Adding and Subtracting Fractions

Unit Review Sheet

Facts and Definitions

Lesson 1: Reviewing Fractions

• Fraction: a number that represents parts in a whole or pieces of a set
• Numerator: the top number in a fraction, how many parts of the whole you have or need
• Denominator: the bottom number in a fraction, the total number of equal parts in a whole
• Unit fraction: a fraction that has a numerator of 1 ($\frac{1}{2},\frac{1}{3},\frac{1}{4}$)
• Mixed number: a number that is a combination of a whole number and a fraction (1 $\frac{1}{2}$, 2 $\frac{3}{4}$, 3 $\frac{4}{5}$)
• Simplified fraction: fraction with the smallest possible numerator and denominator
• Improper fraction: a fraction that has a greater number in the numerator than in the denominator ($\frac{8}{3},\frac{5}{4},\frac{10}{2}$)
• Equivalent fractions: fractions that are the same size but have different numerators and denominators
• Simplifying (or reducing) a fraction means to find an equivalent fraction with the smallest possible numerator and denominator

Lesson 2: Comparing and Ordering Fractions

• When comparing two fractions that both have a numerator of 1, the fraction with the smaller denominator is greater.
• When comparing two fractions that both have the same denominator, the fraction with the larger numerator is greater.
• You can compare two fractions by first seeing how each fraction compares to $\frac{1}{2}$. For example, if $\frac{3}{4}>\frac{1}{2}$ and $\frac{1}{2}>\frac{1}{5}$, then $\frac{3}{4}>\frac{1}{5}$.
• When comparing two fractions that have different denominators, find a multiple that both denominators share, create equivalent fractions using the shared denominator, and then compare those fractions.
• You can compare fractions using cross multiplication. Multiply the numerator in each fraction by the denominator in the other fraction and then compare the products. The greater fraction will have the greater product.
• You can compare fractions by comparing their decimal values. For each fraction, use a calculator to divide the numerator by the denominator. The fraction with the greater decimal number is the greater fraction.

Lesson 3: Improper Fractions and Mixed Numbers

• To convert an improper fraction to a mixed number, first divide the numerator by the denominator, then write the whole number answer, and finally write the remainder above the original denominator.
• To convert a mixed number to an improper fraction, first multiply the whole number by the denominator, then add the numerator to the product of the whole number and the denominator, and finally place this number over the original denominator.

Lesson 4: Working With Like Denominators

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Lesson 5: Working With Unlike Denominators

• A whole fraction has the same numerator and denominator and is equal to 1 (for example, $\frac{3}{3}$).
• In the easiest common denominator method, find the common denominator by multiplying together the denominators of the two fractions being added, then multiply each side by a whole fraction, multiply the numerators and denominators to get equivalent fractions, and then add the equivalent fractions.

Lesson 6: Adding Fractions With Different Denominators

• The lowest common multiple (LCM) between two numbers is the lowest number that is a multiple of both numbers. For example, the lowest common multiple of 4 (4, 8, 12, 16...) and 6 (6, 12, 18, 24...) is 12.
• The least common denominator (LCD) method of adding fractions involves finding the lowest common multiple between the numbers, creating equivalent fractions using the common multiple as the denominator, and then adding the equivalent fractions.

Lesson 7: Subtracting Fractions With Different Denominators

• To subtract fractions with unlike denominators, first find a common denominator for the fractions, create equivalent fractions using that common denominator, subtract the numerator of the smaller fraction from the numerator of the larger fraction (the denominator stays the same), and then simplify as needed. For example, to subtract $\frac{1}{2}$ and $\frac{7}{8}$, the common denominator is 8, so $\frac{1}{2}$ becomes $4÷8$ and $\frac{7}{8}$ stays the same. Since $\frac{7}{8}$ is greater than $\frac{4}{8}$, subtract $\frac{4}{8}$ from $\frac{7}{8}$ to find a difference of $\frac{3}{8}$.

Lesson 8: Mixed Numbers With Unlike Denominators

• To add mixed numbers, first add the whole numbers, then find the common denominator of the fractions and convert (as needed), add the fraction parts, and finally put the whole and fraction parts together.

Lesson 9: Problem Solving With Fractions

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Lesson 10: Unit Review and Test

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Final Project: Adding and Subtracting Fractions BINGO

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