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1

Explanation

To subtract decimals you place the first decimal over the top of the other aligned by the decimal point. If there are no numbers after a tens, hundredths, or thousandths place or further to the right of the decimal just add a zero in the required areas.

For example becomes

Then go through each place and subtract the top number by the bottom number. Subtract the numbers in each place like you would any number.

The example we are working with will look like this

The answer after subtraction is

2

Multiply:

Explanation

First, multiply the numbers, ignoring the decimal points:

Since the two factors in the original product have three digits to the right of the decimal points between them, position the decimal point in the product such that three digits are at its right. The result, therefore, is

3

A trapezoid has height 32 inches and bases 25 inches and 55 inches. What is its area?

Explanation

Use the following formula, with :

4

The ratio of the perimeter of one square to that of another square is . What is the ratio of the area of the first square to that of the second square?

Explanation

For the sake of simplicity, we will assume that the second square has sidelength 1; Then its perimeter is , and its area is .

The perimeter of the first square is , and its sidelength is . The area of this square is therefore .

The ratio of the areas is therefore .

5

Spinner target

Above is a target. The radius of the smaller quarter-circles is half that of the larger quarter-circles.

A blindfolded man throws a dart at the above target. Assuming the dart hits the target, and that no skill is involved, give the odds against the dart landing in the yellow region.

39 to 1

13 to 1

14 to 1

40 to 1

Explanation

Call the radius of one of the smaller quarter-circles 1 (the reasoning is independent of the actual radius). Then the area of each quarter-circle is

.

Each of the four wedges of one such quarter-circle has area

.

The yellow region is one such wedge.

The radius of each of the larger quarter-circles is 2, so the area of each is

The total area of the target is

Therefore, the yellow wedge is

of the target, and the odds against the dart landing in that region are 39 to 1.

6

Explanation

To most effectively add a positive and negative number, ignore the signs and pick the greater of the two numbers.

In this case the positive number has a higher value if we don’t pay attention to the signs. Due to this fact we know the answer will be positive.

We then subtract the smaller number value from the higher value which gives us

Then we add the sign of the greater value to arrive at our answer .

7

A trapezoid has height 32 inches and bases 25 inches and 55 inches. What is its area?

Explanation

Use the following formula, with :

8

A square is 9 feet long on each side. How many smaller squares, each 3 feet on a side can be cut out of the larger square?

Explanation

Each side can be divided into three 3-foot sections. This gives a total of squares. Another way of looking at the problem is that the total area of the large square is 81 and each smaller square has an area of 9. Dividing 81 by 9 gives the correct answer.

9

What is 16.7548 rounded to the nearest tenth?

\dpi{100} 16.8

\dpi{100} 16.7

\dpi{100} 16.755

\dpi{100} 16.75

Explanation

The tenth's place is the position one unit to the right of the decimal point. In this case, that is the 7.

After identifying the position, we need to determine if this number remains 7 or if we need to round it up to 8. If the number to the right of the tenth's place is 4 or lower, then our number will remain 7. If it is 5 or greater, then we will round the 7 up to 8.

In this case, the number is indeed 5, so our tenth's place becomes 8. All numbers to the left of the tenth's place will remain the same.

10

Find the area of a square if the length is .

Explanation

The area of a square is:

Substitute the length and simplify.

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