Arithmetic

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PSAT Math › Arithmetic

Questions 1 - 10

What property of arithmetic is demonstrated below?

$t (r + 7) = t \cdot r + t \cdot 7$

Distributive

Associative

Commutative

Transitive

Symmetric

Explanation

The statements demonstrates that the product of a number and a sum can be found by multiplying the number by each of the addends and adding the products. This is the distributive property of multiplication over addition.

The price of a computer is reduced by 1/8. The new price is then reduced by 1/6. What fraction of the original price is the current price?

1/48

1/24

35/48

23/24

13/48

Explanation

Let the original price = p.

After the first reduction, the price is (7/8)p

After the second reduction, the price is (5/6)(7/8)p = (35/48)p

Write 7.5% as a fraction.

$\frac{7}{5}$

$\frac{14}{100}$

$\frac{3}{40}$

$\frac{15}{2000}$

$\frac{7.5}{10}$

Explanation

First convert the percentage to a decimal:

7.5% = .075

Then turn this into a fraction:

.075 = 75/1000

Simplify by dividing the numerator and denominator by 25:

75/1000 = 3/40

What property of arithmetic is demonstrated here?

$3 \cdot (K \cdot 7) = (3 \cdot K) \cdot 7$

Associative

Commutative

Transitive

Symmetric

Explanation

The symbols express the idea that if three numbers are multiplied, the same product results regardless of which numbers are multiplied first. This is the associative property of multiplication.

What property of arithmetic is demonstrated here?

If and , then .

Transitive

Associative

Commutative

Symmetric

Inverse

Explanation

The symbols express the idea that if a number is less than a second number, which is less than a third, then the first number is less than the third. This is the transitive property of inequality.

There is a 5 to 3 ratio of red marbles to green marbles in a bucket. How many red marbles can be in a bucket of 40 marbles?

Explanation

In this problem, we use a proportion to solve for the number of red marbles in the bucket. Since the ratio is 5 to 3 we can set up a proportion of the red over total where the total is (red marbles + green marbles). We then set this proportion equal to over our new total, which is 40. Then we cross multiply and divide to get the number of red marbles in a bucket of 40 total marbles.

$\frac{red}{total}= \frac{x}{new\ total}\newline \newline \frac{5}{8}=\frac{x}{40} \newline \newline 5*40= 200 \newline \newline 200/8 = 25$

In the 30-day month of January, for every three days it snowed, there were seven days it did not snow. The number of days in January on which it did not snow was how much greater than the number of days in January on which it snowed?

Explanation

The question tells us that for every ten-day period in January (a three-day period plus a seven-day period), it snowed on 3 of those days and did not snow on 7 of those days. Since January has 30 days, it has 3 ten-day periods, so we multiply the numbers given for the 10-day period by 3 to find the number of days with and without snow during the 30-day period. Doing this, we see that it snowed 3 * 3 = 9 days and did not snow 7 * 3 = 21 days during the 30-day period. Since the question asks how much greater the number of days on which it did not snow is than the number of days on which it snowed, we subtract as follows: number of days it did not snow - number of days it snowed = 21 – 9 = 12.

An ice cream parlor serves 36 ice cream flavors. You can order any flavor in a small, medium or large and can choose between a waffle cone and a cup. How many possible combinations could you possibly order?

108

144

172

216

Explanation

36 possible flavors * 3 possible sizes * 2 possible cones = 216 possible combinations.

Shannon decided to go to nearby café for lunch. She can have a sandwich made on either wheat or white bread. The café offers cheddar, Swiss, and American for cheese choices. For meat, Shannon can choose ham, turkey, bologna, roast beef, or salami. How many cheese and meat sandwich options does Shannon have to choose from?