164, and Olivia scored 20 points fewer than Phyllis, or 144. This makes the order, from greatest to least:

Phyllis, Olivia, Melanie, Ned, Quinn

Melanie scored third among the five.

To simplify this expression, regroup and combine like-terms.

We can write 18 pounds, 2 ounces as just ounces as follows:

Divide:

Convert 58 ounces to pounds and ounces as follows:

That is, 3 pounds 10 ounces.

Multiply both numerator and denominator by the conjugate of the denominator, which is :

Multiply both numerator and denominator by the conjugate of the denominator, which is :

Multiply both numerator and denominator by :

Multiply both numerator and denominator by the conjugate of the denominator, which is :

Multiply both numerator and denominator by the conjugate of the denominator, which is :

This is not among the given choices.

Multiply both numerator and denominator by the conjugate of the denominator, which is

The values are of the same power. Divide the terms.

The correct answer is:

First multiply the fraction in the numerator.

$\frac{1}{2}$times $\frac{1}{3}$=\frac{1times 1}{2times 3}$=\frac{1}{6}$

Now we have $\frac{frac{1}{6}$}{$\frac{1}{9}$}

Never divide fractions. We multiply the numerator by the reciprocal of the denominator.

$\frac{frac{1}{6}$}{$\frac{1}{9}$}=\frac{1}{6}$div $\frac{1}{9}$=\frac{1}{6}$times $\frac{9}{1}$=\frac{1times 9}{6times 1}$=\frac{9}{6}$=\frac{3}{2}$

The easiest way to see that all four are equivalent is to convert each to a decimal product, noting that twenty percent and one-fifth are equal to , and twenty-five percent and one fourth are equal to .

One fourth of 0.2:

One fifth of 0.25:

Twenty-five percent of one fifth:

Twenty percent of one fourth: