How to multiply variables - SSAT Middle Level Math

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Question

Which of the following is NOT the same as

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

Answer

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

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Question

Simplify:

Answer

Apply the distributive property:

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

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Question

Simplify:

Answer

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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Question

Simplify: $-6 \left ( 5x - 3y - 9 \right )$

Answer

Apply the distributive property:

$-6 \left ( 5x - 3y - 9 \right )= -6 \cdot 5x - \left (-6 \right ) \cdot 3y - \left (-6 \right ) \cdot 9$

$= -6 \cdot 5x + 6 \cdot 3y + 6 \cdot 9$

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Question

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

Answer

Apply the distributive property:

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

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Question

Shaun has twice as much money as Jessica. Jessica has one third as much money as Chris. Shaun has half as much money as Carmen. Who has the most money?

Answer

In order to figure out who has the most money, we must organize the data we have. Since Shaun has more money than Jessica, let us use Jessica as our baseline. So, if the money that Jessica has is represented by , the money Shaun has will be because he has twice as much money as Jessica.

Jessica =

Shaun =

Next, we know that Jessica has one third as much money as Chris. In other words, Chris has three times as much money as Jessica. This can be represented by . We then learn that Shaun has half as much money as Carmen or, in other words, Carmen has two times the amount of money Shaun has. Since Shaun has dollars, that must mean Carmen has dollars because $2\times 2m = 4m$ . So, by comparing everyone side-by-side, we can see that Carmen has the most money as she has four times the amount of money that Jessica has.

Jessica =

Shaun =

Chris =

Carmen =

Carmen is the answer.

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Question

Given , , and , compute .

Answer

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

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Question

Simplify:

$4m\cdot3m$

Answer

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 $12m^{2}$ .

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Question

Simplify:

Answer

When simplifying this expression, the first step is to apply the distributive property.

$(3a\times2a)+(3a\times4)-7$

$6a^{2}+12a-7$

Next, we assert whether the expression can be reduced further. It cannot, as there are no like-terms to combine.

Therefore, the correct answer is $6a^{2}+12a-7$ .

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Question

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

Answer

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".

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Question

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?

Answer

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

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Question

Suppose you know the values of all variables in the expression

$r+ n \cdot k -q$

and you want to evaluate the expression.

In which order will you carry out the operations?

Answer

By the order of operations, in the absence of grouping symbols, multiplication takes precedence over addition and subtraction. Addition and subtraction are then carried out with equal priority, but from left to right, so the addition is performed second and the subtraction last.

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Question

Multiply in modulo 8:

$6 \times 3 \times 2$

Answer

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.

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Question

Solve the following expression,

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

Answer

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 $10x^{5}$ .

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Question

Solve:

$(x^{4}y^{5}) (x^{2}yz)$

Answer

When multiplying variables with exponents, add the exponents.

$(x^{4 })(x^{2}) = x^{4+2} = x^{6}$

$(y^{5})(y^{1}) =y ^{5+1} =y^{6}$

$z^{1} = z$

The correct answer is $x^{6}y^{6}z$

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Question

Solve:

$(ab^{3}c^{4})(ab^{4}c^{2})$

Answer

When multiplying variables with exponents the exponents are added.

$(a)(a) = a^{1+1} =a^{2}$

$(b^{3}) (b^{4})= b^{3+4} = b^{7}$

$(c^{4}) (c^{2}) = c^{4+2} = c^{6}$

The correct answer is $a^{2}b^{7}c^{6}$

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