ISEE Upper Level Mathematics Achievement Flashcards: Fraction Operations

What this deck covers

This deck focuses on Fraction Operations, giving you a quick way to review the definitions, rules, and examples that matter most for ISEE Upper Level Mathematics Achievement.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: What is the sign rule for a negative fraction $\frac{-a}{b}$ compared to $\frac{a}{-b}$?

Answer: $\frac{-a}{b}=\frac{a}{-b}=-\frac{a}{b}$. A negative sign can be placed in the numerator, denominator, or in front of the fraction equivalently.

Flashcard 2: What is the general method to subtract $\frac{a}{b} - \frac{c}{d}$ using a common denominator?

Answer: $\frac{ad-bc}{bd}$. Convert to a common denominator of $bd$ and subtract the adjusted numerators.

Flashcard 3: What is $\left(-\frac{2}{3}\right) + \frac{5}{6}$ in simplest form?

Answer: $\frac{1}{6}$. Convert to a common denominator of 6 and add the numerators.

Flashcard 4: What does it mean for $\frac{a}{b}$ to be in simplest form?

Answer: $\gcd(a,b)=1$. The fraction is in simplest form when the numerator and denominator have no common factors other than 1.

Flashcard 5: What is the rule for multiplying fractions, $\frac{a}{b} \times \frac{c}{d}$?

Answer: $\frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd}$. Multiply the numerators together and the denominators together.

Flashcard 6: What is the least common denominator (LCD) of denominators $b$ and $d$?

Answer: $\mathrm{LCD} = \mathrm{lcm}(b,d)$. The least common denominator is the least common multiple of the denominators.

Flashcard 7: What is the reciprocal of a nonzero fraction $\frac{a}{b}$?

Answer: $\frac{b}{a}$. The reciprocal is obtained by swapping the numerator and denominator.

Flashcard 8: What is $\frac{1}{2} + \frac{2}{5}$ in simplest form?

Answer: $\frac{9}{10}$. Convert to a common denominator of 10 and add the numerators.

Flashcard 9: What is $\frac{7}{9} \div \frac{14}{3}$ in simplest form?

Answer: $\frac{1}{6}$. Multiply by the reciprocal, then simplify by dividing by 21.

Flashcard 10: What is $\left(-\frac{4}{7}\right) \div \left(\frac{2}{3}\right)$ in simplest form?

Answer: $-\frac{6}{7}$. Multiply by the reciprocal, retaining the negative sign, and simplify by dividing by 2.

Flashcard 11: What is $\left(-\frac{3}{5}\right) \times \left(\frac{10}{9}\right)$ in simplest form?

Answer: $-\frac{2}{3}$. Multiply numerators and denominators, retaining the negative sign, and simplify by dividing by 15.

Flashcard 12: What is $\frac{3}{4} - \frac{2}{3}$ in simplest form?

Answer: $\frac{1}{12}$. Convert to a common denominator of 12 and subtract the numerators.

Flashcard 13: What is $\frac{4}{7} \times \frac{21}{8}$ in simplest form?

Answer: $\frac{3}{2}$. Multiply numerators and denominators, then simplify by dividing by 28.

Flashcard 14: What is $\frac{2}{3} + \frac{1}{6}$?

Answer: $\frac{5}{6}$. Convert to a common denominator of 6 and add the numerators.

Flashcard 15: What is $\frac{11}{12} - \frac{5}{18}$ in simplest form?

Answer: $\frac{23}{36}$. Convert to a common denominator of 36 and subtract the numerators; the result is already simplest.

Flashcard 16: What is $\frac{5}{12} - \frac{1}{4}$?

Answer: $\frac{1}{6}$. Convert to a common denominator of 12, subtract the numerators, and simplify by dividing by 2.

Flashcard 17: What is $\frac{3}{5} \times \frac{10}{9}$ in simplest form?

Answer: $\frac{2}{3}$. Multiply numerators and denominators, then simplify by dividing by 15.

Flashcard 18: What is $\frac{3}{8} + \frac{1}{8}$?

Answer: $\frac{1}{2}$. Add the numerators over the common denominator and simplify by dividing by 4.

Flashcard 19: What is the rule for subtracting fractions with the same denominator, $\frac{a}{b} - \frac{c}{b}$?

Answer: $\frac{a}{b} - \frac{c}{b} = \frac{a-c}{b}$. Subtract the numerators while keeping the common denominator.

Flashcard 20: What is $\frac{2}{9} + \frac{5}{12}$ in simplest form?

Answer: $\frac{23}{36}$. Convert to a common denominator of 36 and add the numerators; the result is already simplest.

Flashcard 21: What is the rule for adding fractions with the same denominator, $ \frac{a}{b} + \frac{c}{b}$?

Answer: $\frac{a}{b} + \frac{c}{b} = \frac{a+c}{b}$. Add the numerators while keeping the common denominator.

Flashcard 22: What is the general method to add $\frac{a}{b} + \frac{c}{d}$ using a common denominator?

Answer: $\frac{ad+bc}{bd}$. Convert to a common denominator of $bd$ and add the adjusted numerators.

Flashcard 23: What is $\frac{5}{6} \div \frac{10}{9}$ in simplest form?

Answer: $\frac{3}{4}$. Multiply by the reciprocal, then simplify by dividing by 15.

Flashcard 24: What is $\frac{7}{10} - \frac{3}{10}$?

Answer: $\frac{2}{5}$. Subtract the numerators over the common denominator and simplify by dividing by 2.

Flashcard 25: What is the rule for dividing fractions, $\frac{a}{b} \div \frac{c}{d}$, where $c \neq 0$?

Answer: $\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$. Dividing by a fraction is equivalent to multiplying by its reciprocal.