3B · Chapter 10 · Lesson 3
Simplifying Fractions
Divide numerator and denominator by a common factor without changing value.
Today's mathematical question
Simplify 12/24 fully.
Learning target
Divide numerator and denominator by a common factor without changing value.
Before starting: Prior lesson: Finding Equivalent Fractions. 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.
- P1
Complete the equivalent fraction: 3/8 = ?/24.
Reveal explanation
Answer: 9
Subdivide each of the 8 equal parts into 3 pieces. That multiplies shaded parts and total parts by 3, so 3/8 = 9/24.
Each full bar represents the same-sized whole; shaded parts show the fraction. - P2
Complete the equivalent fraction: 1/5 = ?/15.
Reveal explanation
Answer: 3
Subdivide each of the 5 equal parts into 3 pieces. That multiplies shaded parts and total parts by 3, so 1/5 = 3/15.
Each full bar represents the same-sized whole; shaded parts show the fraction. - P3
Complete the equivalent fraction: 4/10 = ?/40.
Reveal explanation
Answer: 16
Subdivide each of the 10 equal parts into 4 pieces. That multiplies shaded parts and total parts by 4, so 4/10 = 16/40.
Each full bar represents the same-sized whole; shaded parts show the fraction.
Learn and understand
Simplifying a fraction means naming the same quantity with larger equal-size parts and smaller numbers. If 6 of 8 small cells are shaded, grouping cells into pairs produces 3 of 4 larger cells. No shaded area disappears. The numerator and denominator must share a common factor to reduce. For 6/8, pair the eight equal pieces into four equal groups of two. Six pieces become three such groups, showing 6/8 = 3/4. The shaded length stays unchanged.
Represent it three ways
- Concrete: Build equal pieces, measures, counters or shapes with real objects when useful.
- Pictorial: Draw the original equal partitions; regroup equal adjacent cells, then write the new numerator and denominator.
- Abstract: Write the matching number sentence, calculation, comparison or mathematical description. Explain each number's unit.
Important vocabulary
- simplest form
- numerator and denominator have no common factor greater than one
- common factor
- whole number dividing both values
- equivalent
- same quantity
Fully worked examples and checks
Try each new understanding check before revealing the explanation.
Worked example 1
Explore, calculate, verify
Simplify 12/24 fully.
- Identify the whole, the units, and what the question asks.
- Divide numerator and denominator by their greatest common factor 12. The equivalent simplest fraction is 1/2.
- Check that the answer uses the right units and makes sense.
Answer: 1/2
Check your understanding 1
Simplify 3/15 fully.
Reveal answer and explanation
1/5 — Divide numerator and denominator by their greatest common factor 3. The equivalent simplest fraction is 1/5.
Worked example 2
Explore, calculate, verify
Simplify 4/12 fully.
- Identify the whole, the units, and what the question asks.
- Divide numerator and denominator by their greatest common factor 4. The equivalent simplest fraction is 1/3.
- Check that the answer uses the right units and makes sense.
Answer: 1/3
Check your understanding 2
Simplify 12/18 fully.
Reveal answer and explanation
2/3 — Divide numerator and denominator by their greatest common factor 6. The equivalent simplest fraction is 2/3.
Worked example 3
Explore, calculate, verify
Simplify 6/12 fully.
- Identify the whole, the units, and what the question asks.
- Divide numerator and denominator by their greatest common factor 6. The equivalent simplest fraction is 1/2.
- Check that the answer uses the right units and makes sense.
Answer: 1/2
Check your understanding 3
Simplify 18/24 fully.
Reveal answer and explanation
3/4 — Divide numerator and denominator by their greatest common factor 6. The equivalent simplest fraction is 3/4.
Guided · 5 questions
Guided practice
Keep the model and earlier examples visible while practising.
- G1
Simplify 9/15 fully.
Reveal explanation
Answer: 3/5
Divide numerator and denominator by their greatest common factor 3. The equivalent simplest fraction is 3/5.
Each full bar represents the same-sized whole; shaded parts show the fraction. - G2
Simplify 8/24 fully.
Reveal explanation
Answer: 1/3
Divide numerator and denominator by their greatest common factor 8. The equivalent simplest fraction is 1/3.
Each full bar represents the same-sized whole; shaded parts show the fraction. - G3
Simplify 8/40 fully.
Reveal explanation
Answer: 1/5
Divide numerator and denominator by their greatest common factor 8. The equivalent simplest fraction is 1/5.
Each full bar represents the same-sized whole; shaded parts show the fraction. - G4
Simplify 2/8 fully.
Reveal explanation
Answer: 1/4
Divide numerator and denominator by their greatest common factor 2. The equivalent simplest fraction is 1/4.
Each full bar represents the same-sized whole; shaded parts show the fraction. - G5
Simplify 2/10 fully.
Reveal explanation
Answer: 1/5
Divide numerator and denominator by their greatest common factor 2. The equivalent simplest fraction is 1/5.
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.
- I1
Simplify 28/32 fully.
Reveal explanation
Answer: 7/8
Divide numerator and denominator by their greatest common factor 4. The equivalent simplest fraction is 7/8.
Each full bar represents the same-sized whole; shaded parts show the fraction. - I2
Simplify 9/24 fully.
Reveal explanation
Answer: 3/8
Divide numerator and denominator by their greatest common factor 3. The equivalent simplest fraction is 3/8.
Each full bar represents the same-sized whole; shaded parts show the fraction. - I3
Simplify 3/18 fully.
Reveal explanation
Answer: 1/6
Divide numerator and denominator by their greatest common factor 3. The equivalent simplest fraction is 1/6.
Each full bar represents the same-sized whole; shaded parts show the fraction. - I4
Simplify 20/40 fully.
Reveal explanation
Answer: 1/2
Divide numerator and denominator by their greatest common factor 20. The equivalent simplest fraction is 1/2.
Each full bar represents the same-sized whole; shaded parts show the fraction. - I5
Simplify 3/9 fully.
Reveal explanation
Answer: 1/3
Divide numerator and denominator by their greatest common factor 3. The equivalent simplest fraction is 1/3.
Each full bar represents the same-sized whole; shaded parts show the fraction. - I6
Simplify 4/8 fully.
Reveal explanation
Answer: 1/2
Divide numerator and denominator by their greatest common factor 4. The equivalent simplest fraction is 1/2.
Each full bar represents the same-sized whole; shaded parts show the fraction. - I7
Simplify 21/36 fully.
Reveal explanation
Answer: 7/12
Divide numerator and denominator by their greatest common factor 3. The equivalent simplest fraction is 7/12.
Each full bar represents the same-sized whole; shaded parts show the fraction. - I8
Simplify 6/9 fully.
Reveal explanation
Answer: 2/3
Divide numerator and denominator by their greatest common factor 3. The equivalent simplest fraction is 2/3.
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.
- C1
A student changes 2/7 to 4/7 and says the fractions are equivalent. Is this correct? Give the correct denominator if the numerator doubles.
Reveal explanation
Answer: 4/14
No. Both numerator and denominator must be multiplied by 2 to preserve the same portion: 2/7 = 4/14.
- C2
Explain why reducing 6/18 by dividing numerator and denominator by 3 preserves the value.
Reveal explanation
Answer: 2/6
Grouping numerator and denominator into threes gives 2/6; both represent the same share of the same whole.
Exit · 3 questions
Exit check
Solve independently, then return on another day to check retention.
- E1
Simplify 15/30 fully.
Reveal explanation
Answer: 1/2
Divide numerator and denominator by their greatest common factor 15. The equivalent simplest fraction is 1/2.
Each full bar represents the same-sized whole; shaded parts show the fraction. - E2
Simplify 14/16 fully.
Reveal explanation
Answer: 7/8
Divide numerator and denominator by their greatest common factor 2. The equivalent simplest fraction is 7/8.
Each full bar represents the same-sized whole; shaded parts show the fraction. - E3
Simplify 10/16 fully.
Reveal explanation
Answer: 5/8
Divide numerator and denominator by their greatest common factor 2. The equivalent simplest fraction is 5/8.
Each full bar represents the same-sized whole; shaded parts show the fraction.