Part A – Solving Equations with Inverse Operations
Directions: Use inverse operations to isolate the variable. Show your thinking in the boxes provided.
Worked Example
$x + 5 = 12$ $- 5 \quad - 5$ (Inverse of +5 is -5)
$x \quad \quad = 7$
"To undo adding 5, I subtract 5 from both sides."
1 $x + 9 = 15$
Inverse: Subtract 9
$x =$
2 $n + 13 = 27$
Inverse: Subtract 13
$n =$
3 $22 = y + 8$
Inverse: Subtract 8
$y =$
4 $a - 11 = 16$
Inverse: Add 11
$a =$
5 $m - 14 = 23$
$m =$
6 $35 = p - 9$
$p =$
7 $28 - x = 19$
Hint: What number taken from 28 makes 19?
$x =$
8 $4x = 36$
Inverse: Divide by 4
$x =$
9 $7n = 56$
Inverse: Divide by 7
$n =$
10 $60 = 12y$
$y =$
11 $\frac{x}{5} = 9$
Inverse: Multiply by 5
$x =$
12 $\frac{a}{8} = 6$
$a =$
Part B – Factors & Multiples
Directions: Show your thinking clearly. List pairs for factors and skip-count for multiples.
Factors
Worked Example: Factors of 12
1 × 12, 2 × 6, 3 × 4
Factors: 1, 2, 3, 4, 6, 12
(13) List all factors of 24:
1 × __2 × __3 × __4 × __
(14) List all factors of 36:
(15) Find the Greatest Common Factor (GCF) of 18 and 24:
Factors of 18:
Factors of 24:
GCF =
Multiples & LCM
Worked Example: LCM of 3 and 4
Multiples of 3: 3, 6, 9, 12, 15
Multiples of 4: 4, 8, 12, 16
LCM = 12
(16) List first 5 multiples of 7:
(17) List first 5 multiples of 9:
(18) Find LCM of 6 and 8:
6: 8:
LCM =
(19) Find LCM of 12 and 15:
12: 15:
LCM =
Challenge Problem (20)
Two bells ring at different intervals. Bell A rings every 12 minutes, and Bell B rings every 18 minutes. If both bells ring together at noon, at what time will they next ring together?
Hint: Find the LCM of 12 and 18.
Time:
Check your work!
I checked my equation by substituting my answer back.
I listed all factor pairs before choosing my GCF.
I used skip-counting to double check my multiples.