Chapter 4 - Number Theory and Fractions

NC Standards -- Number System & Expressions & Equations

NS2

Math Study Jams

Math Scoring Guide - Practice Questions

Lessons

Divisibility and Mental Math
Exponents
Prime Numbers and Prime Factorization
Greatest Common Factor
Equivalent Fractions
Mixed Numbers and Improper Fractions
Least Common Multiplle
Comparing and Ordering Fractions
Fractions and Decimals

4-1, Divisibility and Mental Math

A whole number is divisible by:

2 if it ends in 0, 2, 4,6 ,or 8
3 if the sum of its digits is divisible by 3
5 if it ends in 0 or 5
9 if the sum of its digits is divisible by 9
10 if it ends in 9

Long Division

NC.6.NS.2 Fluently divide using long division with a minimum of a four-digit dividend and interpret the quotient and remainder in context.

4-2, Exponents

Exponents -- how many times a number is multiplied by itself.

4-3, Prime Numbers

Numbers whose product can be derived only by multiplying itself by one.

Examples: 2, 3, 5, and 7.

Composite Numbers: can be produced by multiplying factors other than one.

4-3, Prime Factorization

NC.6.NS.4 Understand and use prime factorization and the relationships between factors to:

● Find the unique prime factorization for a whole number.
● Find the greatest common factor of two whole numbers less than or equal to 100.
● Use the greatest common factor and the distributive property to rewrite the sum of two whole numbers, each less than or equal to 100.
● Find the least common multiple of two whole numbers less than or equal to 12 to add and subtract fractions with unlike denominators.

4-4, Greatest Common Factor

NC.6.NS.4 Understand and use prime factorization and the relationships between factors to: ● Find the unique prime factorization for a whole number. ● Find the greatest common factor of two whole numbers less than or equal to 100. ● Use the greatest common factor and the distributive property to rewrite the sum of two whole numbers, each less than or equal to 100. ● Find the least common multiple of two whole numbers less than or equal to 12 to add and subtract fractions with unlike denominators.

4-5, Equivalent Fractions

Find the least common denominator.

4-6, Converting Mixed Numbers to Improper Fractions

Multiply the whole number by the denominator, then add the numerator.

The denominator stays the same.

4-7, Least Common Multiple

NC.6.NS.4 Understand and use prime factorization and the relationships between factors to: ● Find the unique prime factorization for a whole number. ● Find the greatest common factor of two whole numbers less than or equal to 100. ● Use the greatest common factor and the distributive property to rewrite the sum of two whole numbers, each less than or equal to 100. ● Find the least common multiple of two whole numbers less than or equal to 12 to add and subtract fractions with unlike denominators.