Arithmetic is a discipline of mathematics that is concerned with the study of numbers and the application of various operations to those numbers. Addition, subtraction, multiplication, and division are the four fundamental operations of mathematics. The arithmetic concepts that are tested in the GRE are part of the quantitative reasoning measure. It is included to assess basic mathematical skills, the ability to solve problems with quantitative methods, and even understand elementary math concepts. The math questions you will encounter on the GRE General Test Quantitative section or the GRE Mathematics Subject Test will include factorization, integers, remainders, decimals, and other basic topics in arithmetic.
Arithmetic is part of the quantitative test, and this part is defined as the manipulation of numbers. Here are the arithmetic topics tested on the GRE.
- Integers, Fractions, and Decimals. In this part of the tests, the following will be questioned as to how they work. may be from using whole numbers to express parts of an item or in its decimal form.
- PEMDAS. This is used for the order of operations in solving a question. Based on its first letters, solve all the numbers inside the parenthesis, followed by the exponents, then all multiplied numbers, then division, and add or subtract.
- Exponents and Square Roots. In this part, you can see or encounter numbers that are expressed in terms of their base and their exponent, power, or index.
- Absolute Values. Absolute values are also defined as the positive value of x.
- Prime Numbers. These numbers are defined as numbers greater than 1 and are divisible only by 1 and itself.
- Even and Odd Numbers. Here you can see that all even numbers are divisible by two and would give no remainders. On the other hand, odd numbers are not divisible by two.
- Percents and Percent Changes. On this part of the test, you will be asked how to find the percentage of the number.
- Sequences. In this portion of the test, you will see arithmetic progressions or sequences where you will be asked for the difference between the successive terms.
- Ratios, Proportions, and Cross Multiplications. In this area, you’ll see certain questions about the proportions of a number, its ratio, and the use of cross multiplication.
These are some of the fundamental concepts taught in a mathematics class. In the arithmetic concept part of the test, you may be able to encounter these possible topics. (1)
Number properties have four fundamental features, which include commutative, associative, distributive, and identity properties. The properties are exclusively applicable to the operations of addition and multiplication.
The four basic arithmetic operations are addition, subtraction, multiplication, and division, as well as their combinations. Arithmetic covers more complicated operations such as percentage manipulation, square root manipulation, exponentiation manipulation, logarithmic functions, and even trigonometric functions, which are similar to logarithms (prosthaphaeresis). Arithmetic expressions must be evaluated in the order in which the operations are intended to be performed. There are numerous ways to define this, including explicitly using parentheses and relying on precedence rules or using a prefix or postfix notation, which both fix the order of execution in a unique way by themselves. The precedence rules are the most commonly used technique, along with infix notation. Generally speaking, a field is a collection of objects on which all four arithmetic operations (except division by zero) can be performed and on which these four operations fulfill the conventional principles of mathematics (including distributivity).
In solving prime numbers and factorization, you will go from:
- Dividing the given number by the smallest prime number.
- Divide the quotient by the smallest prime number.
- Repeat until your quotient becomes 1.
- Finally, multiply all your prime factors.
In solving factors and multiples, always remember that a multiple is a number that can be divided by another number for a certain time, showing a result with a remainder. The factor on hand is a number of one or two that shows no remainder when we divide them.
All odd numbers or numbers that end with 1, 3, 5, 7, and 9 are not divided by two or two equal groups, while even is a number that can be divided by two or two equal groups and it ends with 2, 4, 6, 8, and 0.
PEMDAS is an order of operations that is used to indicate the sequence of operations that should be performed when solving expressions that contain multiple operations. PEMDAS is an acronym that stands for P-Parenthesis, E-Exponents, M-Multiplication, D-Divide, A-Addition, and S-Subtraction. The PEMDAS is a mathematical order of operation that is used to deal with difficult calculations quickly and efficiently. Students begin by solving the terms enclosed in parenthesis or brackets, then simplifying exponential terms before moving on to multiplication and division operations. Finally, we can discover the answer by performing addition and subtraction operations on the terms remaining in the parentheses or brackets.
When you encounter a question regarding the PEMDAS. Always remember the rules for how to solve it.
- First, start with the parentheses.
- Operations are then performed on the exponents or powers.
- Next, perform the operation of multiplication or division from left to right.
- Lastly, perform operations of addition and subtraction from left to right.
Keep in mind the PEMDAS rule mentioned above to get a correct score on any mathematics test.
When an exponential equation has the same base on each side, the exponents must be equal. If it has different bases, follow this:
- Isolate the exponential part of the equation.
- Take the logarithm of each side of the equation.
- Apply the power property to rewrite the exponent.
- Lastly, solve for the variable.
The formula stated above is helpful in answering exponent and base types of questions. In addition, make sure to use logarithms to solve exponential equations whose terms cannot be rewritten at the same base.
In solving percentages, you may use the basic rules, such as the rule of three.
- Calculate the percentage of a given number.
- Calculate a quantity based on its percentage.
- Calculate the percentage represented as a quantity of another.
Remember that when solving percentages, particularly on the GRE, you calculate the percent of a number, divide it by whole, and multiply it by 100.
Here are some of the GRE arithmetic practice questions:
Directions: Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given, and select one of the following four answer choices:
(A) Quantity A is greater.
(B) Quantity B is greater.
(C) The two quantities are equal.
(D) The relationship cannot be determined from the information given.
Quantity A: 8997 × 9003
Quantity B: 8996 × 9004
Quantity A: 2001/3001
Quantity B: ⅔
Quantity A: (0.625 × 0.4)2
Quantity B: 1.25 × 0.05
Quantity A: 30/49
Quantity B: ⅝
Quantity A: 83 × 83/82
Quantity B: 83 + 83/82
These are some of the practice questions regarding the GRE arithmetic concept. If you want to see and learn more, you can also get your own GRE review materials. (2)