Literal Equations and Units

Rearranging a formula for the letter you need.

12 problems · about 21 minutes · A-CED.A.4, N-Q.A.1

What this lesson teaches

The student rearranges formulas for a specified variable and uses units to check reasoning.

Solve a literal equation by isolating the wanted letter, treating others as numbers.
Units multiply and divide alongside the numbers.
A wrong final unit means a wrong setup.

Straightforward practice. Get the method working first.

5 problems

A = lw with A = 42 and w = 7. What is l?
Answer 6
Why 6.
How do units help check a calculation?
Answer A wrong resulting unit reveals a wrong setup.
Why Units expose setup errors that arithmetic checks miss.
A = lw with A = 48 and l = 6. What is w?
Answer 8
Why 48 ÷ 6.
d = rt with d = 240 and t = 4. What is r?
Answer 60
Why 240 ÷ 4.
P = 2l + 2w with P = 20 and l = 6. What is w?
Answer 4
Why 20 = 12 + 2w.

The same ideas with more to keep track of.

3 problems

C = 2πr with C = 31.4. What is r, using π as 3.14?
Answer 5
Why 31.4 ÷ 6.28.
Miles per hour times hours gives which unit? 1 miles, 2 hours.
Answer 1
Why The hours cancel.
A = bh ÷ 2 with A = 24 and b = 8. What is h?
Answer 6
Why 48 ÷ 8.

Mixed problems. Work out what kind of question it is before you start.

4 problems

Match each formula with the rearrangement for the named letter.
Answer A = lw, solve for w → w = A divided by l; d = rt, solve for r → r = d divided by t; C = 2 pi r, solve for r → r = C divided by 2 pi
Why Divide by whatever multiplies the letter you want.
V = lwh with V = 60, l = 5 and w = 3. What is h?
Answer 4
Why 60 ÷ 15.
The Rearrangement: A = lw with A = 36 and w = 4. What is l?
Answer 9
Why 9.
The Trip: d = rt with d = 180 miles and r = 60 mph. What is t, in hours?
Answer 3 hours
Why 3 hours.