Understanding Equivalent Fractions

Equivalent Fractions

• Equivalent fractions appear different but have the same value
• Multiplying or dividing the numerator and denominator of a fraction by the same number creates an equivalent fraction
• Three steps to find equivalent fractions: decide to multiply or divide, apply that function to the denominator, then apply that function to the numerator
• The denominator is the bottom number of a fraction, representing the number of parts the whole is divided into
• The numerator is the top number of a fraction, representing how many parts of the whole are being considered
• If the numerator cannot be divided, multiplication is a viable pathway
• Whatever operation (multiplication or division) is performed on the denominator must also be performed on the numerator to maintain the fraction's value
• It's possible to find an infinite number of equivalent fractions by multiplying or dividing
• Dividing can simplify fractions to their lowest terms, also known as the simplified version
• The same process must be applied to both the numerator and the denominator to maintain equivalence
• Finding equivalent fractions is important for adding or comparing fractions, especially when denominators or numerators need to be the same

Finding Equivalent Fractions with a Known Denominator or Numerator

• Find the connection between the known denominators
• Determine the multiplier or divisor between the denominators
• Apply the same multiple or divisor to the numerator to find the missing value
• Find the connection between the known numerators
• Determine the multiple or divisor between the numerators
• Apply the same multiple or divisor to the denominator to find the missing value

Comparing Fractions with the Same Denominator

• Fractions can represent parts of a whole or parts of a group
• A fraction consists of a numerator (top) and a denominator (bottom)
• The denominator indicates how many equal parts the whole is divided into
• The numerator indicates how many of those parts are being considered
• Comparing fractions involves determining which fraction represents a greater or lesser value
• Symbols for comparison: greater than (>), equal to (=), less than (<)
• When fractions have the same denominator, the fraction with the larger numerator is the greater value
• Bar models can visually represent fractions to aid comparison
• The crocodile analogy illustrates choosing the larger value

Comparing Fractions with Different Denominators

• Comparing fractions with different denominators is a topic for future lessons

Comparing Fractions

• To determine which fraction has a greater value, compare them
• Both fractions must be fractions of one the same value, if comparing
• The bars have to be the same length; it cannot have different lengths
• An alternative method is equivalent fractions, which have the same value but look different
• If the fractions have the same denominator, it is easier to compare them
• If not, find an equivalent fraction of one to make the denominators the same

Finding Equivalent Fractions

• If the numbers have a relationship, one can be turned into an equivalent fraction
• Multiply the denominator to turn it into the other denominator
• Whatever you do to the denominator, you also need to do to the numerator
• If there is no obvious relationship, find a number that would be in both of their times tables

Finding a Common Factor

• Go up in multiples/times tables for both denominators until you find a common number
• Create equivalent fractions for both using the common denominator
• If there is no obvious relationship between the numbers, there is a trick
• Multiply the two denominators together; the result will be a multiple of both
• Use this as the common denominator when creating equivalent fractions

Fraction Symbols

• ">" means greater than
• "=" means equal to
• "<" means less than

Converting Improper Fractions to Mixed Numbers

• An improper fraction has a larger numerator than its denominator
• A mixed number has both a whole number and a fraction
• To convert, divide the numerator by the denominator
• The quotient is the whole number, and the remainder is the new numerator
• Keep the same denominator

Division Method

• Put the numerator (of the improper fraction) inside the bus stop, and the denominator on the outside
• The number of times the denominator goes into the numerator becomes the whole number
• The remainder becomes the numerator of the fractional part
• The original denominator is kept
• Result is the mixed number

Converting Mixed Numbers to Improper Fractions

• A mixed number includes a whole number and a fraction
• An improper fraction has a larger numerator than the denominator
• Times the denominator by the whole number
• Add the result to the numerator
• Keep the same denominator

Adding Fractions with the Same Denominator

• Add the numerators while keeping the denominators the same
• Adding fractions with the same denominator is different from adding fractions with different denominators
• Adding fractions with the same denominator will be our next lesson
• All of the the denominators are the same in the four questions
• The fractions must have the same denominator to do
• If you are adding one half and one half you should get a whole
• You might want to add a numerator and a denominator but this is the most common mistake

Adding Fractions with Like Denominators

• When adding fractions with the same denominator, the denominator remains the same; only add the numerators.
• The denominator represents the type of fraction (fifths, sixths, etc.) and does not change when adding.
• Simplify the resulting fraction if possible by finding common factors between the numerator and denominator.
• If the numerator is larger than the denominator (improper fraction), simplify to a mixed number.
• 8/8 equals one whole.

Quick Method for Adding Fractions with Like Denominators

• Add the numerators while keeping the denominator the same.
• Simplify the fraction if possible.

Adding Fractions with Unlike Denominators

• To add fractions with different denominators, first find a common denominator.
• Convert the fractions into equivalent fractions with the common denominator.
• Multiply the numerator and denominator of each fraction to find the equivalent fraction.
• Add the numerators of the equivalent fractions, keeping the denominator the same.
• Simplify if needed

Using Bar Models to Visualize Adding Fractions

• Adding fractions with differing volumes, and quantities ie. thirds and ninths can be difficult to add
• Finding a common multiple makes it easier to see when we're adding the same quantity every time.

Method: Finding a Common Multiple

• Find a common multiple (denominator) for both fractions.
• Multiply the denominators by one another.
• Multiply the numerator by the same number you multiplied the denominator by.
• If the result is an improper fraction, convert it to a mixed number.