Algebraic Concepts

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ISEE Middle Level Quantitative Reasoning › Algebraic Concepts

Questions 1 - 10

1

Solve for :

$- \frac{1}{4}r - (-3)=34$

Explanation

$- \frac{1}{4}r - (-3)=34$

$- \frac{1}{4}r - (-3) + (-3) =34 + (-3)$

$- \frac{1}{4}r =34 -3$

$- \frac{1}{4}r =31$

$- \frac{1}{4}r \div \left ( - \frac{1}{4} \right ) =31 \div \left ( - \frac{1}{4} \right )$

$r =31 \cdot \left ( - 4 \right )$

2

Which is the greater quantity?

(a)

(b)

(a) is the greater quantity

(b) is the greater quantity

(a) and (b) are equal

It is impossible to determine which is greater from the information given

Explanation

Solving both equations:

$4t \div 4 = 59 \div 4$

$t = 14 \frac{3}{4}$

$3u \div 3 = 41 \div 3$

$u = 13\frac{2}{3}$

.

3

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

The sum of a number and seven subtracted from one hundred

The difference of a number and seven added to one hundred

The difference of seven and a number added to one hundred

One hundred subtracted from the sum of a number and seven

The correct answer is not given among the other responses

Explanation

is $x + \textrm{7}$ subtracted from one hundred.

$x + \textrm{7}$ is the sum of a number () and seven.

Therefore,

is the sum of a number and seven subtracted from one hundred.

4

Which is the greater quantity?

(a)

(b)

(a) is the greater quantity

(a) and (b) are equal

It is impossible to determine which is greater from the information given

(b) is the greater quantity

Explanation

5

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

The sum of a number and seven subtracted from one hundred

The difference of a number and seven added to one hundred

The difference of seven and a number added to one hundred

One hundred subtracted from the sum of a number and seven

The correct answer is not given among the other responses

Explanation

is $x + \textrm{7}$ subtracted from one hundred.

$x + \textrm{7}$ is the sum of a number () and seven.

Therefore,

is the sum of a number and seven subtracted from one hundred.

6

Which is greater?

(A)

(B)

(B) is greater

(A) is greater

(A) and (B) are equal

It is impossible to determine which is greater from the information given

Explanation

$-7K\div (-7) = 91 \div (-7)$

$-6M \div (-6) = 72 \div (-6)$

, so .

Therefore , so (B) is greater.

7

Solve the equation:

Explanation

To solve to the equation isolate the variable on one side of the equation with all other constants on the other side. To accomplish this perform opposite operations to manipulate the equations.

First subtract 18 from both sides.

Now divide by 8 on both sides.

$8t \div 8 = 114 \div 8$

8

Evaluate .

Explanation

.

9

Which is the greater quantity?

(a)

(b)

(a) is the greater quantity

(a) and (b) are equal

It is impossible to determine which is greater from the information given

(b) is the greater quantity

Explanation

10

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

The sum of a number and seven subtracted from one hundred

The difference of a number and seven added to one hundred

The difference of seven and a number added to one hundred

One hundred subtracted from the sum of a number and seven

The correct answer is not given among the other responses

Explanation

is $x + \textrm{7}$ subtracted from one hundred.

$x + \textrm{7}$ is the sum of a number () and seven.

Therefore,

is the sum of a number and seven subtracted from one hundred.

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