How to multiply variables

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SSAT Middle Level Quantitative › How to multiply variables

Questions 1 - 10

1

Which of the following is NOT the same as

$z\times \frac{(2x+3y)}{3}$

$\frac{2zx +zy}{3}$

$\frac{2zx}{3}+zy$

$\frac{2zx+3zy}{3}$

$\frac{z}{3}\times(2x+3y)$

$z\times(\frac{2x}{3}+y)$

Explanation

The answer shows that the 3 in front of the has been cancelled, but not removed from the denomitator for the .

2

Solve the following expression,

$5x^{2}*2x^{3}$ .

$10x^{5}$

$7x^{5}$

$10x^{6}$

$7x^{6}$

The expression is already solved.

Explanation

When multiplying like variables, the constants are multiplied together.

For the exponents, when you multply variable exponents you have to add the exponents together.

and so that gives you an answer of $10x^{5}$ .

3

Simplify:

Explanation

Apply the distributive property:

$-7 (3x - 11) = -7 \cdot 3x - \left (-7 \right ) \cdot 11 = -7 \cdot 3x + 7\cdot 11= -21x + 77$

4

Multiply in modulo 8:

$6 \times 3 \times 2$

None of the other choices give the correct answer.

Explanation

In modulo 8 arithmetic, a number is congruent to the remainder of the divison of that number by 8. Since

$6 \times 3 \times 2 = 36$

and

$36 \div 8 = 4 \textrm{ R }4$

then

$6 \times 3 \times 2 \equiv 4 \mod 8$ .

The correct response is 4.

5

Suppose you know the values of all variables in the expression

$x \cdot\left ( y + b \right )^{2}$

and you want to evaluate the expression.

In which order will you carry out the operations?

Adding, squaring, multiplying

Squaring, multiplying, adding

Multiplying, adding, squaring

Multiplying, squaring, adding

Adding, multiplying, squaring

Explanation

By the order of operations, the operation inside grouping symbols, which here is addition, takes precendence, followed by, in order, squaring and multiplication.

6

Which of the following phrases can be written as the algebraic expression ?

Fifty-five subtracted from the product of nine and a number

The product of nine and a number subtracted from fifty-five

Nine multiplied by the difference of a number and fifty-five

Nine multiplied by the difference of fifty-five and a number

The correct answer is not given among the other responses.

Explanation

is fifty-five subtracted from .

is the product of nine and a number.

Subsequently, is "fifty-five subtracted from the product of nine and a number".

7

Simplify:

$4m\cdot3m$

$12m^{2}$

$6m^{2}$

$12m^{3}$

Explanation

To solve, you can use the commutative and associative properties of multiplication to group like-terms together.

$4m\cdot3m=4\times m\times 3\times m=4\times3\times m\times m$

The 4 and 3 should be first multiplied, resulting in 12.

$12\times m\times m$

Next should be multiplied by , giving us $m^{2}$ .

$12\times m^2$

12 times $m^{2}$ is equal to $12m^{2}$ .

Therefore, the correct answer is $12m^{2}$ .

8

Given , , and , compute .

Explanation

refers to the product of the three variables: $3\cdot 6\cdot 3=54$ .

9

Simplify: $6 \left ( 5x - 3y + 7 \right )$

Explanation

Apply the distributive property:

$6 \left ( 5x - 3y + 7 \right ) = 6 \cdot 5x - 6 \cdot 3y + 6 \cdot 7=30x - 18y + 42$

10

Simplify:

Explanation

Apply the distributive property:

$-5 (-3x + 13) = -5 (-3x) + \left (-5 \right ) \cdot 13= 5\cdot 3x - 5\cdot 13 = 15x -65$

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