ISEE Middle Level Mathematics Achievement Flashcards: Fraction Multiplication Division

What this deck covers

This deck focuses on Fraction Multiplication Division, giving you a quick way to review the definitions, rules, and examples that matter most for ISEE Middle 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: Identify the correct operation for: "How many bc\frac{3}{4}bc-cup servings are in bc^2\frac{1}{4}bc cups?"

Answer: $2\frac{1}{4} \div \frac{3}{4}$. Determining number of servings in a total amount requires dividing the total by the serving size.

Flashcard 2: A class has $30$ students; bc\frac{2}{5}bc are in band. How many are in band?

Answer: $12$ students. Fraction of students in band is found by multiplying the fraction by total students: $\frac{2}{5} \times 30 = 12$.

Flashcard 3: A tank is bc\frac{3}{4}bc full; you use bc\frac{2}{5}bc of what is in it. What fraction of the tank is used?

Answer: $\frac{3}{10}$. Fraction used of the tank is the product of the fraction full and the fraction used of that: $\frac{3}{4} \times \frac{2}{5} = \frac{6}{20} = \frac{3}{10}$.

Flashcard 4: What is bc^2 \times \frac{3}{7}bc in simplest form?

Answer: $\frac{6}{7}$. Treat the whole number as a fraction $\frac{2}{1}$ and multiply numerators and denominators: $2 \times 3 = 6$ over $1 \times 7 = 7$.

Flashcard 5: A ribbon is bc\frac{7}{8}bc m long; each piece is bc\frac{1}{4}bc m. How many pieces?

Answer: $\frac{7}{2}$ pieces. Number of pieces is determined by dividing total length by piece length: $\frac{7}{8} \div \frac{1}{4} = \frac{7}{8} \times 4 = \frac{7}{2}$.

Flashcard 6: What is bc\frac{11}{12} \div \frac{11}{18}bc in simplest form?

Answer: $\frac{3}{2}$. Divide by multiplying by reciprocal: $\frac{11}{12} \times \frac{18}{11} = \frac{198}{132}$, simplify by dividing by 66 to get $\frac{3}{2}$.

Flashcard 7: A $12$-inch board is cut to bc\frac{5}{6}bc of its length. What is the new length?

Answer: $10$ inches. Reducing to a fraction of original length requires multiplying: $\frac{5}{6} \times 12 = 10$.

Flashcard 8: What is bc\frac{3}{4} \times \frac{2}{5}bc in simplest form?

Answer: $\frac{3}{10}$. Multiply numerators $3 \times 2 = 6$ and denominators $4 \times 5 = 20$, then simplify $\frac{6}{20}$ by dividing by 2.

Flashcard 9: What is bc\frac{5}{6}bc of $18$?

Answer: $15$. To find a fraction of a whole number, multiply: $\frac{5}{6} \times 18 = 15$, as 18 divided by 6 is 3, times 5 is 15.

Flashcard 10: A runner completes bc\frac{2}{3}bc of a $9$-mile route. How many miles is that?

Answer: $6$ miles. Completing a fraction of a distance involves multiplying the fraction by the total: $\frac{2}{3} \times 9 = 6$.

Flashcard 11: What is bc\frac{5}{6} \div \frac{2}{3}bc in simplest form?

Answer: $\frac{5}{4}$. Divide by multiplying by the reciprocal: $\frac{5}{6} \times \frac{3}{2} = \frac{15}{12}$, then simplify by dividing by 3.

Flashcard 12: A recipe needs bc\frac{3}{4}bc cup sugar; you make bc\frac{2}{3}bc of it. How many cups?

Answer: $\frac{1}{2}$ cup. Scaling a recipe by a fraction requires multiplying the required amount by that fraction: $\frac{2}{3} \times \frac{3}{4} = \frac{6}{12} = \frac{1}{2}$.

Flashcard 13: What rule lets you multiply fractions bc\frac{a}{b} \times \frac{c}{d}bc quickly?

Answer: $\frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd}$. To multiply fractions, multiply the numerators together and the denominators together, resulting in the product of the fractions.

Flashcard 14: What is bc^2\frac{1}{4} \div \frac{3}{2}bc in simplest form?

Answer: $\frac{3}{2}$. Convert mixed number to $\frac{9}{4}$, then divide by multiplying by reciprocal: $\frac{9}{4} \times \frac{2}{3} = \frac{18}{12}$, simplify by 6.

Flashcard 15: You have bc\frac{3}{5}bc lb nuts; servings are bc\frac{1}{10}bc lb. How many servings?

Answer: $6$ servings. Number of servings is found by dividing total amount by serving size: $\frac{3}{5} \div \frac{1}{10} = \frac{3}{5} \times 10 = 6$.

Flashcard 16: What rule lets you divide fractions bc\frac{a}{b} \div \frac{c}{d}bc quickly?

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, which inverts the divisor.

Flashcard 17: What is the reciprocal of the fraction bc\frac{a}{b}bc (with $a,b \ne 0$)?

Answer: $\frac{b}{a}$. The reciprocal of a fraction is obtained by swapping its numerator and denominator, ensuring the product with the original is 1.

Flashcard 18: What is bc^1\frac{1}{2} \times \frac{2}{3}bc in simplest form?

Answer: $1$. Convert mixed number to improper fraction $\frac{3}{2}$, then multiply: $\frac{3}{2} \times \frac{2}{3} = \frac{6}{6} = 1$.

Flashcard 19: What is bc^3 \div \frac{3}{8}bc?

Answer: $8$. Divide by multiplying by the reciprocal: $3 \times \frac{8}{3} = \frac{24}{3} = 8$, canceling the 3s.

Flashcard 20: A $2$-liter bottle is poured into cups of bc\frac{1}{8}bc liter. How many cups can be filled?

Answer: $16$ cups. Number of cups is total volume divided by cup size: $2 \div \frac{1}{8} = 2 \times 8 = 16$.

Flashcard 21: A $15$-mile trip is split into equal legs of bc\frac{3}{4}bc mile. How many legs are there?

Answer: $20$ legs. Number of equal legs in a trip is total distance divided by leg length: $15 \div \frac{3}{4} = 15 \times \frac{4}{3} = 20$.

Flashcard 22: What is bc\frac{7}{8} \times \frac{4}{21}bc in simplest form?

Answer: $\frac{1}{6}$. Multiply numerators $7 \times 4 = 28$ and denominators $8 \times 21 = 168$, then simplify by dividing by 28.

Flashcard 23: What is bc\frac{9}{10} \div \frac{3}{5}bc in simplest form?

Answer: $\frac{3}{2}$. Divide by multiplying by the reciprocal: $\frac{9}{10} \times \frac{5}{3} = \frac{45}{30}$, then simplify by dividing by 15.

Flashcard 24: What is bc\frac{4}{9} \times \frac{27}{8}bc in simplest form?

Answer: $\frac{3}{2}$. Multiply numerators $4 \times 27 = 108$ and denominators $9 \times 8 = 72$, then simplify $\frac{108}{72}$ by dividing by 36.