Section 3-4: Least Common Multiple and Greatest Common Factor

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Laurence West
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1 Section -: Fraction Terminology Identify the following as proper fractions, improper fractions, or mixed numbers:, proper fraction;,, improper fractions;, mixed number. Write the following in decimal notation:,,. 0.0; 0.;.00. 0, 000 Section -: Multiples, Divisibility, and Factor Pairs Find the first five multiples of : x, x 6, x, x, x. The first five multiples of are, 6,,, and. Is divisible by? Yes, the last two digits form a number,, which is divisible by. That is,. Learning Outcome Find all the factors of : Write factor pairs. x, x, x 6, x ; is not a factor; 6 x ; is not a factor; x 6 is a repeat. Factors are,,,, 6,,, 6,, and. Section -: Prime and Composite Numbers Is prime or composite? Factor pairs of are x and x ; therefore is composite. Find the prime factorization of : x x x, so the prime factorization is x x or x. Section -: Least Common Multiple and Greatest Common Factor Find the LCM for,, and 0: x, x, 0 x x or x LCM x x or 60 Find the GCF of,, and : x,, x GCF Section -: Equivalent Fractions and Decimals,,,.

2 Write three fractions equivalent to Multiplying by n n the original value is unchanged. is the same as multiplying by. So, Reduce: Learning Outcome Write. as a fraction Dividing by is the same as dividing by. So, the original value is unchanged.. 0 Learning Outcome Convert to a decimal. Divide the numerator by the denominator...0 That is, 0.. Section -6: Improper Fractions and Mixed Numbers Convert the following to whole or mixed numbers: Convert 6 to an improper fraction: ( 6) + 6,. ;

3 Section -: Finding Common Denominators and Comparing Fractions Find the lowest common denominator (LCD) for and x x or LCD x x The smallest number that can be divided evenly by both and is. Which fraction is larger, Since is larger than, is larger than or? 6 Section -: Adding Fractions and Mixed Numbers Add: + + Add: Add: Add the numerators. Keep the comon demoninator. Change to equivalent fractions that have common denominators. 6, so + Add fractional parts and whole-number parts. Combine the results.

4 Section -: Subtracting Fractions and Mixed Numbers Subtract: Change to equivalent fractions that have common denominators. Subtract numerators. Subtract: - 6 Borrow from and add it as to. Section -: Multiplying Fractions and Mixed Numbers Multiply: / / / / Reduce numerators and denominators before multiplying. Multiply numerators and multiply denominators. Multiply: Write whole or mixed numbers as improper fractions. / / Reduce numerator and denominator before multiplying.

5 Learning Outcome Simplify: 6 Write as repeated factors. Multiply. Section -: Dividing Fractions and Mixed Numbers Find the reciprocal of,,.. The reciprocal of or is ; the reciprocal of is ; Write whole or mixed numbers as improper fractions. the reciprocal of or is. Interchange the numerator and denominator. Divide: 6 Multiply by the reciprocal of, that is, by.. Learning Outcome Divide: / / Change mixed numbers to improper fractions as a first step. Multiply the dividend (first number) by the reciprocal of the divisor (second number). Learning Outcome Simplify the following complex fraction. / Change mixed numbers to improper fractions and write complex fraction as division. Change division to equivalent multiplication and multiply.

6 Section -: Signed Fractions and Decimals Write three equivalent signed fractions for , which can be written as + or - or Change any two of the three signs of the fraction. Add: Learning Outcome Add: Add:. + (.)... Use rules for adding fractions and for adding signed numbers. Use rules for adding decimals and for adding signed numbers. Learning Outcome Simplify: Multiply and divide. Add. +

Arithmetic. Integers: Any positive or negative whole number including zero

Arithmetic. Integers: Any positive or negative whole number including zero Arithmetic Integers: Any positive or negative whole number including zero Rules of integer calculations: Adding Same signs add and keep sign Different signs subtract absolute values and keep the sign of