Key Concepts
- Fraction Addition
- If [latex]a,b[/latex], and [latex]c[/latex] are numbers where [latex]c\ne 0[/latex] , then [latex]{\Large\frac{a}{c}}+{\Large\frac{b}{c}}={\Large\frac{a+c}{c}}[/latex] .
- To add fractions, add the numerators and place the sum over the common denominator.
- Fraction Subtraction
- If [latex]a,b[/latex], and [latex]c[/latex] are numbers where [latex]c\ne 0[/latex] , then [latex]{\Large\frac{a}{c}}-{\Large\frac{b}{c}}={\Large\frac{a-b}{c}}[/latex] .
- To subtract fractions, subtract the numerators and place the difference over the common denominator.
- Find the prime factorization of a composite number using the tree method.
- Find any factor pair of the given number, and use these numbers to create two branches.
- If a factor is prime, that branch is complete. Circle the prime.
- If a factor is not prime, write it as the product of a factor pair and continue the process.
- Write the composite number as the product of all the circled primes.
- Find the prime factorization of a composite number using the ladder method.
- Divide the number by the smallest prime.
- Continue dividing by that prime until it no longer divides evenly.
- Divide by the next prime until it no longer divides evenly.
- Continue until the quotient is a prime.
- Write the composite number as the product of all the primes on the sides and top of the ladder.
- Find the LCM using the prime factors method.
- Find the prime factorization of each number.
- Write each number as a product of primes, matching primes vertically when possible.
- Bring down the primes in each column.
- Multiply the factors to get the LCM.
- Find the LCM using the prime factors method.
- Find the prime factorization of each number.
- Write each number as a product of primes, matching primes vertically when possible.
- Bring down the primes in each column.
- Multiply the factors to get the LCM.
- Find the least common denominator (LCD) of two fractions.
- Factor each denominator into its primes.
- List the primes, matching primes in columns when possible.
- Bring down the columns.
- Multiply the factors. The product is the LCM of the denominators.
- The LCM of the denominators is the LCD of the fractions.
- Equivalent Fractions Property
- If [latex]a,b[/latex] , and [latex]c[/latex] are whole numbers where [latex]b\ne 0[/latex] , [latex]c\ne 0[/latex] then[latex]\Large\frac{a}{b}=\Large\frac{a\cdot c}{b\cdot c}[/latex]
and [latex]\Large\frac{a\cdot c}{b\cdot c}=\Large\frac{a}{b}[/latex]
- If [latex]a,b[/latex] , and [latex]c[/latex] are whole numbers where [latex]b\ne 0[/latex] , [latex]c\ne 0[/latex] then[latex]\Large\frac{a}{b}=\Large\frac{a\cdot c}{b\cdot c}[/latex]
- Convert two fractions to equivalent fractions with their LCD as the common denominator.
- Find the LCD.
- For each fraction, determine the number needed to multiply the denominator to get the LCD.
- Use the Equivalent Fractions Property to multiply the numerator and denominator by the number from Step 2.
- Simplify the numerator and denominator.
- Add or subtract fractions with different denominators.
- Find the LCD.
- Convert each fraction to an equivalent form with the LCD as the denominator.
- Add or subtract the fractions.
- Write the result in simplified form.
Glossary
- composite number
- A composite number is a counting number that is not prime
- divisibility
- If a number [latex]m[/latex] is a multiple of [latex]n[/latex] , then we say that [latex]m[/latex] is divisible by [latex]n[/latex]
- least common denominator (LCD)
- The least common denominator (LCD) of two fractions is the least common multiple (LCM) of their denominators
- multiple of a number
- A number is a multiple of [latex]n[/latex] if it is the product of a counting number and [latex]n[/latex]
- ratio
- A ratio compares two numbers or two quantities that are measured with the same unit. The ratio of [latex]a[/latex] to [latex]b[/latex] is written [latex]a[/latex] to [latex]b[/latex] , [latex]\Large\frac{a}{b}[/latex] , or [latex]a:b[/latex]
- prime number
- A prime number is a counting number greater than 1 whose only factors are 1 and itself
Candela Citations
CC licensed content, Original
- Authored by: Deborah Devlin. Provided by: Lumen Learning. License: CC BY: Attribution