Question

40 people were asked what their favourite fruit is.
draw the symbols to complete the pictogram.

favourite fruit
banana: two full circle symbols with crosshairs
peach: one three-quarter circle symbol
apple: empty box

key:
one full circle symbol with crosshairs = 8 people

Explanation:

🆕 New Concept Discovered: Pictograms and Keys
Representing data using symbols and fractional parts of symbols.

Step 1: Calculate the number of people represented by Banana and Peach

The key shows that one full circle symbol represents \( 8 \) people.

• Banana: Has \( 2 \) full symbols.

$$ 2 \times 8 = 16 \text{ people} $$

• Peach: Has a fraction of a symbol. The circle is split into four equal quarters, and only three quarters are shown.
• One quarter represents:

$$ \frac{8}{4} = 2 \text{ people} $$

• Three quarters represent:

$$ 3 \times 2 = 6 \text{ people} $$

Step 2: Find the remaining number of people for Apple

The total number of people surveyed is \( 40 \).

• Total people accounted for so far:

$$ 16 \text{ (Banana)} + 6 \text{ (Peach)} = 22 \text{ people} $$

• Remaining people who chose Apple:

$$ 40 - 22 = 18 \text{ people} $$

Step 3: Determine the symbols needed for Apple

We need to represent \( 18 \) people using the symbols where one full symbol equals \( 8 \) people.

• Number of full symbols:

$$ 18 \div 8 = 2 \text{ full symbols with a remainder of } 2 $$

$$ 2 \times 8 = 16 \text{ people} $$

• Remaining value to represent:

$$ 18 - 16 = 2 \text{ people} $$

• Since one quarter of a circle represents \( 2 \) people, we need exactly \( 1 \) quarter of a circle.

Answer:

To complete the pictogram for Apple, you need to draw:

• 2 full circle symbols and 1 quarter of a circle symbol (a single slice representing \( 2 \) people).