Ratio and Proportion - URBrainy.com - Free Printable

Let’s solve each part step by step.

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Problem 1: Pattern of squares (first strip)

The strip has 10 squares total. Let’s count:

Black tiles: positions 2, 4, 6 → that’s 3 black tiles

White tiles: the rest → 10 - 3 = 7 white tiles

a. How many black tiles to white tiles?
→ That’s a ratio: 3 to 7

b. Proportion of black tiles in the strip?
→ Black / Total = 3 / 10 → 3/10

c. Proportion of white tiles in the strip?
→ White / Total = 7 / 10 → 7/10

✔ Check: 3 + 7 = 10 → correct.

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Problem 2: Checkerboard pattern (second strip)

This is a 3-row by 10-column grid → 3 × 10 = 30 squares total

It’s a checkerboard — alternating black and white.

In a full checkerboard with even number of columns (10), each row will have 5 black and 5 white.

So for 3 rows:

Black tiles: 3 rows × 5 = 15

White tiles: 3 rows × 5 = 15

a. Black to white tiles?
→ 15 to 15, which simplifies to 1 to 1

b. Proportion of black tiles?
→ 15 / 30 = 1/2

c. Proportion of white tiles?
→ 15 / 30 = 1/2

✔ Check: 15 + 15 = 30 → correct.

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Problem 3: Two shapes made of small squares

First shape (left): looks like an “L” made of 4 small squares.

Second shape (right): looks like a cross or plus sign — let’s count:

- Center square
- One above, one below, one left, one right → that’s 5 more? Wait, no — actually, it’s symmetric.

Looking carefully:

Right shape:
Top row: 1 square
Middle row: 3 squares (left, center, right)
Bottom row: 1 square
Total = 1 + 3 + 1 = 5 squares

Left shape:
It’s 3 in a column, and 1 sticking out to the right on the bottom → so 4 squares.

Wait — let me recount both clearly.

Left shape:
Imagine coordinates:

(0,0), (0,1), (0,2), (1,0) → that’s 4 squares.

Right shape:
(0,1), (1,0), (1,1), (1,2), (2,1) → that’s 5 squares.

Yes.

So:

Larger shape = 5 squares
Smaller shape = 4 squares

How many times bigger is the larger than the smaller?

→ 5 ÷ 4 = 1.25 times OR as a fraction: 5/4 times

But sometimes they want “how many times bigger” meaning the multiplier — so 5/4.

Alternatively, if they mean “how much bigger”, that would be difference: 5 - 4 = 1, but the question says “how many times bigger”, which usually means ratio.

Let’s read again:
“How many times bigger is the larger shape than the smaller shape?”

That’s asking: Larger = ? × Smaller → 5 = ? × 4 → ? = 5/4

So answer: 5/4 times or 1¼ times

Next question:
“What fraction of the two shapes together is the smaller shape?”

Together: 4 + 5 = 9 squares

Smaller shape: 4

Fraction: 4/9

✔ Check: 4 + 5 = 9 → yes.

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Final Answers:

Problem 1:
a. 3 to 7
b. 3/10
c. 7/10

Problem 2:
a. 1 to 1
b. 1/2
c. 1/2

Problem 3:
- Larger shape is 5/4 times bigger than the smaller shape.
- Smaller shape is 4/9 of the two shapes together.

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Final Answer:
1a. 3 to 7
1b. 3/10
1c. 7/10
2a. 1 to 1
2b. 1/2
2c. 1/2
3. 5/4 times; 4/9