A student folds a paper strip in half and shades one part (1/2). Then they fold the same strip in half again, creating four equal sections. The shaded portion now covers 2 of the 4 sections. What does this demonstrate?
AThe shaded portion grew when the strip was folded again, so 2/4 is greater than 1/2
B1/2 and 2/4 are equivalent fractions — different names for the same amount of paper
CFractions always change value whenever the denominator changes
DThe folding tore the strip, so the two fractions now represent different amounts
No paper was added or removed — the shaded region is physically unchanged. Folding again only changed how many equal parts the strip is divided into. So 1/2 and 2/4 name the same amount. This is the definition of equivalent fractions: different-looking expressions that represent the same quantity.
Question 2 Multiple Choice
Which of the following is an equivalent fraction for 1/3?
A2/3 — double the numerator only
B1/6 — because 6 is a multiple of 3
C2/6 — multiply both numerator and denominator by 2
D3/1 — flip the fraction
To create an equivalent fraction, you must multiply (or divide) BOTH the numerator and denominator by the same number. 1/3 × (2/2) = 2/6. Option A doubles only the numerator, making the fraction larger (2/3 ≠ 1/3). Option B (1/6) is actually smaller than 1/3. Option D creates a completely different number.
Question 3 True / False
1/2 and 3/6 represent the same amount, even though they look different.
TTrue
FFalse
Answer: True
3/6 = 1/2 because 3 ÷ 3 = 1 and 6 ÷ 3 = 2 — dividing both by 3 reduces 3/6 to 1/2. Equivalently, 1/2 × (3/3) = 3/6. These fractions look different but name the same point on the number line and the same portion of any equal whole.
Question 4 True / False
When you convert a fraction to an equivalent fraction, both the number of pieces and the size of each piece stay the same.
TTrue
FFalse
Answer: False
When creating an equivalent fraction, the number of pieces changes AND the size of each piece changes — but they change proportionally, so the total amount stays the same. Going from 1/2 to 2/4: you now have twice as many pieces (2 instead of 1), but each piece is half as large. The changes cancel out, preserving the total amount. What stays the same is the value, not the pieces themselves.
Question 5 Short Answer
Explain why multiplying both the numerator and denominator of a fraction by the same number does not change the fraction's value.
Think about your answer, then reveal below.
Model answer: Multiplying the denominator by a number cuts each piece into that many smaller pieces — increasing the total count. Multiplying the numerator by the same number takes that many of the new smaller pieces. The two changes cancel: you have more pieces, but each is proportionally smaller, so the shaded amount is unchanged. For example, 1/2 × (3/3) = 3/6: the whole is now cut into 6 pieces instead of 2, but you take 3 of them — still exactly half.
This is equivalent to multiplying by 1 (since any number divided by itself equals 1). Multiplying a fraction by 1 cannot change its value. The key insight is that changing the 'unit size' (how big each piece is) and the 'unit count' (how many pieces you take) by the same factor leaves the total amount invariant.