Let’s solve each row one by one. The rule is:
each row has one missing digit that repeats in all the blank circles — and we need to find that digit, then write it in the shaded circle at the end.
We’ll go row by row.
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Row 1:
_ _ + _ 2 = 170
Let the missing digit be
x. So the equation becomes:
xx + x2 = 170
That means: (10*x + x) + (10*x + 2) = 170
→ 11x + 10x + 2 = 170
→ 21x + 2 = 170
→ 21x = 168
→ x = 8
Check: 88 + 82 = 170 →
✔ Correct!
So shaded circle =
8
---
Row 2:
_ 5 + 4 _ = 111
Missing digit = x → x5 + 4x = 111
→ (10*x + 5) + (40 + x) = 111
→ 10x + 5 + 40 + x = 111
→ 11x + 45 = 111
→ 11x = 66
→ x = 6
Check: 65 + 46 = 111 →
✔ Correct!
Shaded circle =
6
---
Row 3:
_ _ + 4 _ = 124
Missing digit = x → xx + 4x = 124
→ (10x + x) + (40 + x) = 124
→ 11x + 40 + x = 124
→ 12x + 40 = 124
→ 12x = 84
→ x = 7
Check: 77 + 47 = 124 →
✔ Correct!
Shaded circle =
7
---
Row 4:
_ 5 + 2 _ = 113
Missing digit = x → x5 + 2x = 113
→ (10x + 5) + (20 + x) = 113
→ 11x + 25 = 113
→ 11x = 88
→ x = 8
Check: 85 + 28 = 113 →
✔ Correct!
Shaded circle =
8
---
Row 5:
_ 4 + _ _ = 109
Missing digit = x → x4 + xx = 109
→ (10x + 4) + (10x + x) = 109
→ 10x + 4 + 11x = 109
→ 21x + 4 = 109
→ 21x = 105
→ x = 5
Check: 54 + 55 = 109 →
✔ Correct!
Shaded circle =
5
---
Row 6:
_ 3 + _ _ = 129
Missing digit = x → x3 + xx = 129
→ (10x + 3) + (10x + x) = 129
→ 10x + 3 + 11x = 129
→ 21x + 3 = 129
→ 21x = 126
→ x = 6
Check: 63 + 66 = 129 →
✔ Correct!
Shaded circle =
6
---
Row 7:
7 _ + _ 4 = 129
Missing digit = x → 7x + x4 = 129
→ (70 + x) + (10x + 4) = 129
→ 70 + x + 10x + 4 = 129
→ 11x + 74 = 129
→ 11x = 55
→ x = 5
Check: 75 + 54 = 129 →
✔ Correct!
Shaded circle =
5
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Final Answer:
8, 6, 7, 8, 5, 6, 5
Parent Tip: Review the logic above to help your child master the concept of missing numbers in equations worksheet.
