Let’s solve each problem step by step using the area model. The area model shows a rectangle divided into parts — the shaded part represents the product of two fractions.
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Problem 1:
The grid is 5 columns wide and 4 rows tall → total = 20 small squares.
Shaded region: 3 columns × 3 rows = 9 squares.
So, the fraction shown is
9/20.
But we’re told it’s multiplying
3/5 × 3/4.
Let’s check:
3/5 means 3 out of 5 columns are shaded horizontally.
3/4 means 3 out of 4 rows are shaded vertically.
Where they overlap (the double-shaded part) is 3×3 = 9 out of 5×4 = 20 →
9/20 ✔
Final Answer for #1:
9/20
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Problem 2:
Grid is 3 columns × 3 rows = 9 total squares.
Shaded: 2 columns × 2 rows = 4 squares →
4/9
Given:
2/3 × 2/3
2/3 of columns × 2/3 of rows → overlap = 2×2 = 4 out of 3×3 = 9 →
4/9 ✔
Final Answer for #2:
4/9
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Problem 3:
Grid is 6 columns × 5 rows = 30 total squares.
Shaded: 3 columns × 2 rows = 6 squares →
6/30, which simplifies to
1/5
Given:
3/6 × 2/5
First, simplify 3/6 to 1/2 → so it’s 1/2 × 2/5 = (1×2)/(2×5) = 2/10 = 1/5
Or without simplifying: 3/6 × 2/5 = (3×2)/(6×5) = 6/30 = 1/5
✔
Final Answer for #3:
1/5
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Problem 4:
Grid is 5 columns × 5 rows = 25 total squares.
Shaded: 4 columns × 3 rows = 12 squares →
12/25
Given:
4/5 × 3/5
Multiply numerators: 4×3 = 12
Multiply denominators: 5×5 = 25 →
12/25 ✔
Final Answer for #4:
12/25
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Problem 5:
Grid is 6 columns × 6 rows = 36 total squares.
Shaded: 5 columns × 4 rows = 20 squares →
20/36, simplify by dividing numerator and denominator by 4 →
5/9
Given:
5/6 × 4/6
Multiply: (5×4)/(6×6) = 20/36 = 5/9
✔
Final Answer for #5:
5/9
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Problem 6:
Grid is 5 columns × 5 rows = 25 total squares.
Shaded: 3 columns × 2 rows = 6 squares →
6/25
Given:
3/5 × 2/5
Multiply: (3×2)/(5×5) = 6/25
✔
Final Answer for #6:
6/25
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Final Answer:
1) 9/20
2) 4/9
3) 1/5
4) 12/25
5) 5/9
6) 6/25
Parent Tip: Review the logic above to help your child master the concept of multiplying fractions using models worksheet.
