Multiplying is resizing. The factor says how much bigger or smaller the result is.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Three cases, and only three
A factor over 1 makes it bigger. Under 1, smaller. Exactly 1, unchanged.
You can answer without multiplying
2/3 × 15 must be less than 15, because 2/3 is under 1. No working needed.
Why multiplying by a form of 1 is safe
Multiplying by 3/3 is multiplying by 1, which is why equivalent fractions work.
Predict the size before calculating
Multiplying by a number greater than 1 enlarges. Multiplying by exactly 1 leaves things alone. Multiplying by a number between 0 and 1 shrinks. You can state which will happen just by looking at the multiplier, before doing any arithmetic.
Three examples
8 × 3/2 = 12, larger than 8. 8 × 1 = 8, unchanged. 8 × 3/4 = 6, smaller than 8. Same starting number, three different directions, decided entirely by whether the multiplier is above, at, or below one.
Comparing without calculating
Is 7/8 × 42 more or less than 42? Less, because 7/8 is under one. You did not need the product. Questions like this test whether you understand scaling, and they are answerable in a second once you do.
Where scaling appears
Sale prices multiply by a fraction less than one. Recipes doubled multiply by 2. Map scales, enlargement, shrinking a photo — all are multiplication by a scale factor, and knowing whether the factor is above or below one tells you what will happen before you compute.
Step 2: Try It Yourself
Change the factor and watch which way the bar goes.
Before: 15
After: 10
The factor is less than 1, so the bar got shorter. Multiplying does not always make things bigger.
Step 3: Watch an Example
One step at a time.
Watch Leo Answer Without Multiplying
Leo is asked whether 3/4 × 20 is more or less than 20.
- Step 1
He checks the factor against 1: 3/4 is less than 1.
Step 4: Your Turn
Practice makes it stick.
Bigger or Smaller?
Problem 1 of 2
Is 5/4 × 12 more or less than 12?
The Exact One
Problem 2 of 2
What is 3/4 × 20?
Judge It First
1 of 4
Is 7/8 × 40 more or less than 40?
2 of 4
Is 9/8 × 40 more or less than 40?
3 of 4
What is 6/6 × 30?
4 of 4
What is 2/5 × 20?
Step 5: Quick Check
Show what you know.
Question 1 of 2
What is 3/5 × 25?
Question 2 of 2
Can you tell if a product is bigger than its factor without multiplying?
What You Learned
- Multiplying resizes a number.
- Over 1 grows it, under 1 shrinks it, exactly 1 leaves it.
- You can answer "bigger or smaller?" without any working.