Fifth Grade · Math · week 20

Fraction times fraction with arrays

Multiply a fraction by a fraction using an area model, understanding the product as part of a part.

Multiplying two fractions means finding "a part of a part." 1/2 x 1/3 asks: what is one half of one third? You can see this with a rectangle split both ways.

To multiply fractions, multiply the numerators together and the denominators together: (a/b) x (c/d) = (a x c) / (b x d).

📋 For the teacher
Teach it (10–15 min):
  • Draw the array together at least once, shading rows one color and columns another so the overlap is visible as the product.
  • Introduce the "multiply straight across" rule only after the picture makes sense, so it is not just a memorized trick.
  • Notice out loud that multiplying two fractions less than 1 gives an answer SMALLER than either fraction -- a part of a part is tiny.
  • Practice simplifying every product at the end, every time.
Talk about it:
  • What does "a part of a part" mean when multiplying two fractions?
  • Why does multiplying two fractions less than 1 give a smaller answer, unlike whole-number multiplication?
  • How does the array picture connect to the "multiply straight across" rule?

Mastery looks like: They can multiply two fractions using the straight-across rule and explain the result using an area-model picture.

Common stumbles: Expecting the product to be bigger, as with whole numbers; adding across instead of multiplying; forgetting to simplify.

See it visually

Interactive, spoken-aloud tools that show this idea in motion.

FractionsSlice bars and circles into equal parts and compare them.try →MultiplicationEqual groups and arrays make products finally click.try →
Homework for this lessonType it, write it with a stylus, or print it for pencil & paper.open →
Records attendance + 15 min of Math for this learner.
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