# SSAT Upper Level Math : Basic Addition, Subtraction, Multiplication and Division

## Example Questions

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### Example Question #31 : Basic Addition, Subtraction, Multiplication And Division

Fill in the circle to yield a true statement:

The other answer choices are incorrect.

The other answer choices are incorrect.

Explanation:

The problem is asking for a number whose product with 6 yields a number congruent to 5 in modulo 12 arithmetic - that is, a number which, when divided by 12, yields remainder 6.

However, 6 multiplied by any odd number yields a number which, when divided by 12, yields remainder 6, as is demonstrated using our choices:

Each of the choices yields a product congruent to 6 modulo 12, so none of them is a correct choice.

### Example Question #32 : Basic Addition, Subtraction, Multiplication And Division

Write  in scientific notation.

Explanation:

Scientific notation is used to simplify exceptionally complex numbers and to quickly present the number of significant figures in a given value. The value is converted to an exponent form using base ten, such that only a single-digit term with any given number of decimal places is used to represent the significant figures of the given value. Non-significant zeroes can be omitted from the leading term, and represented only in the base ten exponent.

The given number has three significant figure () so we write out number as

You must move the decimal place two places to the right, or in other words multiply by . When you move the decimal place to the right, you multiply the number by , so it is .

### Example Question #33 : Basic Addition, Subtraction, Multiplication And Division

Divide:

Explanation:

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.

### Example Question #34 : Basic Addition, Subtraction, Multiplication And Division

Simplify by rationalizing the denominator:

Explanation:

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

### Example Question #35 : Basic Addition, Subtraction, Multiplication And Division

Simplify by rationalizing the denominator:

Explanation:

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

### Example Question #36 : Basic Addition, Subtraction, Multiplication And Division

Simplify by rationalizing the denominator:

None of the other responses is correct.

Explanation:

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

### Example Question #37 : Basic Addition, Subtraction, Multiplication And Division

Simplify by rationalizing the denominator:

The correct answer is not among the other responses.

The correct answer is not among the other responses.

Explanation:

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

This is not among the given choices.

### Example Question #38 : Basic Addition, Subtraction, Multiplication And Division

Simplify by rationalizing the denominator:

Explanation:

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

### Example Question #39 : Basic Addition, Subtraction, Multiplication And Division

Simplify by rationalizing the denominator:

Explanation:

Multiply both numerator and denominator by :

Divide: