Unit 5 · Topic 03 · Fractions and Decimals
Kabir ate half a chocolate bar. Anaya ate 2 out of 4 equal pieces of an identical bar.
They argued about who ate more — until they lined up both bars side by side.
The eaten portions covered the exact same amount of chocolate, even though the fractions 1/2 and 2/4 look completely different written down.
"Line up the bars," said Ms. Rao. Kabir's bar was split into 2 equal pieces, 1 eaten: 1/2. Anaya's identical-sized bar was split into 4 equal pieces, 2 eaten: 2/4. Placed side by side, the eaten chocolate covered the EXACT same length on both bars.
"1/2 and 2/4 are called EQUIVALENT fractions," said Ms. Rao. "Different numerators and denominators, but the same value." She showed the rule: multiply (or divide) both the numerator AND denominator by the same number, and the value never changes. 1/2 x 2/2 = 2/4. Try again: 1/2 x 3/3 = 3/6.
Anaya tested it backwards: could she SIMPLIFY 6/8 down to a smaller equivalent fraction? She found both 6 and 8 share a common factor of 2: 6÷2=3, 8÷2=4, so 6/8 = 3/4. "Simplifying is just the same rule in reverse — dividing both top and bottom by the same number."
"Here's a way to CHECK if two fractions are equivalent without simplifying," said Ms. Rao. "Cross-multiply: for a/b and c/d, check if a×d equals b×c." For 1/2 and 2/4: 1×4=4, and 2×2=4 — equal, so they're equivalent. Kabir tried 2/3 and 3/5: 2×5=10, and 3×3=9 — NOT equal, so these are NOT equivalent fractions, confirmed instantly without drawing a single chocolate bar.
Equivalent fractions represent the same value even though they're written with different numerators and denominators.
To find an equivalent fraction, multiply both the numerator and denominator by the same number.
To simplify a fraction, divide both the numerator and denominator by their common factor.
Cross-multiplication check: a/b equals c/d exactly when a×d equals b×c.
Show 1/2, 2/4, 3/6, 4/8 on circles — same half shaded each time.
Find the blank: 1/2 = ?/16 and 5/6 = 35/?.
Use cross multiplication for 8/9 = x/15.
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