Multiplication I - How to Multiply Fractions With Whole Numbers

Cookie Baking

There is a delicious recipe for cookies. You take:

  • 3 parts flour
  • 2 parts butter
  • 1 part sugar

That's a total of 6 parts. So:

3/6 of flour, 2/6 of butter and 1/6 of sugar

If you want to make 300g of dough, that is:

Flour:  3/6 of 300g
Butter:  2/6 of 300g
Sugar:  1/6 of 300g

Formula: Multiply Fractions and Whole Numbers

If you write "any fraction of something", it always means that you have to multiply these two numbers with each other.

A fraction is multiplied by a whole number by multiplying the numerator by the whole number and keeping the denominator.

The result often can be simplified / reduced:

Example: 5/12 × 18

For example the fraction 5/12 should be multiplied by 18:

Trick: Simplify the Fraction or Whole Number BEFORE multiplying!

Before multiplying the fraction by the whole number, first check whether you can simplify the fraction. This reduces the numbers and makes the multiplication easier.

The whole number may also be simplified with the denominator of the fraction.

If you have simplified as much as possible before multiplying the fraction with the whole number, the result cannot be further simplified.

Simplify the Fraction before Multiplying:

Simplify the Whole Number with the Denominator:

Multiplying Fractions and Whole Numbers

Cookie Baking (Follow-Up)

Now we can continue to bake our cookies. The list of ingredients:

3/6 of 300g
   = 3/6 × 300g
   = 1/2 × 300g
   = 1/1 × 150g
   = 150g
2/6 of 300g
   = 2/6 × 300g
   = 1/3 × 300g
   = 1/1 × 100g
   = 100g
1/6 of 300g
   = 1/6 × 300g
   = 1/1 × 50g
   = 50g

Add another breeze of salt and mix well. Then shape the biscuits as desired and place them in the oven at 180°C for about 15 minutes. Tasty!

Let's continue with: "Multiplying Fractions"