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Discover how multiplying a fraction by a whole number is like repeated addition.
Imagine you are baking 5 batches of cookies for a school party, and each batch needs exactly cup of sugar. Do you have to measure and add every single time, or is there a faster 'math shortcut' to find the total?
Quick Check
How would you write as a repeated addition sentence?
Answer
To multiply a whole number by a fraction quickly, you don't need to draw models every time. There is a simple rule: Multiply the whole number by the numerator and keep the denominator the same.
Why does the denominator stay the same? Because the denominator tells us the size of the slices. If you have 3 slices of a pizza cut into 8ths, you still have 8ths—you just have more of them! You are changing the count, not the size.
Calculate .
1. Identify the whole number (2) and the numerator (3). 2. Multiply them together: . 3. Place that result over the original denominator (8). 4. Result: .
Quick Check
If you calculate , what is the resulting numerator?
Answer
10
We use this math constantly in real life, especially with distance and time. If you walk of a mile every day for 4 days, you are repeating that distance. Instead of adding, you can multiply . This gives you miles. Since is an improper fraction, you can even turn it into a mixed number () to make it easier to understand!
A runner completes of a lap around a track. If they do this 5 times, how many laps did they run?
1. Set up the equation: . 2. Multiply the whole number by the numerator: . 3. Keep the denominator: . 4. (Optional) Convert to a mixed number: laps.
You are hosting a party with 9 guests. Each guest drinks of a liter of juice. How many liters do you need in total?
1. Equation: . 2. Multiply: . 3. Result: liters. 4. Convert: Since with left over, the total is liters.
What is ?
Which addition sentence is the same as ?
True or False: To multiply , you should multiply both the top and the bottom numbers by 4.
Review Tomorrow
In 24 hours, try to explain to someone why the denominator stays the same when we multiply a whole number by a fraction.
Practice Activity
Look at a recipe today. If you wanted to triple the recipe, pick one ingredient that uses a fraction (like tsp salt) and calculate the new amount using multiplication.