# Add and Subtract Fractions & Mixed Numbers

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Common Denominator – A common denominator is the least common multiple of the denominators of two or more fractions, essential for adding or subtracting fractions. For example, to add 1/3 and 1/4, we need to find a common denominator, which in this case is 12 (3 × 4).

Composite Number – A composite number is a positive integer that has more than two distinct positive divisors. In other words, it is not a prime number. For instance, 6 is a composite number because it has divisors other than 1 and 6 (2 and 3).

Denominator – The denominator in a fraction represents the total number of equal parts into which a whole is divided, and it is the bottom number of a fraction. In the fraction 3/5, 5 is the denominator, indicating the whole is divided into 5 equal parts.

Difference – Difference is the result of subtracting one number from another. In the context of fractions, it refers to finding the numerical distance between two quantities represented by fractions or mixed numbers.

Dividend – In division, the dividend is the number being divided by another number. When considering fractions, the dividend is the number from which another number (divisor) is being divided.

Divisible – A number is divisible by another number if it can be divided evenly without leaving a remainder. For example, 15 is divisible by 3 because 15 can be divided into 3 equal parts.

Divisor – The divisor is the number by which another number (dividend) is divided in a division operation. When working with fractions, the divisor is the number that represents the number of equal parts into which the dividend is divided.

Fraction – A fraction represents a part of a whole, consisting of a numerator and a denominator. Fractions are used in mathematics to represent portions, ratios, and quantities that are not whole numbers.

Greatest Common Divisor (GCD) – The greatest common divisor (GCD) of two or more numbers is the largest positive integer that divides each of the numbers without leaving a remainder. It is crucial for simplifying fractions by dividing both the numerator and the denominator by their GCD.

Improper Fraction – An improper fraction is a fraction in which the numerator is greater than or equal to the denominator. It can be converted into a mixed number by dividing the numerator by the denominator.

Integer – An integer is a whole number that can be positive, negative, or zero, without any fractional or decimal parts. Integers are used in arithmetic operations, including adding and subtracting fractions, and represent counts or quantities.

Least Common Denominator (LCD) – The least common denominator (LCD) of two or more fractions is the smallest common multiple of their denominators, used for adding and subtracting fractions with different denominators.

Mixed Number – A mixed number is a combination of a whole number and a fraction. It represents a quantity that is greater than one and less than a whole.

Multiple – A multiple of a number is the product of that number and an integer. For example, multiples of 3 include 3, 6, 9, 12, and so on.

Numerator – The numerator in a fraction represents the number of equal parts being considered, and it is the top number of a fraction. For example, in the fraction 3/5, 3 is the numerator, indicating 3 out of 5 equal parts.

Prime Factorization – Prime factorization is the process of expressing a composite number as a product of prime numbers. It is crucial for finding the least common denominator and simplifying fractions.

Prime Number – A prime number is a positive integer greater than 1 that has exactly two distinct positive divisors – 1 and itself. Examples of prime numbers include 2, 3, 5, 7, 11, and so on.

Product – The product is the result of multiplying two or more numbers together. In the context of fractions, it refers to the result obtained when multiplying two or more fractions or mixed numbers.

Proper Fraction – A proper fraction is a fraction in which the numerator is less than the denominator. It represents a quantity that is less than one.

Quotient – In division, the quotient is the result obtained by dividing one number (the dividend) by another number (the divisor). In the context of fractions, the quotient represents the result of dividing one fraction by another.

Reciprocal – The reciprocal of a fraction is another fraction obtained by interchanging the numerator and the denominator. When multiplying a fraction by its reciprocal, the result is always 1.

Simplify – To simplify a fraction means to reduce it to its simplest form by dividing both the numerator and the denominator by their greatest common divisor. It results in a fraction with the smallest possible numerator and denominator.

Sum – Sum is the result of adding two or more numbers together. In the context of fractions, it refers to the result obtained when adding two or more fractions or mixed numbers.

Whole Number – A whole number is a non-negative integer, including zero, that does not have any fractional or decimal parts. Whole numbers are used in arithmetic operations and represent counts or quantities.

Zero – Zero is the integer that represents the absence of quantity or value. In fractions, zero can serve as the numerator or the denominator, resulting in fractions or mixed numbers with a value of zero.