Fraction addition concepts · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Splitting fractions into parts

Mathematics · Fractions · ages 9-10
Name ______________________   Date ____________

  1. A bar is one whole divided into seven equal parts. Three parts are shaded. Which two-part sum matches the shaded amount?

    • 1/3 + 2/3
    • 1/7 + 2/7
    • 1/7 + 3/7
    • 1/4 + 2/4

  2. Which sum of unit eighths equals 3/8?

    • 1/8 + 1/8 + 1/8
    • 1/8 + 1/8 + 2/8
    • 1/4 + 1/4 + 1/4

  3. A fraction can have only one valid split into smaller fraction parts.

    Circle one:   True   False

  4. Which pair of sevenths adds to 4/7?

    • 2/7 + 3/7
    • 1/7 + 3/7
    • 1/7 + 2/7

  5. Noah joins 1/4 of a small bar and 2/4 of a larger bar. He calls the total 3/4 of the small bar. Why does adding the numerators not work here?

    • The numerators must match before adding.
    • Each part needs a different denominator.
    • Fourth-pieces cannot be put into groups.
    • The parts use different-size wholes.

  6. Split 8/10 into equal groups of 2/10. How many groups do you get?

    Answer: ______________

  7. Split 8/9 into two equal parts, each written with denominator 9. What numerator does each part have?

    Answer: ______________

  8. 9/11 - 4/11 = ?/11. What is the remaining numerator?

    Answer: ______________

  9. Kai writes 6/9 = 2/9 + 3/9. What does his proposed split total?

    • 4/9
    • 5/9
    • 6/9

  10. A ribbon is 2 3/8 meters long. How many eighths are in its fraction part?

    Answer: ______________

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Answer key

For grown-ups. Fold this page away before handing over the rest.

Splitting fractions into parts W1-mt_VgOePicFYK-s1

  1. 1/7 + 2/7 · The three shaded parts are sevenths. Grouping them as one and two gives 1/7 + 2/7.
  2. 1/8 + 1/8 + 1/8 · Three unit eighths count the three pieces in 3/8.
  3. False · Different groups of pieces can add back to the same fraction.
  4. 1/7 + 3/7 · 1 + 3 = 4, so 1/7 + 3/7 equals 4/7.
  5. The parts use different-size wholes. · A fourth of the larger bar is larger than a fourth of the small bar. These pieces do not share one whole size.
  6. 4 · Eight tenth-pieces make four groups of two: 2 + 2 + 2 + 2 = 8.
  7. 4 · Share eight ninth-pieces equally between two groups. Each group has four pieces, so each part is 4/9.
  8. 5 · Separating four pieces from nine leaves five eleventh-pieces.
  9. 5/9 · 2 + 3 = 5. His split totals 5/9, one ninth short of 6/9.
  10. 3 · The fraction part is 3/8 meter, which contains three eighths.
Worksheet · LightMySky