F9 · A Natural Number Times a Fraction
“I can multiply a natural number by a fraction. I can show it as repeated addition. I can explain why the answer can be smaller than the natural number.”
2 × 1/4. Read it as repeated addition: 1/4 + 1/4. Add the numerators. The denominator stays 4, because the size of the parts does not change: 2/4. Simplify: 2/4 = 1/2. Model both ways, side by side: a bar split in quarters with 2 quarters shaded, AND jumps of 1/4 on a 0–2 number line — two jumps land on 2/4, which is the point 1/2.
In 2 × 1/4, why does the denominator stay 4?
3 × 1/6 → 1/6 + 1/6 + 1/6 = 3/6 = 1/2.
4 × 1/8 = 1/8 + 1/8 + 1/8 + 1/8 = 4/8 = ___. Finish the last step: simplify the product. → 1/2
10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.