How to multiply integers

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PSAT Math › How to multiply integers

Questions 1 - 5

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 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.

Multiply in modulo 8:

$5 \times 6 \times 7$

None of the other responses is correct.

Explanation

In modulo 8 arithmetic, a number is congruent to the remainder of its division by 8.

$5 \times 6 \times 7 = 210$

and

$210 \div 8 = 26\textrm{ R }2$

$5 \times 6 \times 7 \equiv 2 \mod 8$

making the correct response.

An office wants to buy 22 computers at $900 each. The budget is $20,000 and the tax on computers is 9%. How many computers can the office afford?

Explanation

The office can only afford 20 computers.

1.09 * 900 = $981 is the actual price of each computer, with tax.

Divide:

20,000/981 = 20.39

Since the office cannot purchase a partial computer, we round down to 20 computers.

$F=ma$ in physics where $Force=mass\times acceleration$ .

If the mass is increased by 3 three times the original and the acceleration is increased by 7 times the original, how many times greater is the new force than the original force?

$21$

$7$

$3$

$0$

$10$

Explanation

We simply multiply the new mass by the new acceleration to obtain a new force that is 21 times greater than the original.

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