Multiplying fractions · Kode bersama Martin

Numerator times numerator, denominator times denominator. And the cross-cancel trick that saves you work.

Multiplying fractions is easier than adding them

Surprise: multiplying fractions is simpler than adding them. No common denominator. No expanding. Just one rule.

Numerator times numerator, denominator times denominator. So 2/3 × 4/5 = 8/15. On top 2 × 4, on the bottom 3 × 5. Done.

Why does that work? Take 1/2 × 1/3. That means “a half of a third”. Cut a chocolate bar into thirds, then cut one third in half. You get a piece of which six would fit in the whole bar. So 1/6. And that is exactly what you get: 1 × 1 on top, 2 × 3 on the bottom.

The word “of” in questions means times: a half of a third, three quarters of a kilo of flour. Whenever you see “how much is a fraction of something”, you multiply. Today you will also learn a trick to shrink the multiplication before you start counting.

Tereza and Jonáš bake from a recipe for 12 muffins, but they want only half a batch. The recipe says: 3/4 cup of sugar. Jonáš tries 3/4 + 1/2 and gets nonsense. Tereza stops him: “A half of three quarters. Of means times.” She writes on the recipe edge: 1/2 × 3/4 = 3/8. Jonáš measures three eighths of a cup and frowns: “And how do I measure that?” Tereza laughs: “Fill a quarter-cup one and a half times. Maths told you how much, your head invents how.”

💡

Before you multiply, try cancelling crossways: a numerator of one fraction against a denominator of the other. Smaller numbers = fewer mistakes.

How to multiply fractions step by step

The basic method. Multiply the numerators together and the denominators together: a/b × c/d = (a × c)/(b × d). Then simplify, if you can.

The smarter method: cancel crossways. Before you multiply, look whether a numerator of one fraction cancels with a denominator of the other. Example: 4/9 × 3/8. The four on top and the eight on the bottom have a common divisor 4 → they become 1 and 2. The three on top and the nine on the bottom have a common divisor 3 → they become 1 and 3. Then you only count 1/3 × 1/2 = 1/6. Without cancelling you would multiply 12/72 and only then simplify a big number.

A fraction times a whole number. Rewrite the whole number as a fraction with denominator 1: 5 = 5/1. So 2/3 × 5 = 2/3 × 5/1 = 10/3.

A mixed number (like 1 and 1/2) first convert to an improper fraction: 1 and 1/2 = 3/2. Only then multiply.

Always take the result to simplest form — a simplified fraction is the badge of finished work.

Calculate 2/3 × 4/5

Step 1: I try to cancel crossways. Two against five — no. Four against three — no. No common divisor, I count straight away.

Step 2: numerator times numerator: 2 × 4 = 8. Denominator times denominator: 3 × 5 = 15.

Result: 2/3 × 4/5 = 8/15. Cannot simplify, 8 and 15 have no common divisor. Check with an estimate: I multiply two numbers smaller than 1, so the result must be smaller than both. And 8/15 is roughly a half — smaller than 2/3 and than 4/5. That checks out.

Calculate 5/6 × 9/10 with cancelling crossways

Step 1: five on top and ten on the bottom — common divisor 5. Five becomes 1, ten becomes 2.

Step 2: nine on top and six on the bottom — common divisor 3. Nine becomes 3, six becomes 2.

Step 3: left is 1/2 × 3/2 = 3/4.

Result: 5/6 × 9/10 = 3/4. Without cancelling I would count 45/60 and then hunt for what to cancel with. Crossways I had single-digit numbers the whole time.

How much is 3/4 of 60 minutes?

The word “of” means times. So I count 3/4 × 60.

Step 1: I rewrite 60 as a fraction: 60/1. I count 3/4 × 60/1.

Step 2: cancel crossways — 60 on the bottom against the four… wait, the four is on the bottom and 60 is on top. 60 and 4 have a common divisor 4: 60 becomes 15, 4 becomes 1.

Step 3: 3/1 × 15/1 = 45.

Result: 3/4 of 60 minutes is 45 minutes. That makes sense: three quarters of an hour.

⚠️

Do not add when you should multiply. The most common mistake: for 1/2 × 1/3 looking for a common denominator. That belongs to addition and subtraction. Multiplication goes straight: top times top, bottom times bottom.

Practice: now you do it 🎲

Now try it for real. You will see all the questions at once, like on paper. Mulai with ten. When it goes well, add more.

Multiply fractions. Write the answer as a fraction in the form a/b — even unsimplified, the generator will accept it.

Practise the questions

On paper: the times tables of fractions

For each question first try to cancel crossways. Write the whole method, not just the results.

Calculate: 3/5 × 2/7 and 1/4 × 4/9. On the second one, notice what cancelling crossways does.
Calculate: 8/15 × 5/12. First cancel (eight against twelve, five against fifteen), then multiply.
A recipe wants 2/3 cup of milk. You are making a double batch. How much milk do you need? Write it as a multiplication and also give the result as a mixed number.
How much is 2/5 of 40 Kč? Write the calculation with the word “of” rewritten as times.

Now you 💪

I know the rule: numerator times numerator, denominator times denominator.
Before multiplying I look for cancelling crossways and I can explain why it saves work.
I know that “a fraction of something” means multiplication, not addition.

✅

Done when: You have calculated all four questions with a visible method, and on at least two you cancelled crossways before you multiplied.

What to take from this lesson

Multiplying fractions: top times top, bottom times bottom. No common denominator.
Cancelling crossways before multiplying keeps the numbers small.
A whole number is a fraction with denominator 1.
The word “of” in a question = times.
Always simplify the result to simplest form.