A literal equation contains several letters. Solving for one means isolating it exactly as you would isolate x, treating the other letters as numbers. Units multiply and divide alongside the numbers, and a wrong final unit means a wrong setup.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Treat other letters as numbers
A = lw for l: divide by w, l = A/w. P = 2l + 2w for w: subtract 2l, P − 2l = 2w, divide by 2, w = (P − 2l)/2. The fact that they are letters changes nothing about the method.
A harder one
F = (9/5)C + 32 for C: subtract 32, F − 32 = (9/5)C, multiply by 5/9, C = (5/9)(F − 32). Check: F = 212 gives C = (5/9)(180) = 100.
Why it is useful
Rearranging once lets you answer many questions. t = d/r answers every time question in one step: 300 miles at 60 mph is 5 hours; 150 at 50 is 3. No re-solving each time.
Units carry information
60 miles/hour × 3 hours = 180 miles: the hours cancel and miles remain. Treat units as factors that multiply and divide. When the numbers are right, the units come out right too.
Units as a check
If a calculation for time produces miles², the setup is wrong. This catches errors that arithmetic checking misses entirely, because the arithmetic can be perfect on the wrong formula.
Converting units
72 km/h to m/s: 72 km/h × (1000 m/km) × (1 h/3600 s) = 20 m/s. Multiply by fractions equal to 1, arranged so the unwanted units cancel. Report a walking distance in km, not mm.
Step 2: Try It Yourself
Tap and try it out.
Rearrange F = (9/5)C + 32 for C, then convert 72 km/h to m/s, checking the units
- 1F − 32 = (9/5)C− 32subtract 32 from both sides
Step 0 of 4
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: In Real Life
Speed, distance, time
d = rt is written for distance. A driver wants time: t = d/r. Miles over miles per hour leaves hours, and the units confirm the rearrangement was right.
Step 4: 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: t = d ÷ r.
Step 5: 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?
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 6: 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.
- Rearrange once, answer many questions.
- Units multiply and divide alongside the numbers, and a wrong final unit means a wrong setup.
- Convert units by multiplying by fractions equal to 1.