Three guided lessons with explanations, visual steps, practice and a final check.
Original chapter companion covering equivalent fractions, comparisons and addition after renaming. It does not reproduce or solve every textbook exercise.
Another tab updated this learning space. Your current work has not overwritten it.
Read all lessons
These explanations remain available without JavaScript. The separate learner and solution pages can be printed on A4.
LESSON 1
Rename the same fraction
Create equivalent fractions by dividing every part in the same way.
A fraction names equal parts of one whole. Keep the whole the same when comparing pictures.
Start with one half
Shade one of two equal parts of a strip.
Split every part in two
The whole now has four equal parts; two of them are shaded.
Read the new name
The shaded amount did not change: 1/2 = 2/4.
Check the rule
Multiply both numbers by 2: (1 × 2)/(2 × 2) = 2/4. Scaling only one number changes the fraction.
Worked example: 2/3 = 4/6 because each third splits into two sixths. Multiply both 2 and 3 by 2. Four sixths cover the same amount as two thirds.
Watch for this: Multiplying only the denominator makes the parts smaller without increasing the selected parts. That is not the same amount.
Discuss: Draw a strip showing why 3/4 = 6/8. Explain what happened to each old part.
LESSON 2
Compare using equal-sized parts
Compare fractions by renaming them with a common denominator.
Numerators can be compared directly only when the parts have the same size.
Notice different part sizes
Compare 2/3 and 3/4 of the same whole. Thirds and quarters are not the same size.
Rename in twelfths
Split each third into four: 2/3 = 8/12. Split each quarter into three: 3/4 = 9/12.
Compare the numerators
Nine twelfths is greater than eight twelfths because each part is now the same size.
State and check
3/4 > 2/3. The difference in the diagrams is one twelfth of the whole.
Worked example: Compare 3/5 and 1/2. Rename them as 6/10 and 5/10. Since 6 > 5, 3/5 > 1/2.
Watch for this: A larger denominator alone does not mean a larger fraction. For unit fractions of the same whole, more equal parts means each part is smaller.
Discuss: Compare 2/3 and 1/2 using sixths. Explain why your answer needs the same whole.
LESSON 3
Add equal-sized fraction parts
Add fractions after making the part sizes match.
Adding fractions combines amounts. The denominator names the size of a part.
Start with the amounts
Add 1/2 and 1/4 of the same whole. The parts have different sizes.
Rename the half
1/2 = 2/4. Now both amounts use quarters.
Combine the quarters
Two quarters plus one quarter gives three quarters.
Write the calculation
1/2 + 1/4 = 2/4 + 1/4 = 3/4. The denominator stays 4 because the pieces are still quarters.
Worked example: 2/3 + 1/6 = 4/6 + 1/6 = 5/6. First rename two thirds as four sixths, then add the numerators because the parts match.
Watch for this: Do not add the denominators. 1/4 + 1/4 is 2/4, not 2/8: the pieces did not become eighths.
Discuss: A jug has 1/4 litre of water and you add 2/4 litre. Find the total, then explain why it is less than one litre.
Original chapter companion covering equivalent fractions, comparisons and addition after renaming. It does not reproduce or solve every textbook exercise.
Original HelioLearn teaching and questions. Source-aligned companion; not an official NCERT/CBSE publication or full textbook solution bank. Independent teacher review and narrated video are pending.
