HSPT Math : Problem Solving

Example Questions

Example Question #41 : Problem Solving

Divide:

Explanation:

Rewrite the expression using a division sign.

Convert the sign to a multiplication sign, and take the inverse of the second term.

Example Question #1 : How To Multiply And Divide Fractions

A tree feet high casts a shadow 20 feet long at the same time a tree 30 feet high casts a shadow how many feet long? Give your answer in terms of .

Explanation:

The ratio of the height of an object to the length of the shadow it casts at a point in time is the same for all objects, so, if we let the length of the shadow cast by the second tree be :

Set the cross-products equal to each other and solve for

, the correct choice.

Example Question #43 : Problem Solving

The length and width of a given make of car are 4.5 and 1.8 meters, respectively.

A scale model of this make of car will be  feet long. In terms of , how wide will this scale model be?

Explanation:

The ratio of the width of the scale model to its length is the same as the comparable ratio for the actual car, so we can set up this equation:

Example Question #44 : Problem Solving

Edna needs  cups of sugar to make 24 of her world-famous Oatmeal Chocolate Dynamite Cookies.

She has  cups of sugar on hand. If the other ingredients are sufficiently plentiful, then in terms of , how many cookies can she make? (Note: the number of cookies need not be a multiple of 24.)

Explanation:

An easier way to look at the number of cookies Edna can make with her sugar is as follows:

cups of sugar go into making 24 cookies, so

cups of sugar go into making  cookies.

1 cup of sugar, therefore, goes into making  cookies.

cups go into making , or , cookies. This is the correct response.

Example Question #11 : How To Multiply And Divide Fractions

On a map, one half of an inch represents  miles of real distance.

On the map, Lincoln County, which is perfectly rectangular, is four and one-fourth inches wide by three and three-fourths inches high. In terms of , give the area of Lincoln County in square miles.

Explanation:

The dimensions of Lincoln County on the map are inches by inches.

One half of an inch represents miles, so one whole inch represents twice this, or miles. Consequently,

inches represents miles, and

inches represents  miles.

Therefore, in real distance, Lincoln County has dimensions miles and miles, and the area is the product of these two, or

.

Example Question #12 : How To Multiply And Divide Fractions

One of Floyd's World Famous Ooey Gooey Butter Cakes requires two and one-half cups of flour and four eggs, among other ingredients.

Floyd wants to make seven of these cakes for a wedding. He has sixteen cups of flour on hand as well as three dozen eggs. Assuming he has enough of all other ingredients, can Floyd make the seven cakes he wants to make?

No, because he does not have enough flour.

Yes.

No, because he does not have enough eggs.

No, because he does not have enough flour or enough eggs.

No, because he does not have enough flour.

Explanation:

In order to make seven butter cakes, Floyd must use

eggs.

Floyd has three dozen, or 36, eggs on hand, so he has enough eggs.

Floyd must use

cups of flour.

Floyd has 16 cups on hand, so he does not have enough flour.

Example Question #13 : How To Multiply And Divide Fractions

Explanation:

The formula for multiplication of fractions is:

Where  and

Convert each mixed number to an improper fraction; then multiply.

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

Convert the improper fraction back to a mixed number by dividing the numerator by the denominator.

Simplify by dividing the numerator and denominator of the fraction part of the mixed number by the GCF or Greatest Common Factor which is 2.

reduced to simplest form is

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

Example Question #14 : How To Multiply And Divide Fractions

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.

To simplify, divide the numerator and the denominator by the GCF or the greatest common factor, which is 3.

Example Question #41 : Problem Solving

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.

Convert any mixed number (whole number and fraction) to an improper fraction:

To simplify, divide the numerator and the denominator by the GCF, or the greatest common factor, which is 6.

Example Question #16 : How To Multiply And Divide Fractions

What is the area of a rectangle with  cm  and a  cm?

Explanation:

The formula for Area of a rectangle is , where  and

To solve , first convert both mixed numbers to improper fractions.

Then multiply the numerators and the denominators. Simplify.

Because there is a 9 in the numerator and a 9 in the denominator the nines cancel each other out, and you are left with:

Area is 2-dimensional: it has a length and a width. Area is measured in square units.

The area of the rectangle is