A literal equation contains several letters. Solving for one means isolating it exactly as you would isolate x.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Treat other letters as numbers
In A = lw, solving for l means dividing by w. The fact that w is a letter changes nothing about the method.
Why it is useful
Rearranging once lets you answer many questions. Solving d = rt for t answers every time question in one step.
Units carry information
Units multiply and divide with the numbers. Miles per hour times hours gives miles, which confirms the setup.
Units as a check
If a calculation produces the wrong unit, the setup is wrong. This catches errors that arithmetic checking misses entirely.
Choosing sensible units
Report a walking distance in kilometres, not millimetres. The right unit makes an answer readable.
Rearranging for a different letter
The steps are the same as solving numerically: undo operations in reverse, doing the same to both sides. The only difference is that nothing simplifies to a single number.
Fix which letter is the unknown first
Every other letter behaves as a constant for the duration. Writing down which one you are solving for prevents the confusion that otherwise builds up two or three steps in.
Units check the work
If a formula produces metres per second and the answer should be metres, a step went wrong. Carrying units through a calculation turns dimensional consistency into an automatic error check.
Conversion factors equal one
100 cm per 1 m is a ratio of equal quantities, so multiplying by it changes the unit without changing the amount. Letting the units cancel tells you whether to multiply or divide.
Step 2: Try It Yourself
Tap and try it out.
Area · squares inside
24
Perimeter · walk around
20
4 × 6 = 24 · 4 + 6 + 4 + 6 = 20
Area counts the squares inside. Perimeter measures the walk all the way round.
Step 3: Watch an Example
One step at a time.
Watch Sana Rearrange d = rt
Sana needs a formula for time rather than distance.
- Step 1
The t is multiplied by r, so she divides both sides by r.
Step 4: Your Turn
Practice makes it stick.
The Rearrangement
Problem 1 of 2
A = lw with A = 36 and w = 4. What is l?
The Trip
Problem 2 of 2
d = rt with d = 180 miles and r = 60 mph. What is t, in hours?
hours
Solve for the Letter
1 of 8
A = lw with A = 48 and l = 6. What is w?
2 of 8
d = rt with d = 240 and t = 4. What is r?
3 of 8
P = 2l + 2w with P = 20 and l = 6. What is w?
4 of 8
C = 2πr with C = 31.4. What is r, using π as 3.14?
5 of 8
Miles per hour times hours gives which unit? 1 miles, 2 hours.
6 of 8
A = bh ÷ 2 with A = 24 and b = 8. What is h?
7 of 8
Match each formula with the rearrangement for the named letter.
Tap a card on the left to start.
8 of 8
V = lwh with V = 60, l = 5 and w = 3. What is h?
Step 5: Quick Check
Show what you know.
Question 1 of 2
A = lw with A = 42 and w = 7. What is l?
Question 2 of 2
How do units help check a calculation?
What You Learned
- 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.