Fraction Operations

ND State Standard
7.NO.O.2 Add, subtract, multiply, and divide non-negative fractions in multi-step problems, including authentic problems.

Nonnegative - either positive or equal to zero.

Goal:

Build as few fraction statements as possible to satisfy each constraint at least once.
Each addition must contain at least two (two or more) fractions.

Equation format:

Start with at least two (two or more) fractions.
Use parentheses to indicate the order of operations you'd like to include.
Combine the fractions using addition (+), subtraction (-), multiplication (x), or division (/)
Include an equal sign (=) and the final result.

Constraints:

A. Mixed Operations and Unequal Denominators:

- Create a statement where you use at least two different operations (addition, subtraction, multiplication, division) and the final result involves fractions with different denominators.

B. Equivalence through Multi-Step Operations:

- Show that two seemingly different fractions are equivalent by using a series of operations that ultimately lead to the same result.

C. Whole Numbers and Improper Fractions:

- Start with an expression involving fractions and use operations to end up with a result greater than 1 (a whole number) that can also be expressed as an improper fraction.

D. Factoring Denominators with Mixed Operations:

- Create a statement where the denominator of one fraction is a factor of the other's denominator. Use a combination of operations to arrive at the final result.

E. Multi-Step Operations with Sum > 1:

- Show a multi-step statement involving fractions where the final result is a sum greater than 1.

F. Multi-Step Operations with Sum < 1:

Create a statement using various operations with fractions where the final result is a sum less than 1.

G. Reaching a Whole Number with Multi-Step Operations:

Start with an statement involving fractions and use a combination of operations to end up with a whole number as the final result.

H. Multi-Step Operations with Sum < 1/2:

Develop a multi-step statement with fractions where the final result is a sum less than one-half.

Make sure that you are showing all your work for each step, do not turn your fractions into decimals, I want to see your fractional work.