Let’s solve each problem step by step. We’re multiplying fractions using area models — that means we’ll think of the grid as a rectangle divided into parts, and the shaded overlapping part shows the product.
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Problem 1:
We have a grid that is 5 columns wide and 4 rows tall → total 20 small squares.
The first fraction is
3/5 → shade 3 out of 5 columns (vertically).
The second fraction is
1/4 → shade 1 out of 4 rows (horizontally).
Where they overlap? Only 3 small squares are shaded in both directions.
So, 3 out of 20 total squares →
3/20
Check: 3/5 × 1/4 = (3×1)/(5×4) = 3/20
✔
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Problem 2:
Grid is 3 columns × 3 rows = 9 squares.
First fraction:
1/3 → shade 1 column.
Second fraction:
1/3 → shade 1 row.
Overlap: only 1 square where both shades meet.
So, 1 out of 9 →
1/9
Check: 1/3 × 1/3 = 1/9
✔
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Problem 3:
Grid is 4 columns × 2 rows = 8 squares.
First fraction:
3/4 → shade 3 columns.
Second fraction:
1/2 → shade 1 row.
Overlap: 3 squares (since 3 columns × 1 row = 3)
Total squares = 8 → so answer is
3/8
Check: 3/4 × 1/2 = 3/8
✔
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Problem 4:
Grid is 6 columns × 5 rows = 30 squares.
First fraction:
5/6 → shade 5 columns.
Second fraction:
3/5 → shade 3 rows.
Overlap: 5 columns × 3 rows = 15 squares.
Total = 30 → 15/30 simplifies to
1/2
Check: 5/6 × 3/5 = (5×3)/(6×5) = 15/30 = 1/2
✔
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Problem 5:
Grid is 7 columns × 3 rows = 21 squares.
First fraction:
5/7 → shade 5 columns.
Second fraction:
2/3 → shade 2 rows.
Overlap: 5 × 2 = 10 squares.
Total = 21 → answer is
10/21
Check: 5/7 × 2/3 = 10/21
✔ (can’t simplify further)
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Problem 6:
Grid is 2 columns × 5 rows = 10 squares.
First fraction:
1/2 → shade 1 column.
Second fraction:
3/5 → shade 3 rows.
Overlap: 1 × 3 = 3 squares.
Total = 10 → answer is
3/10
Check: 1/2 × 3/5 = 3/10
✔
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Final Answer:
1) 3/20
2) 1/9
3) 3/8
4) 1/2
5) 10/21
6) 3/10
Parent Tip: Review the logic above to help your child master the concept of fraction models worksheet.
