Let's solve each of the six decimal multiplication problems shown in the image. Each problem involves finding a missing value in a decimal equation, and the visual grids help represent the decimals as parts of a whole (10x10 grid = 1 whole unit).
Each small square represents
0.01 (since 100 squares = 1).
---
Problem 1:
Equation:
`□ × 0.4 = 0.36`
- The shaded area is 36 squares → 0.36
- One factor is 0.4 → which is 40 squares (4 rows of 10)
- So we are looking for a number that, when multiplied by 0.4, gives 0.36.
Let’s solve:
$$
x \times 0.4 = 0.36 \\
x = \frac{0.36}{0.4} = 0.9
$$
✔ Answer: 0.9
---
Problem 2:
Equation:
`0.6 × 0.7 = □`
- 0.6 = 60 squares (6 columns)
- 0.7 = 70 squares (7 rows)
- Overlap = 60 × 70 = 4200 hundredths? Wait — better to think multiplicatively.
Actually, since both are decimals:
$$
0.6 \times 0.7 = 0.42
$$
Visually: 60% of 70% = 42% of the whole grid → 42 squares shaded → 0.42
✔ Answer: 0.42
---
Problem 3:
Equation:
`0.8 × □ = 0.32`
- 0.8 is 80 squares (8 columns)
- Product is 0.32 → 32 squares
- We want: $ x = \frac{0.32}{0.8} $
$$
x = \frac{0.32}{0.8} = 0.4
$$
✔ Answer: 0.4
---
Problem 4:
Equation:
`□ × 0.5 = 0.3`
- 0.5 is half the grid → 50 squares
- Product is 0.3 → 30 squares
- So: $ x \times 0.5 = 0.3 $
$$
x = \frac{0.3}{0.5} = 0.6
$$
✔ Answer: 0.6
---
Problem 5:
Equation:
`0.3 × □ = 0.12`
- 0.3 is 30 squares (3 columns)
- Product is 0.12 → 12 squares
- $ x = \frac{0.12}{0.3} = 0.4 $
✔ Answer: 0.4
---
Problem 6:
Equation:
`0.5 × □ = 0.45`
- 0.5 is half the grid
- Product is 0.45 → 45 squares
- $ x = \frac{0.45}{0.5} = 0.9 $
✔ Answer: 0.9
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✔ Final Answers:
1.
0.9
2.
0.42
3.
0.4
4.
0.6
5.
0.4
6.
0.9
These match the visual representations in the grids where the shaded areas correspond to the products or factors.
Parent Tip: Review the logic above to help your child master the concept of decimal multiplication models.
