How to Multiply Fractions (Step by Step)

Multiplying fractions is one of the friendliest topics in arithmetic once you know the rule, and it appears everywhere from NCERT Class 7 Maths to everyday tasks like halving a recipe or calculating a discount. This step-by-step guide, written with Indian students and CBSE conventions in mind, shows you exactly how to multiply fractions correctly every time.

Key takeaway: Multiplying fractions is actually easier than adding them. There is no hunt for a common denominator, you simply go straight across, top times top and bottom times bottom, and simplify.

The Basic Rule for Multiplying Fractions

The rule, as stated in NCERT Class 7 Maths, is simple: the product of two fractions equals the product of their numerators over the product of their denominators. In symbols, a/b x c/d = (a x c)/(b x d). Once you have the product, you reduce it to its lowest terms by dividing the numerator and denominator by their common factors. That is the entire method, and it never changes regardless of the fractions involved.

Step-by-Step Method

1. Convert mixed numbers: If any number is a mixed number like 2 1/2, first turn it into an improper fraction (2 1/2 = 5/2).
2. Multiply the numerators: Multiply the top numbers together to get the new numerator.
3. Multiply the denominators: Multiply the bottom numbers together to get the new denominator.
4. Simplify: Reduce the resulting fraction by dividing both parts by their highest common factor.
5. Convert back if needed: If the answer is an improper fraction, you may write it as a mixed number.

Worked Example 1: Two Proper Fractions

Multiply 5/8 by 3/4. Multiply the numerators: 5 x 3 = 15. Multiply the denominators: 8 x 4 = 32. So the answer is 15/32. Since 15 and 32 share no common factor other than 1, the fraction is already in lowest terms. This is the most common type of question you will see in Class 7 exercises.

Worked Example 2: Simplifying the Result

Multiply 3/4 by 8/9. Going straight across gives (3 x 8)/(4 x 9) = 24/36. Now simplify by dividing both by their highest common factor, 12: 24 divided by 12 is 2, and 36 divided by 12 is 3, giving 2/3. This shows why simplification is a required final step, so the answer appears in its neatest form.

Worked Example 3: A Mixed Number

Multiply 2 1/2 by 3/5. First convert the mixed number: 2 1/2 = 5/2. Then multiply: (5 x 3)/(2 x 5) = 15/10, which simplifies to 3/2 or 1 1/2. Always convert mixed numbers first, because trying to multiply the whole-number and fraction parts separately gives the wrong answer.

Cancelling Before You Multiply

A neat shortcut is to cancel common factors before multiplying, which keeps the numbers small. In 3/4 x 8/9, notice 4 and 8 share a factor of 4, and 3 and 9 share a factor of 3. Cancel to get 1/1 x 2/3 = 2/3 directly, without ever forming 24/36. This technique, sometimes called cross-cancellation, saves time and reduces mistakes in longer calculations.

Multiplying a Fraction by a Whole Number

To multiply a fraction by a whole number, write the whole number as a fraction over 1. For example, 2/5 of 40 means 2/5 x 40/1 = 80/5 = 16. This is common in real Indian contexts, such as finding two-fifths of a class of 40 students, or 3/4 of a Rs 200 bill.

Problem	Straight Across	Simplified
5/8 x 3/4	15/32	15/32
3/4 x 8/9	24/36	2/3
2 1/2 x 3/5	15/10	1 1/2
2/5 x 40	80/5	16

Benefits of Mastering This Skill

Multiplying fractions is a foundation for ratios, percentages, probability and algebra, all of which build on it in later CBSE classes. Beyond exams, it powers everyday Indian life, from scaling a recipe for more guests to working out a portion of a shared expense or a fraction of a discount during a sale. Getting comfortable now makes higher maths far less intimidating.

Challenges and Limitations

The rule itself is easy, but students trip up on mixed numbers, forgetting to convert them first, and on simplification, leaving answers un-reduced. Word problems add another layer, because you must first identify that of signals multiplication. With practice these become automatic, but they are the usual sources of lost marks in exams.

Common Mistakes to Avoid

• Looking for a common denominator: That is only for addition and subtraction, not multiplication.
• Multiplying mixed numbers directly: Always convert to improper fractions first.
• Forgetting to simplify: An un-reduced answer often loses a mark.
• Adding instead of multiplying denominators: Denominators are multiplied, not added.
• Cancelling across a plus sign: Cross-cancellation works only in pure multiplication.
• Misreading of as division: The word of means multiply.

Best Practices and Expert Recommendations

• Convert first: Turn every mixed number into an improper fraction before you start.
• Cancel early: Reduce common factors before multiplying to keep numbers manageable.
• Always simplify: Make reducing to lowest terms the automatic last step.
• Check with estimation: A product of two proper fractions should be smaller than both.
• Practise word problems: Train yourself to translate of into multiplication.
• Verify with a calculator: Use a multiplying fractions calculator to confirm tricky answers.

Multiplying Improper Fractions

Improper fractions, where the numerator is larger than the denominator, follow exactly the same rule. To multiply 7/4 by 5/3, multiply the numerators (7 x 5 = 35) and the denominators (4 x 3 = 12), giving 35/12, which as a mixed number is 2 11/12. There is nothing special to learn here; improper fractions are handled identically to proper ones, and you simply convert the final answer to a mixed number if the question asks for it.

Multiplying Fractions With Negative Signs

In higher classes you will meet negative fractions. The number rule is unchanged; only the sign needs care. A negative times a positive gives a negative, and a negative times a negative gives a positive. For example, (-2/3) x (3/5) = -6/15 = -2/5, while (-2/3) x (-3/5) = +6/15 = 2/5. Handle the fractions exactly as before, then apply the sign rule at the end to keep things simple.

Practice Questions to Try

The best way to lock in the method is to practise. Try these on your own, then simplify each answer to its lowest terms:

1. 2/3 x 3/7
2. 5/6 x 9/10
3. 1 1/4 x 2/3
4. 4/5 of 35
5. 3/8 x 4/9 x 2/3

Work through each using multiply across and simplify, converting any mixed number first, and cross-cancel where you can to keep the numbers small. Checking your answers against a multiplying fractions calculator afterwards will quickly show you whether your method is sound and where any slips crept in.

Multiplying Fractions in Word Problems

Most exam marks for this topic come from word problems, where the challenge is translating the sentence into a multiplication. Watch for the word of, which almost always signals multiply. For example, if 3/5 of a class of 40 students play cricket, the number who play is 3/5 x 40 = 24 students. If a water tank is 2/3 full and you use 1/4 of what is in it, the fraction of the whole tank used is 1/4 x 2/3 = 2/12 = 1/6. Reading slowly and identifying the fraction and the quantity it acts on is the key skill.

A useful habit is to underline the numbers and the word of as you read, then write the multiplication before solving. This prevents the common error of adding or dividing when the situation actually calls for multiplication. With practice on money, marks, distances and capacities, you will start to see these problems as straightforward once the correct expression is set up.

A Quick Recap of the Steps

To multiply any fractions, first convert mixed numbers and whole numbers into fractions, then multiply the numerators together and the denominators together, cancelling common factors early where you can. Finally, simplify the result to its lowest terms and convert back to a mixed number if the question requires it. Keep this four-step routine in mind and every fraction multiplication becomes predictable and quick.

Conclusion

Multiplying fractions comes down to three moves: multiply the numerators, multiply the denominators, and simplify, converting any mixed numbers first. It needs no common denominator, and cancelling early keeps the arithmetic tidy. Practise with the NCERT Class 7 examples above, watch for the common slip-ups, and verify your answers with a calculator until the method feels effortless. This small skill unlocks a great deal of the maths that follows.

Frequently Asked Questions

Do I need a common denominator to multiply fractions?

No. A common denominator is only required for adding or subtracting fractions. To multiply, you simply multiply the numerators together and the denominators together, then simplify.

How do I multiply a mixed number?

Convert the mixed number to an improper fraction first. For example, 2 1/2 becomes 5/2, and then you multiply as usual before simplifying the result.

What does ‘of’ mean in fraction problems?

In maths, of almost always means multiply. So 2/5 of 40 means 2/5 x 40, which equals 16.

Why is my product smaller than the fractions I multiplied?

When you multiply two proper fractions (both less than 1), the result is smaller than either, because you are taking a part of a part. This is normal and a useful way to check your answer.

Can I cancel before multiplying?

Yes. Cancelling common factors between any numerator and any denominator before multiplying, called cross-cancellation, keeps the numbers small and reduces mistakes.