3B · Chapter 10 · Lesson 2
Finding Equivalent Fractions
Generate equivalent fractions by subdividing or combining equal parts.
Today's mathematical question
Complete the equivalent fraction: 1/4 = ?/12.
Learning target
Generate equivalent fractions by subdividing or combining equal parts.
Before starting: Prior lesson: 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
Draw or explain why 8/12 and 32/48 represent the same amount.
Reveal explanation
Answer: They are equal
Subdivide each of the 12 equal parts into 4 pieces. That multiplies shaded parts and total parts by 4, so 8/12 = 32/48.
Each full bar represents the same-sized whole; shaded parts show the fraction. - P2
Draw or explain why 5/10 and 15/30 represent the same amount.
Reveal explanation
Answer: They are equal
Subdivide each of the 10 equal parts into 3 pieces. That multiplies shaded parts and total parts by 3, so 5/10 = 15/30.
Each full bar represents the same-sized whole; shaded parts show the fraction. - P3
Draw or explain why 2/3 and 8/12 represent the same amount.
Reveal explanation
Answer: They are equal
Subdivide each of the 3 equal parts into 4 pieces. That multiplies shaded parts and total parts by 4, so 2/3 = 8/12.
Each full bar represents the same-sized whole; shaded parts show the fraction.
Learn and understand
To rename a fraction using a new denominator, ask how many pieces each old piece is divided into. For example, changing thirds into twelfths makes four small pieces per original third. Every shaded third also becomes four shaded twelfths. You must scale numerator and denominator by the same factor. To rename 2/3 in sixths, split every third into two smaller equal pieces. You now have four selected sixths out of six, so 2/3 = 4/6.
Represent it three ways
- Concrete: Build equal pieces, measures, counters or shapes with real objects when useful.
- Pictorial: Start with a fraction strip. Subdivide each existing cell into the same number of smaller cells; recount shaded and total parts.
- Abstract: Write the matching number sentence, calculation, comparison or mathematical description. Explain each number's unit.
Important vocabulary
- scale factor
- number used to multiply numerator and denominator
- equivalence
- same amount expressed differently
- unit fraction
- one part
Fully worked examples and checks
Try each new understanding check before revealing the explanation.
Worked example 1
Explore, calculate, verify
Complete the equivalent fraction: 1/4 = ?/12.
- Identify the whole, the units, and what the question asks.
- Subdivide each of the 4 equal parts into 3 pieces. That multiplies shaded parts and total parts by 3, so 1/4 = 3/12.
- Check that the answer uses the right units and makes sense.
Answer: 3
Check your understanding 1
Complete the equivalent fraction: 4/6 = ?/12.
Reveal answer and explanation
8 — Subdivide each of the 6 equal parts into 2 pieces. That multiplies shaded parts and total parts by 2, so 4/6 = 8/12.
Worked example 2
Explore, calculate, verify
Complete the equivalent fraction: 1/5 = ?/20.
- Identify the whole, the units, and what the question asks.
- Subdivide each of the 5 equal parts into 4 pieces. That multiplies shaded parts and total parts by 4, so 1/5 = 4/20.
- Check that the answer uses the right units and makes sense.
Answer: 4
Check your understanding 2
Complete the equivalent fraction: 9/12 = ?/36.
Reveal answer and explanation
27 — Subdivide each of the 12 equal parts into 3 pieces. That multiplies shaded parts and total parts by 3, so 9/12 = 27/36.
Worked example 3
Explore, calculate, verify
Complete the equivalent fraction: 1/12 = ?/36.
- Identify the whole, the units, and what the question asks.
- Subdivide each of the 12 equal parts into 3 pieces. That multiplies shaded parts and total parts by 3, so 1/12 = 3/36.
- Check that the answer uses the right units and makes sense.
Answer: 3
Check your understanding 3
Complete the equivalent fraction: 5/6 = ?/18.
Reveal answer and explanation
15 — Subdivide each of the 6 equal parts into 3 pieces. That multiplies shaded parts and total parts by 3, so 5/6 = 15/18.
Guided · 5 questions
Guided practice
Keep the model and earlier examples visible while practising.
- G1
Complete the equivalent fraction: 4/5 = ?/10.
Reveal explanation
Answer: 8
Subdivide each of the 5 equal parts into 2 pieces. That multiplies shaded parts and total parts by 2, so 4/5 = 8/10.
Each full bar represents the same-sized whole; shaded parts show the fraction. - G2
Complete the equivalent fraction: 2/4 = ?/16.
Reveal explanation
Answer: 8
Subdivide each of the 4 equal parts into 4 pieces. That multiplies shaded parts and total parts by 4, so 2/4 = 8/16.
Each full bar represents the same-sized whole; shaded parts show the fraction. - G3
Complete the equivalent fraction: 1/6 = ?/12.
Reveal explanation
Answer: 2
Subdivide each of the 6 equal parts into 2 pieces. That multiplies shaded parts and total parts by 2, so 1/6 = 2/12.
Each full bar represents the same-sized whole; shaded parts show the fraction. - G4
Complete the equivalent fraction: 3/10 = ?/30.
Reveal explanation
Answer: 9
Subdivide each of the 10 equal parts into 3 pieces. That multiplies shaded parts and total parts by 3, so 3/10 = 9/30.
Each full bar represents the same-sized whole; shaded parts show the fraction. - G5
Complete the equivalent fraction: 1/8 = ?/32.
Reveal explanation
Answer: 4
Subdivide each of the 8 equal parts into 4 pieces. That multiplies shaded parts and total parts by 4, so 1/8 = 4/32.
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
Complete the equivalent fraction: 2/3 = ?/12.
Reveal explanation
Answer: 8
Subdivide each of the 3 equal parts into 4 pieces. That multiplies shaded parts and total parts by 4, so 2/3 = 8/12.
Each full bar represents the same-sized whole; shaded parts show the fraction. - I2
Complete the equivalent fraction: 3/4 = ?/8.
Reveal explanation
Answer: 6
Subdivide each of the 4 equal parts into 2 pieces. That multiplies shaded parts and total parts by 2, so 3/4 = 6/8.
Each full bar represents the same-sized whole; shaded parts show the fraction. - I3
Complete the equivalent fraction: 5/8 = ?/16.
Reveal explanation
Answer: 10
Subdivide each of the 8 equal parts into 2 pieces. That multiplies shaded parts and total parts by 2, so 5/8 = 10/16.
Each full bar represents the same-sized whole; shaded parts show the fraction. - I4
Complete the equivalent fraction: 2/5 = ?/20.
Reveal explanation
Answer: 8
Subdivide each of the 5 equal parts into 4 pieces. That multiplies shaded parts and total parts by 4, so 2/5 = 8/20.
Each full bar represents the same-sized whole; shaded parts show the fraction. - I5
Complete the equivalent fraction: 2/8 = ?/24.
Reveal explanation
Answer: 6
Subdivide each of the 8 equal parts into 3 pieces. That multiplies shaded parts and total parts by 3, so 2/8 = 6/24.
Each full bar represents the same-sized whole; shaded parts show the fraction. - I6
Complete the equivalent fraction: 3/4 = ?/16.
Reveal explanation
Answer: 12
Subdivide each of the 4 equal parts into 4 pieces. That multiplies shaded parts and total parts by 4, so 3/4 = 12/16.
Each full bar represents the same-sized whole; shaded parts show the fraction. - I7
Complete the equivalent fraction: 7/10 = ?/40.
Reveal explanation
Answer: 28
Subdivide each of the 10 equal parts into 4 pieces. That multiplies shaded parts and total parts by 4, so 7/10 = 28/40.
Each full bar represents the same-sized whole; shaded parts show the fraction. - I8
Complete the equivalent fraction: 7/8 = ?/32.
Reveal explanation
Answer: 28
Subdivide each of the 8 equal parts into 4 pieces. That multiplies shaded parts and total parts by 4, so 7/8 = 28/32.
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 2/6 to 4/6 and says the fractions are equivalent. Is this correct? Give the correct denominator if the numerator doubles.
Reveal explanation
Answer: 4/12
No. Both numerator and denominator must be multiplied by 2 to preserve the same portion: 2/6 = 4/12.
- C2
Explain why reducing 6/15 by dividing numerator and denominator by 3 preserves the value.
Reveal explanation
Answer: 2/5
Grouping numerator and denominator into threes gives 2/5; 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
Complete the equivalent fraction: 7/10 = ?/20.
Reveal explanation
Answer: 14
Subdivide each of the 10 equal parts into 2 pieces. That multiplies shaded parts and total parts by 2, so 7/10 = 14/20.
Each full bar represents the same-sized whole; shaded parts show the fraction. - E2
Complete the equivalent fraction: 4/6 = ?/18.
Reveal explanation
Answer: 12
Subdivide each of the 6 equal parts into 3 pieces. That multiplies shaded parts and total parts by 3, so 4/6 = 12/18.
Each full bar represents the same-sized whole; shaded parts show the fraction. - E3
Complete the equivalent fraction: 2/10 = ?/30.
Reveal explanation
Answer: 6
Subdivide each of the 10 equal parts into 3 pieces. That multiplies shaded parts and total parts by 3, so 2/10 = 6/30.
Each full bar represents the same-sized whole; shaded parts show the fraction.