Start with the meaning
NCERT connection: Grade 7 Ganita Prakash Part I, “Working with Fractions”. These are independent BananaLearn notes and original practice, not official NCERT material or a complete set of textbook exercise solutions. Match the chapter name to the book used by your school. Know equivalent fractions, multiplication facts and how to simplify a fraction. This page covers positive fraction multiplication; it does not cover the chapter’s division work.
Keep the original whole visible
Draw one rectangle and divide it into four equal columns. Mark three columns to show 3/4. Now divide the whole rectangle into two equal rows and take one row of the marked part.
The selected region contains three of the eight equal cells in the original whole. Therefore 1/2 of 3/4 is 3/8. The denominator counts equal parts of the original rectangle, not just the region selected first.
Connect the picture to the rule
For positive proper fractions a/b and c/d, split one whole into b columns and d rows. The whole has b × d equal cells. The overlap representing the product contains a × c cells.
Thus (a/b) × (c/d) = (a × c)/(b × d), with nonzero denominators. The same multiplication rule works for improper fractions, but a picture may need more than one whole. Simplify the resulting fraction. Unlike addition, fraction multiplication does not require a common denominator.
Convert mixed numbers before multiplying
A mixed number is a sum: 1 1/2 means 1 + 1/2, or 3/2. Convert the full quantity to an improper fraction before applying the multiplication rule.
For 1 1/2 × 2/3, calculate 3/2 × 2/3 = 6/6 = 1. Multiplying only the whole-number parts or only the fractional parts loses part of the original amount.
Let the story and an estimate check the answer
If a ribbon is 4/5 metre long and you use 3/4 of it, the calculation is 3/4 × 4/5 = 3/5 metre. The result is less than 4/5 metre because only part of the ribbon was used.
A multiplier greater than one has a different effect. Three lengths of 2/5 metre total 6/5 metre. Name the unit and compare the result with the starting amount; this can expose an incorrect operation even when the arithmetic looks tidy.
Worked examples, step by step
Example 1: Find 2/3 of 3/5
- Write “of” here as multiplication: 2/3 × 3/5.
- Multiply to get 6/15, then divide numerator and denominator by 3.
- The result is 2/5, smaller than 3/5 because the multiplier is less than one.
Example 2: Four pieces are each 3/8 metre long
- Four equal lengths means 4 × 3/8.
- The total is 12/8 = 3/2 metre.
- Write 1 1/2 metres if a mixed number is useful; the total exceeds one piece.
Example 3: Use 2/3 of 1 1/4 litres
- Convert 1 1/4 to 5/4 litres.
- Calculate 2/3 × 5/4 = 10/12 = 5/6 litre.
- The used amount is below 1 1/4 litres, as it should be.
Common mistakes and useful repairs
Finding common denominators as if multiplying were adding
Common denominators help add equal-sized parts. For multiplication, count the overlap parts and multiply the denominators.
Cancelling across a plus sign
Cancelling factors works within a product or quotient of factors. It does not allow removing matching numbers from terms joined by addition. Rewrite a mixed number as one fraction first.
Try before revealing
Quick understanding check
Read the check answers
2/3 × 3/4. Taking a fraction of a quantity is represented by multiplication.
3/2. One whole is 2/2; add 1/2 to get 3/2.
Grade 7 multiplying fractions: models and word problems — practice sheet
Work on paper before opening an answer. Print this question sheet with or without a separate worked key; no account is needed.
Name: ____________________ Date: __________
Calculate 2/5 × 3/4.
Show answer and reasoning
3/10. 6/20 simplifies by dividing numerator and denominator by 2.
Find 3/7 of 14.
Show answer and reasoning
6. 14 ÷ 7 × 3 = 6.
Calculate 5/6 × 3/10.
Show answer and reasoning
1/4. 15/60 simplifies to 1/4.
Calculate 1 2/3 × 3/5.
Show answer and reasoning
1. Convert 1 2/3 to 5/3; 5/3 × 3/5 = 1.
A bottle contains 3/4 litre. You use 2/3 of it. How much do you use?
Show answer and reasoning
1/2 litre. 2/3 × 3/4 = 6/12 = 1/2.
Five pieces of string are each 2/9 metre. Find their total length.
Show answer and reasoning
10/9 metre. 5 × 2/9 = 10/9, or 1 1/9 metres.
Without exact calculation, is 4/5 × 7/8 smaller or larger than 7/8?
Show answer and reasoning
Smaller. The positive starting amount is multiplied by a number between zero and one.
On the practice grid, shade half of the marked three quarters. What fraction of the original whole have you shaded?
Show answer and reasoning
3/8. Three selected cells out of eight equal cells represent the product.
Grade 7 multiplying fractions: models and word problems — worked answer key
3/10. 6/20 simplifies by dividing numerator and denominator by 2.
6. 14 ÷ 7 × 3 = 6.
1/4. 15/60 simplifies to 1/4.
1. Convert 1 2/3 to 5/3; 5/3 × 3/5 = 1.
1/2 litre. 2/3 × 3/4 = 6/12 = 1/2.
10/9 metre. 5 × 2/9 = 10/9, or 1 1/9 metres.
Smaller. The positive starting amount is multiplied by a number between zero and one.
3/8. Three selected cells out of eight equal cells represent the product.
Choose the next practice step
Use the questions in this guide to practise this specific skill. If you need another explanation, return to Finding a fraction of an amount before trying a fresh problem.
Help at home: Fold a rectangle twice
Draw four equal columns, mark three, then split the rectangle into two equal rows. Ask your child to select half of the marked region and count it relative to the original whole.
Before revealing the count, ask whether half of three quarters should be larger or smaller than three quarters. The size prediction checks understanding beyond a memorised rule.
Keep one example of your child’s own working. If the same confusion returns across fresh questions, share that attempt with their teacher and ask which next step fits their current learning.
Questions students and parents ask
Are these NCERT exercise solutions?
No. These are original questions with worked answers that support the named topic. Use the official textbook link for the book itself. Exercise numbers and school sequences can differ between editions.
How should a parent use the practice?
Ask for one independent attempt before revealing an answer. Notice whether the difficulty is reading the question, representing the idea or calculating. Revisit the matching example, then try a fresh question rather than copying the worked answer.
About this resource
BananaLearn created these explanations, diagrams and practice questions. They are not reproduced textbook or past-exam questions. School sequences differ; use the prerequisites to choose a starting point. Read how we prepare learning guides.
Curriculum and teaching references used to check scope:
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