Fraction Operations

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ISEE Upper Level: Mathematics Achievement › Fraction Operations

Questions 1 - 7
1

In a lab, a beaker holds $2,1/3$ L; $5/6$ L is poured out. What volume remains?

$1,1/2$ L

$-1,1/2$ L

$7/12$ L

$3,1/6$ L

Explanation

This question tests ISEE Upper Level Mathematics Achievement skills: add, subtract, multiply, and divide fractions. Fractions are numbers that represent parts of a whole. Operations with fractions involve adding, subtracting, multiplying, and dividing these numbers while adhering to rules specific to fraction arithmetic. In the given scenario, students must apply these rules to solve a problem involving subtracting 5/6 L from 2 1/3 L of liquid in a beaker. The correct answer is choice A, 1 1/2 L, which accurately represents the result of converting to common denominators (2 1/3 = 2 2/6, then 2 2/6 - 5/6 = 1 3/6 = 1 1/2). Choice B (3 1/6) is incorrect due to adding instead of subtracting, a common mistake when students misread the operation. To assist students, encourage the practice of converting fractions to common denominators for addition and subtraction, and using reciprocal operations for division.

2

A lab uses $3,1/5$ mL solution; $4/5$ mL is transferred. What is the remaining volume?

$2,1/4$ mL

$1,3/5$ mL

$2,2/5$ mL

$4$ mL

Explanation

This question tests ISEE Upper Level Mathematics Achievement skills: add, subtract, multiply, and divide fractions. Fractions are numbers that represent parts of a whole. Operations with fractions involve adding, subtracting, multiplying, and dividing these numbers while adhering to rules specific to fraction arithmetic. In the given scenario, students must apply these rules to solve a problem involving subtracting 4/5 mL from 3 1/5 mL of solution. The correct answer is choice A, 2 2/5 mL, which accurately represents the result of converting to common denominators and subtracting (3 1/5 - 4/5 = 3 1/5 - 4/5 = 2 2/5). Choice C (1 3/5) is incorrect due to improper subtraction technique, a common mistake when students subtract whole numbers and fractions separately without regrouping. To assist students, encourage the practice of converting fractions to common denominators for addition and subtraction, and using reciprocal operations for division.

3

A board is $4,1/2$ ft long; it is cut into pieces of $3/4$ ft. Find the quotient.

$5,1/4$ pieces

$3,3/8$ pieces

$6$ pieces

$3,1/2$ pieces

Explanation

This question tests ISEE Upper Level Mathematics Achievement skills: add, subtract, multiply, and divide fractions. Fractions are numbers that represent parts of a whole. Operations with fractions involve adding, subtracting, multiplying, and dividing these numbers while adhering to rules specific to fraction arithmetic. In the given scenario, students must apply these rules to solve a problem involving dividing a 4 1/2 ft board into 3/4 ft pieces. The correct answer is choice B, 6 pieces, which accurately represents the result of dividing fractions (4 1/2 = 9/2, then 9/2 ÷ 3/4 = 9/2 × 4/3 = 36/6 = 6). Choice D (3 1/2) is incorrect due to multiplying instead of dividing or not using the reciprocal, a common mistake when students confuse division with multiplication. To assist students, encourage the practice of converting fractions to common denominators for addition and subtraction, and using reciprocal operations for division.

4

A lab protocol requires $5/4$ g salt; $1/2$ g is removed. What mass remains?

$3/4$ g

$-3/4$ g

$3/8$ g

$1,3/4$ g

Explanation

This question tests ISEE Upper Level Mathematics Achievement skills: add, subtract, multiply, and divide fractions. Fractions are numbers that represent parts of a whole. Operations with fractions involve adding, subtracting, multiplying, and dividing these numbers while adhering to rules specific to fraction arithmetic. In the given scenario, students must apply these rules to solve a problem involving subtracting 1/2 g from 5/4 g of salt in a lab protocol. The correct answer is choice B, 3/4 g, which accurately represents the result of finding common denominators and subtracting (5/4 - 1/2 = 5/4 - 2/4 = 3/4). Choice A (3/8) is incorrect due to improper subtraction technique, a common mistake when students subtract numerators and denominators separately. To assist students, encourage the practice of converting fractions to common denominators for addition and subtraction, and using reciprocal operations for division.

5

A tile strip is $3,3/4$ ft long; each tile is $5/8$ ft. Divide to find tiles needed.

$6$ tiles

$5,1/2$ tiles

$4,2/3$ tiles

$2,11/24$ tiles

Explanation

This question tests ISEE Upper Level Mathematics Achievement skills: add, subtract, multiply, and divide fractions. Fractions are numbers that represent parts of a whole. Operations with fractions involve adding, subtracting, multiplying, and dividing these numbers while adhering to rules specific to fraction arithmetic. In the given scenario, students must apply these rules to solve a problem involving dividing 3 3/4 ft by 5/8 ft to find the number of tiles needed. The correct answer is choice B, 6 tiles, which accurately represents the result of dividing fractions (3 3/4 = 15/4, then 15/4 ÷ 5/8 = 15/4 × 8/5 = 120/20 = 6). Choice A (2 11/24) is incorrect due to multiplying instead of dividing, a common mistake when students forget to use the reciprocal in division. To assist students, encourage the practice of converting fractions to common denominators for addition and subtraction, and using reciprocal operations for division.

6

A recipe uses $1,1/2$ cups flour; you add $3/4$ cup more. What is the total flour?

$2,1/3$ cups

$9/8$ cups

$2,1/4$ cups

$1,1/4$ cups

Explanation

This question tests ISEE Upper Level Mathematics Achievement skills: add, subtract, multiply, and divide fractions. Fractions are numbers that represent parts of a whole. Operations with fractions involve adding, subtracting, multiplying, and dividing these numbers while adhering to rules specific to fraction arithmetic. In the given scenario, students must apply these rules to solve a problem involving adding 1 1/2 cups and 3/4 cup of flour. The correct answer is choice A, 2 1/4 cups, which accurately represents the result of converting to common denominators (1 1/2 = 1 2/4, then 1 2/4 + 3/4 = 1 5/4 = 2 1/4). Choice B (2 1/3) is incorrect due to improper addition without finding common denominators, a common mistake when students add numerators and denominators separately. To assist students, encourage the practice of converting fractions to common denominators for addition and subtraction, and using reciprocal operations for division.

7

A budget allocates $3/5$ of $2,1/2$ hours to homework. How many hours is that?

$1,1/12$ hours

$3,1/7$ hours

$5/6$ hours

$1,1/2$ hours

Explanation

This question tests ISEE Upper Level Mathematics Achievement skills: add, subtract, multiply, and divide fractions. Fractions are numbers that represent parts of a whole. Operations with fractions involve adding, subtracting, multiplying, and dividing these numbers while adhering to rules specific to fraction arithmetic. In the given scenario, students must apply these rules to solve a problem involving finding 3/5 of 2 1/2 hours for homework allocation. The correct answer is choice A, 1 1/2 hours, which accurately represents the result of multiplying fractions (2 1/2 = 5/2, then 3/5 × 5/2 = 15/10 = 3/2 = 1 1/2). Choice C (5/6) is incorrect due to improper multiplication technique, a common mistake when students multiply only the numerators or denominators. To assist students, encourage the practice of converting mixed numbers to improper fractions before multiplying, and simplifying the final result.