Arithmetic

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PSAT Math › Arithmetic

Questions 1 - 10
1

What property of arithmetic is demonstrated here?

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.

2

Write 7.5% as a fraction.

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

3

What is the reciprocal of the following fraction: 18/27

9

27/18

-18/27

9/27

Explanation

A fraction multiplied by its reciprocal will equal 1. To find the reciprocal of a fraction, switch the denominator and numerator. The reciprocal of 18/27 is 27/18.

4

Explanation

Factor each number into prime roots:

5

Write as a fraction: 22%

4/9

2/3

4/7

11/50

11/100

Explanation

22% = 22/100

Divide everything by 2:

22/100 = 11/50

11 is a prime number, so this is as reduced as this fraction can get.

6

If x = 1/3 and y = 1/2, find the value of 2_x_ + 3_y_.

13/6

1

2

6/5

5/6

Explanation

Substitute the values of x and y into the given expression:

2(1/3) + 3(1/2)

= 2/3 + 3/2

= 4/6 + 9/6

= 13/6

7

If x = 1/3 and y = 1/2, find the value of 2_x_ + 3_y_.

13/6

1

2

6/5

5/6

Explanation

Substitute the values of x and y into the given expression:

2(1/3) + 3(1/2)

= 2/3 + 3/2

= 4/6 + 9/6

= 13/6

8

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.

9

If x = 1/3 and y = 1/2, find the value of 2_x_ + 3_y_.

13/6

1

2

6/5

5/6

Explanation

Substitute the values of x and y into the given expression:

2(1/3) + 3(1/2)

= 2/3 + 3/2

= 4/6 + 9/6

= 13/6

10

Write 7.5% as a fraction.

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

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