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Cheat Sheet for Fractions
Converting Fractions:
- Mixed to Improper:
a. Multiply the whole number by the denominator (bottom number)
b. Add the numerator (top number)
c. This number becomes the new numerator
d. The denominator stays the same
Example:
- Improper to Mixed:
a. Divide the numerator by the denominator
b. The number of full times the denominator fits into the numerator is your whole number
c. The remainder goes into a fraction over the original denominator
Example:
Prime Numbers:
- Prime numbers are only dividable by itself and 1
Example: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29
Prime Factorization:
- Tree!
- Start by dividing the number by the first prime number (2)
- When you can’t divide by a prime number, you move on to the next prime number possible
Example:
3 × 5 = 15
- Write as each prime number multiplies by the next
- Simplify with exponents
Example: 2 × 2 × 2 × 3 × 3
Writing Fractions in Lowest Terms
- Divide the numerator (top number) and denominator (bottom number) by common factors
Example:
- Find lowest terms using prime factorization
a. Do a prime factorization tree for both numbers in the fraction
b. Write the product of each tree into a fraction
c. Divide the terms
Example:
Multiplying Fractions
- Proper Fractions:
a. Multiply the numerators
b. Multiply the denominators
c. Write in lowest terms
Example:
- Improper Fractions:
a. Multiply the numerators
b. Multiply the denominators
c. Use long division to write as a mized number
d. Write fraction in lowest terms
3 × 3
2
÷ 2
÷ 3
×
2 × 3
3 × 5
÷ 3
lowest terms
lowest terms
c. Simplify by writing in lowest terms or as a mixed number
Example:
- Finding the Lowest Common Multiple:
a. List Method
i. List the first fe multiples of each denominator
ii. Find the lowest number they have in common
Example:
b. Dividing Prime Numbers Method
i. Start by trying to divide by the first prime number
ii. Continue dividing by prime numbers untill all quotients are 1
iii. Multiply all prime numbers used to get lowest common multiple
Example: 9, 15
- Adding/Subtraciting Unlike Fractions:
a. Find the lowest common multiple
b. Reqrite the fractions with the lowest common multiple as the denominator
c. Add/subtract the numerators (top numbers)
d. Simplify by writing in lowest terms or by writing as a mized number
Example:
÷ 2
3 × 3 × 5 = 45 is the lowest common multiple
2 × 2 × 3 × 5 = 60 is the lowest common multiple
× 20
× 15
× 6
- Adding/Subtracting Mixed Numbers:
a. Change the Mixed Number to an improper fraction
b. Find the lowest common multiple of the denominators (bottom number)
c. Reqrite the fractions with the lowest common multiple as the denominators
d. Add or subtract the numerators (top number)
e. Simplify by writing in lowest terms or by writing as a mixed number
Example:
Estimating Fraction Equations:
- Round the mixed numbers/fractions to a whole number
- Estimate the answer
- Use estimate to check if your exact answer is reasonable
If the numerator of the fraction is at least half of the denominator, you round the whole
number up
If the numerator of the fraction is less than half of the denominator, you round down
(leave the whole number as is)
Example:
Locating Fractions on a Number Line:
LCM = 8, 16, 24, 32, 40
× 3
× 2
improper
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