Equivalent expressions with distribution and combining like terms

The Equivalent expressions with distribution and combining like terms exercise appears under the 6th grade (U.S.) Math Mission, 7th grade (U.S.) Math Mission, 8th grade (U.S.) Math Mission, Algebra basics Math Mission, Algebra I Math Mission, Mathematics II Math Mission, High school geometry Math Mission, Algebra II Math Mission, Trigonometry Math Mission and Mathematics III Math Mission. This exercise introduces the idea of manipulating expressions to make other equivalent expressions.

Types of Problems

There are two types of problems in this exercise:

1. Select equivalent formulations: This problem provides an algebraic expression and several other statements that might be equivalent. The user is expected to select all the equivalent expressions from a multiple select list.

   

   Select equivalent formulations

2. Fill in to make equivalent: This problem provides an algebraic expression and a fill-in-the-blank form of the expression immediately afterward. The user is asked to fill in the blanks to make the statement equivalent to the original.

   

   Fill in to make equivalent

Strategies

This exercise is easy to get accuracy badges with knowledge of the distributive properties and collection of like terms. The speed badges are also easy because the numbers are less than 100 in most cases and can be manipulated mentally.

1. Recommended to collect like terms in all the possible answers and select the ones that end up being the same after this process.

Real-life Applications

1. Work problems often ask us to calculate how long it will take different people working at different speeds to finish a task. The algebraic models of such situations often involve rational equations derived from the work formula, ${W = rt}$. The amount of work done (${W}$) is the product of the rate of work (${r}$) and the time spent working (${t}$). The work formula has 3 versions:
   ${W = rt}$
   ${t = \frac{W}{r}}$
   ${r = \frac{W}{t}}$
2. Knowledge of algebra is essential for higher math levels like trigonometry and calculus. Algebra also has countless applications in the real world.