Write and Solve Equations Using Multiplication or Division
Write one-step multiplication and division equations from real-world
situations, solve them using inverse operations, and check solutions
by substitution.
6.AT.C.8 · Equations & Inequalities
Level
Guided practice with vocabulary support
🟠 Level 0 — Extra Support
Watch first: the worked example and hints are already shown for you.
One at a time: answer one question, check it, then go on.
Read aloud: press 🔊 Read aloud, then click any sentence to hear it.
Sentence starters: “First, I…” · “The answer is… because…” · “I know this because…”
W
Warm-Up
2 questions
Warm-Up 1
Which equation represents the phrase:
"a number multiplied by 4 equals 28"?
Vocabulary: A
coefficient is the number multiplied by the
variable. In 4n, the coefficient is 4. Hint: "A number" means a variable. "Multiplied by 4"
means 4 times that variable. "Equals 28" tells you the right side.
✓Correct! "A number multiplied by 4" translates to 4n, and "equals
28" gives us 4n = 28.
✗Not quite. "Multiplied by 4" means multiplication, so the equation
is B: 4n = 28.
Warm-Up 2
True or false: To solve 5x = 35, you
should divide both sides by 5.
Vocabulary: An
inverse operation "undoes" another
operation. Division undoes multiplication, and multiplication undoes
division. Hint: Since x is being multiplied by 5, ask
yourself: what undoes multiplication?
✓Correct! Division is the inverse operation of multiplication.
Dividing both sides by 5 gives x = 35 / 5 = 7.
✗Actually, this is true. Since x is multiplied by
5, you divide both sides by 5 to isolate x. That gives x = 7.
P
Practice
5 questions
Practice 1
Solve the equation. Write the value of
x.
Vocabulary: The
coefficient of x is the number in front of
it. To isolate x, divide both sides by the coefficient. Step-by-step:
1. The equation is 6x = 54.
2. The coefficient is 6.
3. Divide both sides by 6: x = 54 / 6.
6x = 54
x =
Explain how you solved:
Sentence frame: "To solve 6x = 54, I divided both sides by ___
because division is the ___ of multiplication. So x = ___."
✓Correct! 6x = 54, so x = 54 / 6 = 9. Check: 6 x 9 = 54.
✗Not quite. Divide both sides by 6: x = 54 / 6 = 9.
Check: 6 x 9 = 54.
Practice 2
Solve the equation. Write the value of
n.
Vocabulary: A quotient is
the result of dividing. In n / 8 = 7, the quotient is 7. Step-by-step:
1. n is being divided by 8.
2. The inverse of division is multiplication.
3. Multiply both sides by 8: n = 7 x 8.
n / 8 = 7
n =
Explain how you solved:
Sentence frame: "To solve n / 8 = 7, I multiplied both sides by ___
because multiplication is the inverse of ___. So n = ___."
✓Correct! n / 8 = 7, so n = 7 x 8 = 56. Check: 56 / 8 = 7.
✗Not quite. Multiply both sides by 8: n = 7 x 8 =
56. Check: 56 / 8 = 7.
Practice 3
A box of granola bars has 12 bars. Marcus bought
several boxes and has 96 granola bars in total. Which
equation can you use to find b, the
number of boxes?
Strategy: Think about the relationship. The number of
boxes times 12 bars per box equals 96 total bars. Hint: "Several boxes" is the unknown (b). Each box
has 12 bars. Total = boxes x bars per box.
Explain how you wrote this equation:
Sentence frame: "I used multiplication because ___ boxes times ___
bars per box equals ___ total bars. The equation is ___."
✓Correct! 12 bars per box times b boxes = 96 bars total, so 12b =
96. Solving: b = 96 / 12 = 8 boxes.
✗Think about it: boxes times bars per box = total. That gives us 12b
= 96. The answer is B.
Practice 4
Drag each solution to the equation it solves.
Strategy: For multiplication equations like 3x = 21,
divide both sides by the coefficient. For
division equations like y / 5 = 4, multiply both sides by the divisor.
x = 7
x = 20
x = 12
3x = 21
x / 4 = 3
5x = 100
✓All correct! 3(7) = 21, 12 / 4 = 3, and 5(20) = 100. Each solution
checks out by substitution.
✗Some matches are incorrect. Use inverse operations: divide for
multiplication equations, multiply for division equations. Try
again!
Practice 5
Jada says the solution to
m / 6 = 9 is
m = 48. Is she correct?
How to check: Substitute 48 for m in the equation.
Does 48 / 6 equal 9? Try it: 48 / 6 = ?
Explain Jada's error or confirm her answer:
Sentence frame: "When I substitute ___ for m, I get ___ / 6 = ___.
Since ___ does/does not equal 9, m = 48 is ___."
✓Correct! 48 / 6 = 8, not 9. Jada is wrong. The correct solution is
m = 54, because 54 / 6 = 9.
✗Check by substitution: 48 / 6 = 8, not 9. Jada is incorrect. The
answer is B. The correct solution is m = 54.
★
Challenge
1 question
Challenge
A school is ordering new calculators. Each calculator costs
$12. The school spent a total of
$252 on calculators. Write an equation to find
c, the number of calculators ordered.
Then solve the equation and check your answer.
Think about it: What is the relationship between the
cost per calculator, the number of calculators, and the total cost? Step 1: Write an equation using c for the number of
calculators. (cost per calculator x number = total) Step 2: Solve for c using an
inverse operation. Step 3: Substitute your answer back into the equation
to check.
Your equation:
Solve — what is c?
Check your answer by substitution:
Sentence frame: "I wrote the equation ___ = ___. I solved by
dividing both sides by ___. So c = ___. To check, I substituted: 12
x ___ = ___. Since ___ = 252, my answer is correct."
✓Great work! 12c = 252, so c = 252 / 12 = 21. Check: 12 x 21 = 252.
The school ordered 21 calculators.
✗The equation is 12c = 252. Divide both sides by 12: c = 252 / 12 =
21. Check: 12 x 21 = 252.