# HSPT Math : Arithmetic

## Example Questions

### Example Question #21 : Fractions

The gas tank in Renee's mustang is filled to capacity at  gallons.  She used  of a tank of gas to take a drive to the shore.  How much gas did it take to drive to the shore?

gallons

gallons

gallons

gallons

gallons

Explanation:

To solve this word problem, multiply the fractions.  First convert any mixed number to an improper fraction:

Next, multiply the numerators and the denominators of both improper fractions.

gallons of gas was consumed on Renee's trip to the shore.

### Example Question #52 : Arithmetic

The height or h of a triangle is  inches.  The base or b =  inches. What is the area of the triangle?

Explanation:

The formula for the Area of a triangle is:

where b represents the base and h represents height.

Convert any mixed numbers to improper fractions.

Plug in the values for the base and the height into the formula; multiply.

Reduce to simplest form by dividing the numerator and the denominator by the Greatest Common Factor (GCF) of 18 and 48, which is 6.

Because a triangle is two-dimensional, the answer must be represented in square units.

### Example Question #13 : How To Multiply And Divide Fractions

A rectangular prism has a length of  cm, a width of cm, and a height of  cm.  What is the volume of this rectangular prism?

Explanation:

The formula for the Volume of a rectangular prism is:, where

,    and

Convert mixed numbers (whole number and fraction) to improper fractions.

Reduce to simplest form by dividing the numerator and the denominator of the fraction by the Greatest Common Factor of 12 and 24, which is 12.

A rectangular prism is a 3-dimensional shape, therefore the measurement must be expressed in cubic units.

### Example Question #52 : Arithmetic

Explanation:

The formula for multiplication of fractions is:

Where  and  It doesn't matter if the denominators are not the same. Just multiply the numerators, then multiply the denominators and simplify.

A negative times a positive is a negative.

To simplify, divide the numerator and the denominator by the GCF or the greatest common factor, which is 15.

### Example Question #54 : Arithmetic

Evaluate , if    ,      ,    and   .

Explanation:

Evaluate , if     ,     ,     and

(A positive times a negative is negative, and a negative times a positive is negative.)

Simplify by dividing the numerator and the denominator by the GCF or the Greatest Common Factor, which is 12.

### Example Question #55 : Arithmetic

What is the product of  ?

Explanation:

To begin solving, convert any mixed numbers to improper fractions, and if there is a whole number, place a one underneath that number to make it an improper fraction.

Then multiply the numerators and then multiply the denominators. Remember, a negative times a positive is a negative.

And a negative times a negative is positive.

Reduce the fraction part of the mixed number to simplest form by dividing both the numerator and the denominator by the GCF or the Greatest Common Factor which is 5.

### Example Question #31 : Fractions

A wheel has a radius of  inches.   What is the circumference of the wheel?

Let,

.

Explanation:

The formula for the circumference of a circle is:

The diameter is found by multiplying the radius by 2.

### Example Question #32 : Fractions

Explanation:

To divide algebraic fractions,  change the fraction that comes after the division sign to its multiplicative inverse or reciprocal.  Then change the division sign to a multiplication sign and multiply.

The multiplicative inverse for

Because there is  in the numerator of the first fraction and  in the denominator of the second fraction, they will cancel out. What is left is:

### Example Question #51 : Arithmetic

Explanation:

To divide algebraic fractions,  change the fraction that comes after the division sign to its multiplicative inverse or reciprocal.  Then change the division sign to a multiplication sign and multiply.

The multiplicative inverse for

Reduce this to simplest form by dividing both the numerator and the denominator by the Greatest Common Factor of  and, which is .