Reference / Curriculum / 3B / Chapter 10

3B · Chapter 10 · Lesson 6

Adding and Subtracting Fractions — Part 1

Combine or remove like-sized fractional parts and simplify answers.

MATH-3B-C10-L07Independent and tutor-supported

Today's mathematical question

Calculate 4/6 + 1/6. Give the answer in simplest form.

Learning target

Combine or remove like-sized fractional parts and simplify answers.

Before starting: Prior lesson: Comparing Fractions — Part 2. 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 4/6 and 4/8. Write > or < and justify using equal parts.

    Reveal explanation

    Answer: >

    Rename as 16/24 and 12/24. Compare numerators: 4/6 > 4/8.

    4/64/8
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  2. P2

    Compare 2/3 and 2/7. Write > or < and justify using equal parts.

    Reveal explanation

    Answer: >

    Rename as 14/21 and 6/21. Compare numerators: 2/3 > 2/7.

    2/32/7
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  3. P3

    Compare 4/6 and 2/8. Write > or < and justify using equal parts.

    Reveal explanation

    Answer: >

    Rename as 16/24 and 6/24. Compare numerators: 4/6 > 2/8.

    4/62/8
    Each full bar represents the same-sized whole; shaded parts show the fraction.

Learn and understand

Adding or subtracting fractions works just like adding or subtracting measured pieces: units must match. Three eighths plus two eighths makes five eighths, not five sixteenths. After you find the correct number of pieces, see whether you can rename the result in simplest form. If you add 2/9 and 4/9, both amounts already count ninths, so the sum is 6/9 or 2/3. The ninth-sized pieces do not change size when the counts are combined.

Represent it three ways

  1. Concrete: Build equal pieces, measures, counters or shapes with real objects when useful.
  2. Pictorial: Shade the first group of equal cells; add or remove the second group using the same denominator. Count the remaining selected cells.
  3. Abstract: Write the matching number sentence, calculation, comparison or mathematical description. Explain each number's unit.

Important vocabulary

like denominators
equal-size fractional units
sum
result of addition
difference
result of subtraction

Fully worked examples and checks

Try each new understanding check before revealing the explanation.

Worked example 1

Explore, calculate, verify

Calculate 4/6 + 1/6. Give the answer in simplest form.

4/61/6
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 6ths. 4 + 1 pieces make 5/6 of a whole after simplification.
  3. Check that the answer uses the right units and makes sense.

Answer: 5/6

Check your understanding 1

Calculate 4/8 + 1/8. Give the answer in simplest form.

Reveal answer and explanation

5/8 — Both fractions use 8ths. 4 + 1 pieces make 5/8 of a whole after simplification.

4/81/8
Each full bar represents the same-sized whole; shaded parts show the fraction.

Worked example 2

Explore, calculate, verify

Calculate 4/10 − 3/10. Give the answer in simplest form.

4/103/10
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. Both fractions use 10ths. 4 − 3 pieces make 1/10 of a whole after simplification.
  3. Check that the answer uses the right units and makes sense.

Answer: 1/10

Check your understanding 2

Calculate 1/5 − 1/5. Give the answer in simplest form.

Reveal answer and explanation

0 — Both fractions use 5ths. 1 − 1 pieces make 0 of a whole after simplification.

1/51/5
Each full bar represents the same-sized whole; shaded parts show the fraction.

Worked example 3

Explore, calculate, verify

Calculate 2/6 + 3/6. Give the answer in simplest form.

2/63/6
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 6ths. 2 + 3 pieces make 5/6 of a whole after simplification.
  3. Check that the answer uses the right units and makes sense.

Answer: 5/6

Check your understanding 3

Calculate 4/8 + 4/8. Give the answer in simplest form.

Reveal answer and explanation

1 — Both fractions use 8ths. 4 + 4 pieces make 1 of a whole after simplification.

4/84/8
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

    Calculate 8/10 − 1/10. Give the answer in simplest form.

    Reveal explanation

    Answer: 7/10

    Both fractions use 10ths. 8 − 1 pieces make 7/10 of a whole after simplification.

    8/101/10
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  2. G2

    Calculate 2/5 + 1/5. Give the answer in simplest form.

    Reveal explanation

    Answer: 3/5

    Both fractions use 5ths. 2 + 1 pieces make 3/5 of a whole after simplification.

    2/51/5
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  3. G3

    Calculate 4/5 − 1/5. Give the answer in simplest form.

    Reveal explanation

    Answer: 3/5

    Both fractions use 5ths. 4 − 1 pieces make 3/5 of a whole after simplification.

    4/51/5
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  4. G4

    Calculate 3/12 + 1/12. Give the answer in simplest form.

    Reveal explanation

    Answer: 1/3

    Both fractions use 12ths. 3 + 1 pieces make 1/3 of a whole after simplification.

    3/121/12
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  5. G5

    Calculate 2/5 − 1/5. Give the answer in simplest form.

    Reveal explanation

    Answer: 1/5

    Both fractions use 5ths. 2 − 1 pieces make 1/5 of a whole after simplification.

    2/51/5
    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

    Calculate 3/6 − 1/6. Give the answer in simplest form.

    Reveal explanation

    Answer: 1/3

    Both fractions use 6ths. 3 − 1 pieces make 1/3 of a whole after simplification.

    3/61/6
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  2. I2

    Calculate 1/6 + 5/6. Give the answer in simplest form.

    Reveal explanation

    Answer: 1

    Both fractions use 6ths. 1 + 5 pieces make 1 of a whole after simplification.

    1/65/6
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  3. I3

    Calculate 9/12 − 1/12. Give the answer in simplest form.

    Reveal explanation

    Answer: 2/3

    Both fractions use 12ths. 9 − 1 pieces make 2/3 of a whole after simplification.

    9/121/12
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  4. I4

    Calculate 7/12 + 5/12. Give the answer in simplest form.

    Reveal explanation

    Answer: 1

    Both fractions use 12ths. 7 + 5 pieces make 1 of a whole after simplification.

    7/125/12
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  5. I5

    Calculate 5/8 − 1/8. Give the answer in simplest form.

    Reveal explanation

    Answer: 1/2

    Both fractions use 8ths. 5 − 1 pieces make 1/2 of a whole after simplification.

    5/81/8
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  6. I6

    Calculate 3/5 + 1/5. Give the answer in simplest form.

    Reveal explanation

    Answer: 4/5

    Both fractions use 5ths. 3 + 1 pieces make 4/5 of a whole after simplification.

    3/51/5
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  7. I7

    Calculate 3/6 − 2/6. Give the answer in simplest form.

    Reveal explanation

    Answer: 1/6

    Both fractions use 6ths. 3 − 2 pieces make 1/6 of a whole after simplification.

    3/62/6
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  8. I8

    Calculate 1/5 + 3/5. Give the answer in simplest form.

    Reveal explanation

    Answer: 4/5

    Both fractions use 5ths. 1 + 3 pieces make 4/5 of a whole after simplification.

    1/53/5
    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

    Without adding denominators, explain how to find 1/5 + 1/10.

    Reveal explanation

    Answer: 3/10

    Rename 1/5 as 2/10; then add 2/10 + 1/10 = 3/10.

  2. C2

    A student calculates 4/10 − 1/10 as 3/9. Find and explain the correct difference.

    Reveal explanation

    Answer: 3/10

    The number of equal parts in the whole stays 10; only the count of selected parts changes from 4 to 3.

Exit · 3 questions

Exit check

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

  1. E1

    Calculate 2/5 + 2/5. Give the answer in simplest form.

    Reveal explanation

    Answer: 4/5

    Both fractions use 5ths. 2 + 2 pieces make 4/5 of a whole after simplification.

    2/52/5
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  2. E2

    Calculate 7/10 − 2/10. Give the answer in simplest form.

    Reveal explanation

    Answer: 1/2

    Both fractions use 10ths. 7 − 2 pieces make 1/2 of a whole after simplification.

    7/102/10
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  3. E3

    Calculate 5/8 + 1/8. Give the answer in simplest form.

    Reveal explanation

    Answer: 3/4

    Both fractions use 8ths. 5 + 1 pieces make 3/4 of a whole after simplification.

    5/81/8
    Each full bar represents the same-sized whole; shaded parts show the fraction.
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