Fractions on the GMAT
59 flashcards covering Fractions on the GMAT for the GMAT Quantitative section.
Fractions represent parts of a whole, like 1/2 meaning one piece out of two equal pieces. They are a basic building block of math, used for dividing quantities, comparing sizes, and solving real-world problems such as recipes or budgets. On the GMAT, fractions are crucial because they underpin many quantitative questions, helping you tackle topics like ratios, percentages, and algebraic expressions with confidence.
In the GMAT Quantitative section, fractions appear in problem-solving and data sufficiency questions, often involving operations like addition, multiplication, or conversion to decimals. Common traps include forgetting to find a common denominator or mishandling mixed numbers, which can lead to incorrect answers. Focus on simplifying fractions early, practicing word problems that require fraction manipulation, and double-checking for errors in complex setups.
A concrete tip: Always simplify fractions before performing operations to save time and reduce mistakes.
Terms (59)
- 01
Fraction
A fraction is a numerical quantity that represents a part of a whole, expressed as one integer divided by another integer, with the top number called the numerator and the bottom the denominator.
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Numerator
The numerator is the top number in a fraction, indicating how many parts of the whole are being considered.
- 03
Denominator
The denominator is the bottom number in a fraction, indicating the total number of equal parts the whole is divided into.
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Proper Fraction
A proper fraction is a fraction where the numerator is less than the denominator, meaning it represents a quantity less than one.
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Improper Fraction
An improper fraction is a fraction where the numerator is greater than or equal to the denominator, representing a quantity of one or more.
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Mixed Number
A mixed number is a whole number combined with a proper fraction, used to express quantities greater than one in a more readable form.
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Equivalent Fractions
Equivalent fractions are different fractions that represent the same value, such as 1/2 and 2/4, and can be created by multiplying or dividing both numerator and denominator by the same number.
- 08
Simplifying a Fraction
Simplifying a fraction means reducing it to its lowest terms by dividing both the numerator and denominator by their greatest common divisor.
- 09
Greatest Common Divisor
The greatest common divisor of two numbers is the largest number that divides both of them without leaving a remainder, essential for simplifying fractions.
- 10
Least Common Multiple
The least common multiple of two numbers is the smallest number that is a multiple of both, used to find a common denominator for adding or subtracting fractions.
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Least Common Denominator
The least common denominator is the least common multiple of the denominators of two or more fractions, required to add or subtract them.
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Adding Fractions
Adding fractions requires a common denominator; add the numerators and keep the denominator the same, then simplify if possible.
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Subtracting Fractions
Subtracting fractions involves finding a common denominator, subtracting the numerators, and keeping the denominator, followed by simplification.
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Multiplying Fractions
Multiplying fractions means multiplying the numerators together and the denominators together, then simplifying the result.
- 15
Dividing Fractions
Dividing fractions involves multiplying the first fraction by the reciprocal of the second, then multiplying numerators and denominators.
- 16
Reciprocal of a Fraction
The reciprocal of a fraction is obtained by swapping its numerator and denominator, used in division of fractions.
- 17
Comparing Fractions
Comparing fractions requires a common denominator or converting to decimals; the fraction with the larger numerator when denominators are the same is larger.
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Fraction to Decimal Conversion
Converting a fraction to a decimal involves dividing the numerator by the denominator, which can be done manually or with a calculator.
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Decimal to Fraction Conversion
Converting a decimal to a fraction means expressing the decimal as a fraction in its simplest form, such as 0.5 becoming 1/2.
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Fractions and Percentages
Fractions and percentages are related, as a percentage is a fraction with a denominator of 100; convert by multiplying the fraction by 100.
- 21
Reducing Fractions
Reducing fractions is the process of dividing both numerator and denominator by their greatest common divisor to express the fraction in lowest terms.
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Common Denominator
A common denominator is a shared denominator for two or more fractions, necessary for addition, subtraction, or comparison.
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Improper Fraction to Mixed Number
Converting an improper fraction to a mixed number involves dividing the numerator by the denominator to get the whole number and remainder.
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Mixed Number to Improper Fraction
Converting a mixed number to an improper fraction means multiplying the whole number by the denominator, adding the numerator, and placing over the denominator.
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Multiplying by a Fraction
Multiplying a whole number by a fraction involves multiplying the whole number by the numerator and placing it over the denominator, then simplifying.
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Dividing by a Fraction
Dividing a whole number by a fraction requires multiplying the whole number by the reciprocal of the fraction.
- 27
Adding Mixed Numbers
Adding mixed numbers involves adding the whole numbers separately and the fractions separately after finding a common denominator, then combining if needed.
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Subtracting Mixed Numbers
Subtracting mixed numbers requires borrowing if necessary, subtracting the whole numbers and fractions separately after a common denominator.
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Multiplying Mixed Numbers
Multiplying mixed numbers involves first converting them to improper fractions, multiplying as usual, and then converting back if desired.
- 30
Dividing Mixed Numbers
Dividing mixed numbers means converting them to improper fractions, dividing by multiplying by the reciprocal, and simplifying.
- 31
Fractions in Word Problems
In word problems, fractions represent parts of a whole or ratios; identify the parts and wholes to set up and solve equations involving fractions.
- 32
Rates as Fractions
Rates are expressed as fractions, such as speed as distance over time, and require understanding how to manipulate fractions for calculations.
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Ratios as Fractions
Ratios can be written as fractions, where the numerator and denominator represent the quantities being compared, and can be simplified like fractions.
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Complex Fractions
A complex fraction has a fraction in the numerator, denominator, or both, and is simplified by multiplying numerator and denominator by the least common denominator.
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Simplifying Complex Fractions
Simplifying complex fractions involves multiplying the top and bottom by the least common denominator of all fractions involved to eliminate the inner fractions.
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Fractional Exponents
Fractional exponents represent roots and powers, such as x^(1/2) meaning the square root of x, and follow rules for exponents in algebraic expressions.
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Solving Equations with Fractions
Solving equations with fractions requires eliminating the denominators by multiplying through by the least common denominator, then solving for the variable.
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Common Trap: Adding Numerators and Denominators
A common error is adding fractions by adding numerators and denominators separately, which is incorrect and leads to wrong results; always use a common denominator.
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Common Trap: Dividing Fractions Incorrectly
Mistakenly dividing fractions by dividing numerators and denominators directly instead of multiplying by the reciprocal can produce incorrect answers.
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Order of Operations with Fractions
In expressions with fractions, follow PEMDAS: parentheses, exponents, multiplication and division from left to right, addition and subtraction from left to right.
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Positive and Negative Fractions
Fractions can be positive or negative based on the signs of the numerator and denominator; rules for operations with negatives apply as with whole numbers.
- 42
Absolute Value of Fractions
The absolute value of a fraction is its distance from zero on the number line, making it positive regardless of the original sign.
- 43
Fractions on the Number Line
Fractions are placed on the number line by dividing the line into equal parts based on the denominator, helping visualize their values relative to whole numbers.
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Estimating Sums of Fractions
Estimating sums of fractions involves rounding to simpler fractions or using benchmarks like halves or thirds to approximate without exact calculation.
- 45
Unit Fractions
Unit fractions have a numerator of 1, such as 1/2 or 1/3, and are building blocks for adding to form other fractions.
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Fractions Greater Than One
Fractions greater than one are either improper fractions or mixed numbers, representing quantities larger than a whole.
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Cross-Multiplication for Equality
Cross-multiplication checks if two fractions are equal by multiplying the numerator of one by the denominator of the other and comparing products.
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Fractional Parts in Percentages
Fractional parts can represent percentages, such as 1/4 equaling 25%, useful in problems involving discounts or interest.
- 49
Reciprocals in Equations
Reciprocals are used in equations to solve for variables, such as isolating a term by multiplying both sides by its reciprocal.
- 50
Multiplying Fractions by Whole Numbers
Multiplying a fraction by a whole number treats the whole number as a fraction over 1, then multiplies numerators and denominators.
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Dividing Whole Numbers by Fractions
Dividing a whole number by a fraction means multiplying the whole number by the reciprocal of the fraction.
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Least Common Denominator for Three Fractions
For three fractions, the least common denominator is the least common multiple of all three denominators, used in addition or subtraction.
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Fractions in Ratios and Proportions
Fractions express ratios and proportions, where setting up a proportion allows solving for unknown values using cross-multiplication.
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Benchmark Fractions
Benchmark fractions like 1/2, 1/3, and 2/3 are common values used for quick comparisons or estimations in problems.
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Example: Adding 1/4 and 1/4
Adding two identical fractions like 1/4 and 1/4 results in 2/4, which simplifies to 1/2.
This shows how adding numerators with the same denominator works.
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Example: Multiplying 2/3 by 3
Multiplying the fraction 2/3 by the whole number 3 gives (23)/3 = 6/3 = 2.
This demonstrates multiplication by a whole number.
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Example: Simplifying 10/15
Simplifying 10/15 involves dividing both numerator and denominator by 5, resulting in 2/3.
GCD of 10 and 15 is 5.
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Example: Dividing 1/2 by 1/4
Dividing 1/2 by 1/4 means multiplying 1/2 by 4/1, resulting in 4/2 = 2.
This shows the reciprocal method.
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Example: Comparing 3/4 and 2/3
To compare 3/4 and 2/3, find a common denominator of 12; 3/4 = 9/12 and 2/3 = 8/12, so 3/4 is larger.
Cross-multiplication: 33=9 and 24=8, so 9>8.