Reference / Curriculum / 3B / Chapter 9

3B · Chapter 9 · Lesson 3

Comparing Fractions with Like Denominators

Compare same-sized parts of the same whole by numerator.

MATH-3B-C09-L03Independent and tutor-supported

Today's mathematical question

Compare 7/8 and 4/8. Write > or <.

Learning target

Compare same-sized parts of the same whole by numerator.

Before starting: Prior lesson: Fractions on a Number Line. 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

    Between 0 and 1, a line is split into 12 equal intervals. What fraction is at the 3rd tick after 0?

    Reveal explanation

    Answer: 1/4

    Each interval represents 1/12. Moving 3 intervals from zero reaches 3/12, or 1/4 in simplest form.

    03/1213/12
    An interval from zero to one divided into equal segments.
  2. P2

    Between 0 and 1, a line is split into 5 equal intervals. What fraction is at the 3rd tick after 0?

    Reveal explanation

    Answer: 3/5

    Each interval represents 1/5. Moving 3 intervals from zero reaches 3/5, or 3/5 in simplest form.

    03/513/5
    An interval from zero to one divided into equal segments.
  3. P3

    Between 0 and 1, a line is split into 5 equal intervals. What fraction is at the 1st tick after 0?

    Reveal explanation

    Answer: 1/5

    Each interval represents 1/5. Moving 1 intervals from zero reaches 1/5, or 1/5 in simplest form.

    01/511/5
    An interval from zero to one divided into equal segments.

Learn and understand

When two fractions have the same denominator, they describe pieces of the same size. Comparing 3/8 with 5/8 means comparing three eighth-size parts with five eighth-size parts. Since five equal parts are more than three, 5/8 is greater. This rule only works when the wholes are equal in size. Compare 2/7 with 5/7 using two identical strips. Each strip has seven equal parts; the second has more shaded parts. Ask what would happen if the two wholes had different lengths.

Represent it three ways

  1. Concrete: Build equal pieces, measures, counters or shapes with real objects when useful.
  2. Pictorial: Use equally long fraction strips divided into the same number of cells. Shade the two numerators and compare the lengths.
  3. Abstract: Write the matching number sentence, calculation, comparison or mathematical description. Explain each number's unit.

Important vocabulary

like denominators
equal numbers of pieces per whole
compare
determine greater, less, or equal
numerator
selected pieces

Fully worked examples and checks

Try each new understanding check before revealing the explanation.

Worked example 1

Explore, calculate, verify

Compare 7/8 and 4/8. Write > or <.

7/84/8
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. Both fractions use pieces of size 1/8, so compare 7 pieces with 4 pieces: 7/8 > 4/8.
  3. Check that the answer uses the right units and makes sense.

Answer: >

Check your understanding 1

Compare 3/12 and 11/12. Write > or <.

Reveal answer and explanation

< — Both fractions use pieces of size 1/12, so compare 3 pieces with 11 pieces: 3/12 < 11/12.

3/1211/12
Each full bar represents the same-sized whole; shaded parts show the fraction.

Worked example 2

Explore, calculate, verify

Compare 1/4 and 3/4. Write > or <.

1/43/4
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. Both fractions use pieces of size 1/4, so compare 1 pieces with 3 pieces: 1/4 < 3/4.
  3. Check that the answer uses the right units and makes sense.

Answer: <

Check your understanding 2

Compare 3/10 and 9/10. Write > or <.

Reveal answer and explanation

< — Both fractions use pieces of size 1/10, so compare 3 pieces with 9 pieces: 3/10 < 9/10.

3/109/10
Each full bar represents the same-sized whole; shaded parts show the fraction.

Worked example 3

Explore, calculate, verify

Compare 5/6 and 4/6. Write > or <.

5/64/6
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. Both fractions use pieces of size 1/6, so compare 5 pieces with 4 pieces: 5/6 > 4/6.
  3. Check that the answer uses the right units and makes sense.

Answer: >

Check your understanding 3

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

Reveal answer and explanation

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

1/32/3
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 5/6 and 3/6. Write > or <.

    Reveal explanation

    Answer: >

    Both fractions use pieces of size 1/6, so compare 5 pieces with 3 pieces: 5/6 > 3/6.

    5/63/6
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  2. G2

    Compare 1/5 and 2/5. Write > or <.

    Reveal explanation

    Answer: <

    Both fractions use pieces of size 1/5, so compare 1 pieces with 2 pieces: 1/5 < 2/5.

    1/52/5
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  3. G3

    Compare 2/4 and 1/4. Write > or <.

    Reveal explanation

    Answer: >

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

    2/41/4
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  4. G4

    Compare 1/6 and 3/6. Write > or <.

    Reveal explanation

    Answer: <

    Both fractions use pieces of size 1/6, so compare 1 pieces with 3 pieces: 1/6 < 3/6.

    1/63/6
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  5. G5

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

    Reveal explanation

    Answer: >

    Both fractions use pieces of size 1/10, so compare 6 pieces with 2 pieces: 6/10 > 2/10.

    6/102/10
    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 2/12 and 6/12. Write > or <.

    Reveal explanation

    Answer: <

    Both fractions use pieces of size 1/12, so compare 2 pieces with 6 pieces: 2/12 < 6/12.

    2/126/12
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  2. I2

    Compare 8/12 and 3/12. Write > or <.

    Reveal explanation

    Answer: >

    Both fractions use pieces of size 1/12, so compare 8 pieces with 3 pieces: 8/12 > 3/12.

    8/123/12
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  3. I3

    Compare 6/8 and 4/8. Write > or <.

    Reveal explanation

    Answer: >

    Both fractions use pieces of size 1/8, so compare 6 pieces with 4 pieces: 6/8 > 4/8.

    6/84/8
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  4. I4

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

    Reveal explanation

    Answer: <

    Both fractions use pieces of size 1/6, so compare 2 pieces with 3 pieces: 2/6 < 3/6.

    2/63/6
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  5. I5

    Compare 1/6 and 2/6. Write > or <.

    Reveal explanation

    Answer: <

    Both fractions use pieces of size 1/6, so compare 1 pieces with 2 pieces: 1/6 < 2/6.

    1/62/6
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  6. I6

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

    Reveal explanation

    Answer: >

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

    3/42/4
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  7. I7

    Compare 6/10 and 1/10. Write > or <.

    Reveal explanation

    Answer: >

    Both fractions use pieces of size 1/10, so compare 6 pieces with 1 pieces: 6/10 > 1/10.

    6/101/10
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  8. I8

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

    Reveal explanation

    Answer: <

    Both fractions use pieces of size 1/5, so compare 2 pieces with 3 pieces: 2/5 < 3/5.

    2/53/5
    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 10: 2/10 and 5/10. Which is larger, and why?

    Reveal explanation

    Answer: 5/10

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

  2. C2

    Without converting to decimals, explain why 3/9 is greater than 3/10 for equal-sized wholes.

    Reveal explanation

    Answer: 3/9 > 3/10

    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 2/8 and 7/8. Write > or <.

    Reveal explanation

    Answer: <

    Both fractions use pieces of size 1/8, so compare 2 pieces with 7 pieces: 2/8 < 7/8.

    2/87/8
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  2. E2

    Compare 3/5 and 1/5. Write > or <.

    Reveal explanation

    Answer: >

    Both fractions use pieces of size 1/5, so compare 3 pieces with 1 pieces: 3/5 > 1/5.

    3/51/5
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  3. E3

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

    Reveal explanation

    Answer: <

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

    2/84/8
    Each full bar represents the same-sized whole; shaded parts show the fraction.
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