Let’s solve each equation one by one. We’re solving for the variable
y in each case. The goal is to get
y alone on one side of the equation.
We’ll use inverse operations — that means if something is added, we subtract it from both sides; if something is multiplied or divided, we do the opposite to both sides.
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Problem 1:
$\frac{y}{1} + 6 = 11$
→ $\frac{y}{1}$ is just $y$, so:
$y + 6 = 11$
Subtract 6 from both sides:
$y = 11 - 6$
$y = 5$
✔ Check: $5 + 6 = 11$ → Correct!
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Problem 2:
$5 + \frac{y}{9} = 6$
Subtract 5 from both sides:
$\frac{y}{9} = 1$
Multiply both sides by 9:
$y = 9$
✔ Check: $5 + \frac{9}{9} = 5 + 1 = 6$ → Correct!
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Problem 3:
$\frac{y}{11} + 6 = 7$
Subtract 6 from both sides:
$\frac{y}{11} = 1$
Multiply both sides by 11:
$y = 11$
✔ Check: $\frac{11}{11} + 6 = 1 + 6 = 7$ → Correct!
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Problem 4:
$8 + \frac{y}{5} = 8.8$
Subtract 8 from both sides:
$\frac{y}{5} = 0.8$
Multiply both sides by 5:
$y = 0.8 × 5 = 4$
✔ Check: $8 + \frac{4}{5} = 8 + 0.8 = 8.8$ → Correct!
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Problem 5:
$\frac{y}{4} + 4 = 5.3$
Subtract 4 from both sides:
$\frac{y}{4} = 1.3$
Multiply both sides by 4:
$y = 1.3 × 4 = 5.2$
✔ Check: $\frac{5.2}{4} + 4 = 1.3 + 4 = 5.3$ → Correct!
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Problem 6:
$\frac{y}{12} + 1 = 1.6$
Subtract 1 from both sides:
$\frac{y}{12} = 0.6$
Multiply both sides by 12:
$y = 0.6 × 12 = 7.2$
✔ Check: $\frac{7.2}{12} + 1 = 0.6 + 1 = 1.6$ → Correct!
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Problem 7:
$\frac{y}{12} + 3 = 3.3$
Subtract 3 from both sides:
$\frac{y}{12} = 0.3$
Multiply both sides by 12:
$y = 0.3 × 12 = 3.6$
✔ Check: $\frac{3.6}{12} + 3 = 0.3 + 3 = 3.3$ → Correct!
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Problem 8:
$\frac{y}{3} + 10 = 13$
Subtract 10 from both sides:
$\frac{y}{3} = 3$
Multiply both sides by 3:
$y = 9$
✔ Check: $\frac{9}{3} + 10 = 3 + 10 = 13$ → Correct!
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Problem 9:
$\frac{y}{10} + 2 = 2.5$
Subtract 2 from both sides:
$\frac{y}{10} = 0.5$
Multiply both sides by 10:
$y = 5$
✔ Check: $\frac{5}{10} + 2 = 0.5 + 2 = 2.5$ → Correct!
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Problem 10:
$\frac{y}{12} + 1 = 1.3$
Subtract 1 from both sides:
$\frac{y}{12} = 0.3$
Multiply both sides by 12:
$y = 0.3 × 12 = 3.6$
✔ Check: $\frac{3.6}{12} + 1 = 0.3 + 1 = 1.3$ → Correct!
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Final Answer:
1. y = 5
2. y = 9
3. y = 11
4. y = 4
5. y = 5.2
6. y = 7.2
7. y = 3.6
8. y = 9
9. y = 5
10. y = 3.6
Parent Tip: Review the logic above to help your child master the concept of solving equations worksheet grade 3.
