3 × 2/5 is three copies of two fifths, which is 2/5 + 2/5 + 2/5.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Count the units
That is 6 fifths in all, written 6/5. The unit never changed.
Only the top number is multiplied
3 × 2/5 = 6/5. The 5 stays, because you still have fifths.
Multiplying does not always make things bigger
1/4 of 8 is 2. Multiplying by a number smaller than 1 makes the answer smaller.
It is repeated addition again
3 × 2/5 means three copies of 2/5, which is 2/5 + 2/5 + 2/5 = 6/5. The unit is fifths throughout, so you are just counting: 2 fifths three times is 6 fifths. Nothing new is happening — this is Grade 3 multiplication with a fractional unit.
The rule and its reason
Multiply the whole number by the numerator and leave the denominator alone: 3 × 2/5 = 6/5. The denominator is untouched because the piece size never changed — you took more pieces, not different ones.
When the answer passes one
6/5 is more than a whole, and can be written 1 1/5. Multiplying fractions by whole numbers usually produces improper fractions, which is why the mixed number lesson comes just before this one.
Where this turns up
A recipe needs 2/3 cup of flour and you are making it 4 times: 4 × 2/3 = 8/3 = 2 2/3 cups. Scaling recipes, distances and quantities is the most common real use of this operation, and it is worth practising with real measures.
Step 2: Try It Yourself
Tap and try it out.
2/5
2/5
4/5
2 fifths plus 2 fifths is 4 fifths, which is written 4/5.
The denominator names what is being counted. It does not change.
Step 3: Watch an Example
One step at a time.
Watch Leo Work Out 4 × 3/8
Leo multiplies a fraction by a whole number.
- Step 1
He reads it as four copies of three eighths.
Step 4: Your Turn
Practice makes it stick.
The Recipe
Problem 1 of 2
A recipe needs 2/3 of a cup. Ana makes it 3 times. How many thirds in all?
thirds
The Walk
Problem 2 of 2
Leo walks 3/10 of a mile, 4 times. How many tenths in all?
tenths
Copies of a Unit
1 of 4
5 × 1/6. What is the top number of the answer?
2 of 4
3 × 2/7. What is the top number of the answer?
3 of 4
3 × 2/7. What is the bottom number of the answer?
4 of 4
What is 1/4 of 12?
Step 5: Quick Check
Show what you know.
Question 1 of 2
4 × 2/9. What is the top number of the answer?
Question 2 of 2
Does multiplying always make a number bigger?
What You Learned
- Multiplying a fraction by a whole number makes copies of it.
- Only the top number is multiplied. The unit stays.
- Multiplying does not always make things bigger.