You're working on
solving 1-step equations — specifically, equations where a variable is divided by a number (or multiplied by a fraction), and you need to isolate the variable using one inverse operation.
The key idea:
> If a variable is
divided by a number, multiply
both sides of the equation by that number to solve for the variable.
> If a variable is
multiplied by a fraction (like `1/3 w`), multiply both sides by the
reciprocal of that fraction to isolate the variable.
---
Let’s solve each equation step-by-step:
---
1. `x/6 = 5`
Multiply both sides by 6:
> `6 * (x/6) = 6 * 5`
> `x = 30`
✔ Answer: x = 30
---
2. `4 = (1/3)w`
Multiply both sides by 3 (the reciprocal of 1/3):
> `3 * 4 = 3 * (1/3)w`
> `12 = w`
✔ Answer: w = 12
---
3. `y/3 = 3`
Multiply both sides by 3:
> `3 * (y/3) = 3 * 3`
> `y = 9`
✔ Answer: y = 9
---
4. `3 = x/10`
Multiply both sides by 10:
> `10 * 3 = 10 * (x/10)`
> `30 = x`
✔ Answer: x = 30
---
5. `t/5 = 7`
Multiply both sides by 5:
> `5 * (t/5) = 5 * 7`
> `t = 35`
✔ Answer: t = 35
---
6. `7 = h/11`
Multiply both sides by 11:
> `11 * 7 = 11 * (h/11)`
> `77 = h`
✔ Answer: h = 77
---
7. `(1/7)p = 4`
Multiply both sides by 7 (reciprocal of 1/7):
> `7 * (1/7)p = 7 * 4`
> `p = 28`
✔ Answer: p = 28
---
8. `8 = (1/8)k`
Multiply both sides by 8:
> `8 * 8 = 8 * (1/8)k`
> `64 = k`
✔ Answer: k = 64
---
9. `(1/6)y = 3`
Multiply both sides by 6:
> `6 * (1/6)y = 6 * 3`
> `y = 18`
✔ Answer: y = 18
---
10. `10 = r/6`
Multiply both sides by 6:
> `6 * 10 = 6 * (r/6)`
> `60 = r`
✔ Answer: r = 60
---
##
✔ Final Answers:
1.
x = 30
2.
w = 12
3.
y = 9
4.
x = 30
5.
t = 35
6.
h = 77
7.
p = 28
8.
k = 64
9.
y = 18
10.
r = 60
---
💡
Tip: Always check your answer by plugging it back into the original equation!
Example: Check #1 → `x/6 = 5` → `30/6 = 5` → ✔️ Correct!
Let me know if you want to practice more or learn how to write these solutions neatly!
Parent Tip: Review the logic above to help your child master the concept of solving equations with multiplication and division worksheet.
