Grade6 rational numbers, factors and fraction operations
Numbers have positions and magnitudes
A number line helps compare signed numbers. Negative three is greater than negative seven because it lies farther to the right, even though seven has a greater absolute value. Absolute value describes distance from zero, so it is never negative. Compare a number's value with its magnitude instead of applying a slogan that a larger written digit always means a larger number.
Fractions, terminating decimals and whole numbers can represent rational quantities. Use a common representation when comparing them. A fraction bar also represents division, and the denominator cannot be zero. When locating a fraction on a number line, identify the unit interval and the equal subdivisions; counting tick marks instead of intervals can shift the point.
Use factors and multiples for a purpose
A factor divides a positive whole number exactly. A multiple results from multiplying it by a whole number. The greatest common factor helps divide quantities into the largest matching groups or simplify a fraction. The least common multiple can help coordinate repeating cycles or choose a common denominator. They are different questions, even when they involve the same pair of numbers.
For a worked example, the GCF of 24 and 36 is 12, while their LCM is 72. The first asks for the largest shared divisor; the second asks for the smallest positive shared multiple. Listing factors and multiples separately prevents interchanging the answers.
Explain fraction operations
For addition or subtraction, express the quantities in equal-sized fractional units before combining numerators. Multiplication can represent taking a fraction of an amount. Division asks how many groups of a given size fit into another amount, or how large a share is.
In a supplied example, four and one half divided by three quarters equals six. Rewrite four and one half as 9/2, then compute 9/2×4/3=6. A model also shows that six groups of three quarters make four and one half. The reciprocal method is a shortcut for a valid division relationship, not permission to invert any fraction in an expression at random.
Check the result through multiplication, estimation and the problem's units. These are mathematical foundations, not a statement of an official test's item counts, calculator rules or passing score.