What is Multiplying a Fraction by a Whole Number?

S1-SA2-0236

Grade Level:

Class 5

Maths, Computing, AI, Physics

Definition

What is it?

Multiplying a fraction by a whole number means finding a part of a whole number, or repeatedly adding the same fraction. It helps us calculate a fraction of a quantity multiple times. For example, if you eat 1/4th of a pizza every day for 3 days, multiplying helps you find the total pizza eaten.

Simple Example

Quick Example

Imagine your mom makes a big batch of ladoos. You get to eat 1/3rd of the ladoos. If there are 12 ladoos in total, how many do you eat? You need to find 1/3rd of 12. This is like multiplying 1/3 by 12, which gives you 4 ladoos.

Worked Example

Step-by-Step

Let's multiply 2/5 by 3.

STEP 1: Write the whole number as a fraction. Any whole number can be written as itself over 1. So, 3 becomes 3/1.

STEP 2: Now the problem is (2/5) x (3/1).

STEP 3: Multiply the numerators (top numbers) together: 2 x 3 = 6.

STEP 4: Multiply the denominators (bottom numbers) together: 5 x 1 = 5.

STEP 5: Put the new numerator over the new denominator. This gives us 6/5.

STEP 6: If the answer is an improper fraction (numerator is bigger than denominator), convert it to a mixed number. 6 divided by 5 is 1 with a remainder of 1. So, 6/5 is 1 and 1/5.

ANSWER: 2/5 multiplied by 3 is 6/5 or 1 and 1/5.

Why It Matters

This concept is fundamental for understanding how parts combine or repeat. In Physics, you might calculate a fraction of a force applied multiple times. In Computing, it's used for scaling images or managing data storage. Engineers use it to scale down designs or calculate material requirements, making it useful in many careers like architecture or software development.

Common Mistakes

MISTAKE: Multiplying both the numerator and the denominator of the fraction by the whole number. For example, (1/2) x 3 becomes (1x3)/(2x3) = 3/6. | CORRECTION: Only multiply the numerator of the fraction by the whole number. The denominator stays the same. So, (1/2) x 3 = (1x3)/2 = 3/2.

MISTAKE: Forgetting to convert the whole number into a fraction (e.g., 5 becomes 5/1) and getting confused. | CORRECTION: Always imagine the whole number has a denominator of 1. This makes it clear that you multiply numerator by whole number, and the denominator by 1 (which means it remains unchanged).

MISTAKE: Not simplifying the final answer or converting an improper fraction to a mixed number. For example, leaving 10/4 as the final answer. | CORRECTION: Always simplify fractions to their simplest form (10/4 becomes 5/2) and convert improper fractions to mixed numbers (5/2 becomes 2 and 1/2) for a complete answer.

Practice Questions

Try It Yourself

QUESTION: What is 3/4 multiplied by 5? | ANSWER: 15/4 or 3 and 3/4

QUESTION: A recipe calls for 1/2 cup of sugar. If you want to make 4 batches of the recipe, how much sugar do you need? | ANSWER: 4/2 cups or 2 cups

QUESTION: Riya walks 2/3 km to school every day. If she goes to school 5 days a week, how many kilometres does she walk to school in total per week? Express your answer as a mixed number. | ANSWER: 10/3 km or 3 and 1/3 km

MCQ

Quick Quiz

What is the result of multiplying 4/7 by 2?

8/14

8/7

4/14

6/7

The Correct Answer Is:

To multiply a fraction by a whole number, you multiply the numerator (4) by the whole number (2), which gives 8. The denominator (7) stays the same. So, 4/7 x 2 = 8/7. Option A is incorrect because the denominator should not be multiplied.

Real World Connection

In the Real World

Imagine you're tracking your mobile data usage. If you use 1/4th of your daily data limit every day, and you do this for 3 days, you can multiply 1/4 by 3 to find out you've used 3/4ths of your total daily limit over those 3 days. Or, a tailor might need 3/5th of a meter of cloth for one shirt; for 4 shirts, they'd multiply 3/5 by 4 to get 12/5 or 2 and 2/5 meters of cloth.

Key Vocabulary

Key Terms

FRACTION: A part of a whole, like 1/2 | WHOLE NUMBER: A number without any fractional or decimal part, like 1, 2, 3 | NUMERATOR: The top number in a fraction, showing how many parts are taken | DENOMINATOR: The bottom number in a fraction, showing the total number of equal parts | IMPROPER FRACTION: A fraction where the numerator is greater than or equal to the denominator, like 5/3

What's Next

What to Learn Next

Great job understanding this! Next, you can explore 'Multiplying a Fraction by Another Fraction'. This will build on what you've learned here and help you solve even more complex problems involving parts of parts.