Definition of Fractions: A fraction represents a part or parts of a whole object.
Components of a Fraction:
Numerator: Indicates how many parts you have.
Denominator: Indicates how many parts the whole is divided into.
Rule: You must have a common denominator to add or subtract fractions.
Example:
For 2/3 + 1/2:
Common denominator: 6
Convert fractions:
2/3 becomes 4/6 (multiplied numerator and denominator by 2).
1/2 becomes 3/6 (multiplied numerator and denominator by 3).
Result: 4 + 3 = 7, so 2/3 + 1/2 = 7/6.
Rule: Multiply the numerators and the denominators separately.
For 2/3 * 4/5:
Multiply: 2 * 4 = 8 and 3 * 5 = 15.
Result: 8/15 (no reduction needed).
Rule: Flip the divisor and multiply.
For 2/3 ÷ 1/4:
Flip 1/4 to become 4/1, then multiply:
2 * 4 = 8 and 3 * 1 = 3.
Result: 8/3 (no mixed numbers).
Importance: A valuable skill for simplifying before multiplication.
For 2/3 * 1/4:
Common factor is 2.
Cross-cancel: 2/2 = 1 and 4/2 = 2.
Then compute: 1 * 1 = 1 and 3 * 2 = 6.
Result: 1/6.
Definition: A mixed number is a combination of a whole number and a fraction.
Conversion: To convert to an improper fraction:
Example: Convert 2 and 1/3:
2 * 3 + 1 = 7 ⇒ 7/3.
Problem: 2 and 12 * 5 and 1/3:
Convert to improper fractions:
2 and 1/2 = 5/2 and 5 and 1/3 = 16/3.
Cross-cancel:
2 goes into 16, 8 times and 2 goes into 2, 1 time.
Calculate: 5 * 8 = 40 and 1 * 3 = 3.
Result: 40/3 (already reduced).
We defined fractions, combined, multiplied and divided fractions, cross-canceled, worked with mixed numbers, and solved a practice problem.