Reference / Curriculum / 3B / Chapter 9

3B · Chapter 9 · Lesson 4

Comparing Fractions with Like Numerators

Reason why fewer equal parts of a whole make larger pieces.

MATH-3B-C09-L04Independent and tutor-supported

Today's mathematical question

Compare 3/6 and 3/8. Write > or <.

Learning target

Reason why fewer equal parts of a whole make larger pieces.

Before starting: Prior lesson: Comparing Fractions with Like Denominators. Try the warm-up independently.

Prerequisite · 3 questions

Check earlier skills first

These are earlier ideas you need for today; revisit them if they are difficult.

  1. P1

    Compare 2/4 and 3/4. Write > or <.

    Reveal explanation

    Answer: <

    Both fractions use pieces of size 1/4, so compare 2 pieces with 3 pieces: 2/4 < 3/4.

    2/43/4
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  2. P2

    Compare 2/3 and 1/3. Write > or <.

    Reveal explanation

    Answer: >

    Both fractions use pieces of size 1/3, so compare 2 pieces with 1 pieces: 2/3 > 1/3.

    2/31/3
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  3. P3

    Compare 4/8 and 2/8. Write > or <.

    Reveal explanation

    Answer: >

    Both fractions use pieces of size 1/8, so compare 4 pieces with 2 pieces: 4/8 > 2/8.

    4/82/8
    Each full bar represents the same-sized whole; shaded parts show the fraction.

Learn and understand

When the numerator is the same, compare the size of each piece. One fourth of a whole is larger than one eighth because a whole cut into four equal parts makes larger pieces than when cut into eight. Therefore 3/4 is larger than 3/8, provided the wholes are equal. Compare 3/5 with 3/8 on equal-sized strips. Fifths are bigger pieces than eighths, so three fifths covers more. Confirm with a drawing before using a rule.

Represent it three ways

  1. Concrete: Build equal pieces, measures, counters or shapes with real objects when useful.
  2. Pictorial: Draw two equal-length bars with different numbers of equal partitions. Shade the same number of parts and compare shaded lengths.
  3. Abstract: Write the matching number sentence, calculation, comparison or mathematical description. Explain each number's unit.

Important vocabulary

like numerators
same count of parts chosen
denominator
number of equal parts in the whole
unit fraction
one equal part

Fully worked examples and checks

Try each new understanding check before revealing the explanation.

Worked example 1

Explore, calculate, verify

Compare 3/6 and 3/8. Write > or <.

3/63/8
Each full bar represents the same-sized whole; shaded parts show the fraction.
  1. Identify the whole, the units, and what the question asks.
  2. There are 3 pieces in each fraction, but 1/6 is a larger piece than 1/8 when the whole is identical.
  3. Check that the answer uses the right units and makes sense.

Answer: >

Check your understanding 1

Compare 3/4 and 3/6. Write > or <.

Reveal answer and explanation

> — There are 3 pieces in each fraction, but 1/4 is a larger piece than 1/6 when the whole is identical.

3/43/6
Each full bar represents the same-sized whole; shaded parts show the fraction.

Worked example 2

Explore, calculate, verify

Compare 2/6 and 2/10. Write > or <.

2/62/10
Each full bar represents the same-sized whole; shaded parts show the fraction.
  1. Identify the whole, the units, and what the question asks.
  2. There are 2 pieces in each fraction, but 1/6 is a larger piece than 1/10 when the whole is identical.
  3. Check that the answer uses the right units and makes sense.

Answer: >

Check your understanding 2

Compare 6/10 and 6/8. Write > or <.

Reveal answer and explanation

< — There are 6 pieces in each fraction, but 1/8 is a larger piece than 1/10 when the whole is identical.

6/106/8
Each full bar represents the same-sized whole; shaded parts show the fraction.

Worked example 3

Explore, calculate, verify

Compare 2/5 and 2/3. Write > or <.

2/52/3
Each full bar represents the same-sized whole; shaded parts show the fraction.
  1. Identify the whole, the units, and what the question asks.
  2. There are 2 pieces in each fraction, but 1/3 is a larger piece than 1/5 when the whole is identical.
  3. Check that the answer uses the right units and makes sense.

Answer: <

Check your understanding 3

Compare 6/12 and 6/10. Write > or <.

Reveal answer and explanation

< — There are 6 pieces in each fraction, but 1/10 is a larger piece than 1/12 when the whole is identical.

6/126/10
Each full bar represents the same-sized whole; shaded parts show the fraction.

Guided · 5 questions

Guided practice

Keep the model and earlier examples visible while practising.

  1. G1

    Compare 3/8 and 3/6. Write > or <.

    Reveal explanation

    Answer: <

    There are 3 pieces in each fraction, but 1/6 is a larger piece than 1/8 when the whole is identical.

    3/83/6
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  2. G2

    Compare 1/10 and 1/4. Write > or <.

    Reveal explanation

    Answer: <

    There are 1 pieces in each fraction, but 1/4 is a larger piece than 1/10 when the whole is identical.

    1/101/4
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  3. G3

    Compare 1/8 and 1/10. Write > or <.

    Reveal explanation

    Answer: >

    There are 1 pieces in each fraction, but 1/8 is a larger piece than 1/10 when the whole is identical.

    1/81/10
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  4. G4

    Compare 3/6 and 3/10. Write > or <.

    Reveal explanation

    Answer: >

    There are 3 pieces in each fraction, but 1/6 is a larger piece than 1/10 when the whole is identical.

    3/63/10
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  5. G5

    Compare 2/3 and 2/5. Write > or <.

    Reveal explanation

    Answer: >

    There are 2 pieces in each fraction, but 1/3 is a larger piece than 1/5 when the whole is identical.

    2/32/5
    Each full bar represents the same-sized whole; shaded parts show the fraction.

Independent · 8 questions

Independent practice

Work these without hints and explain the method used. Write answers on paper.

  1. I1

    Compare 3/8 and 3/5. Write > or <.

    Reveal explanation

    Answer: <

    There are 3 pieces in each fraction, but 1/5 is a larger piece than 1/8 when the whole is identical.

    3/83/5
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  2. I2

    Compare 3/5 and 3/8. Write > or <.

    Reveal explanation

    Answer: >

    There are 3 pieces in each fraction, but 1/5 is a larger piece than 1/8 when the whole is identical.

    3/53/8
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  3. I3

    Compare 1/4 and 1/8. Write > or <.

    Reveal explanation

    Answer: >

    There are 1 pieces in each fraction, but 1/4 is a larger piece than 1/8 when the whole is identical.

    1/41/8
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  4. I4

    Compare 2/3 and 2/6. Write > or <.

    Reveal explanation

    Answer: >

    There are 2 pieces in each fraction, but 1/3 is a larger piece than 1/6 when the whole is identical.

    2/32/6
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  5. I5

    Compare 1/3 and 1/10. Write > or <.

    Reveal explanation

    Answer: >

    There are 1 pieces in each fraction, but 1/3 is a larger piece than 1/10 when the whole is identical.

    1/31/10
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  6. I6

    Compare 2/4 and 2/3. Write > or <.

    Reveal explanation

    Answer: <

    There are 2 pieces in each fraction, but 1/3 is a larger piece than 1/4 when the whole is identical.

    2/42/3
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  7. I7

    Compare 3/6 and 3/12. Write > or <.

    Reveal explanation

    Answer: >

    There are 3 pieces in each fraction, but 1/6 is a larger piece than 1/12 when the whole is identical.

    3/63/12
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  8. I8

    Compare 2/12 and 2/8. Write > or <.

    Reveal explanation

    Answer: <

    There are 2 pieces in each fraction, but 1/8 is a larger piece than 1/12 when the whole is identical.

    2/122/8
    Each full bar represents the same-sized whole; shaded parts show the fraction.

Challenge · 2 questions

Challenge and error analysis

Go beyond arithmetic: justify a claim, correct reasoning, or connect two representations.

  1. C1

    Two fractions have the same whole and denominator 6: 2/6 and 5/6. Which is larger, and why?

    Reveal explanation

    Answer: 5/6

    The pieces are equal-sized, so five of them exceed two.

  2. C2

    Without converting to decimals, explain why 3/5 is greater than 3/6 for equal-sized wholes.

    Reveal explanation

    Answer: 3/5 > 3/6

    Each piece is larger when the whole is divided into fewer equal parts; taking three larger pieces gives more.

Exit · 3 questions

Exit check

Solve independently, then return on another day to check retention.

  1. E1

    Compare 4/5 and 4/8. Write > or <.

    Reveal explanation

    Answer: >

    There are 4 pieces in each fraction, but 1/5 is a larger piece than 1/8 when the whole is identical.

    4/54/8
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  2. E2

    Compare 2/6 and 2/4. Write > or <.

    Reveal explanation

    Answer: <

    There are 2 pieces in each fraction, but 1/4 is a larger piece than 1/6 when the whole is identical.

    2/62/4
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  3. E3

    Compare 2/5 and 2/10. Write > or <.

    Reveal explanation

    Answer: >

    There are 2 pieces in each fraction, but 1/5 is a larger piece than 1/10 when the whole is identical.

    2/52/10
    Each full bar represents the same-sized whole; shaded parts show the fraction.
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