Multiplying Fractions with Whole Numbers

A fraction is a way of representing a part of a whole or a portion of something. For example, there is pizza divided into 4 equal parts. If you eat 1 slice, you have eaten \(\frac{1}{4} \) of the pizza. Here, 1 is the numerator, which tells us how many parts you have. 4 is the denominator and tells us how many equal parts the whole is divided into.

Whole numbers are the natural numbers, along with zero. The set of whole numbers is 0, 1, 2, … The difference between natural and whole numbers is that whole numbers include 0, while natural numbers begin from 1.

Multiplying fractions by whole numbers is similar to adding the same fraction repeatedly, as many times as the whole number indicates.

To multiply the fractions, we multiply the numerators together and the denominators together, and then simplify the result if needed.

If we are multiplying the fraction by a whole number, we first write that whole number as a fraction by putting 1 over it.

Then we use the multiplication rule, that is,

\(\frac{a}{b} \times \frac{c}{d} \) gives \(\frac{a \times c}{b \times d} \).

The same rule works when multiplying fractions with whole numbers.

To multiply mixed fractions, we first need to convert those mixed fractions to an improper fraction. After converting it to an improper fraction, follow these steps to multiply:

Step 1: Convert the mixed fraction into an improper fraction.

Step 2: Convert a whole number into a fraction by placing 1 over it.

Step 3: Multiply the numerators.

Step 4: Multiply the denominators.

Step 5: Simplify the result if needed.

For example, multiply \(1 \frac{1}{6} \times 5 \)

1. Convert \(1 \frac{1}{6} \) into an improper fraction, that is \(\frac{7}{6} \).
    
2. Now convert 5 into a fraction by putting 1 over it.
    
3.  Now multiply \(\frac{7}{6} \times \frac{5}{1} \)
   
   \(7 × 5 = 35\)
   
   \(6 × 1 = 6\)
    
4.  The result is \(\frac{35}{6} \), which is \(5 \frac{5}{6} \) as a mixed fraction.

Here are some tips and tricks to master multiplying fractions with whole numbers.
 

1. Remember the basic rule that we cannot multiply a whole number with both a numerator and a denominator. A whole number must be multiplied only with the numerator. 
    
2. Always simplify the final answer. After multiplying, reduce the fraction to its simplest form or convert the number to a mixed number. 
    
3. Estimate before and after multiplying. Sometimes, we know whether the answer should be less than or greater than the whole number. This depends upon the type of the fraction. 
    
4. Simplification must also be done before multiplying the fraction with a whole number. It makes the operation easier. 
    
5. For easier understanding and multiplication, try to convert the whole number into a fraction. Keep the denominator as 1.

1. Construction and measurement: This is used when working on home improvement tasks, such as cutting wood or measuring fabric. For example, if one piece of wood is \(\frac{3}{4} \) meter long, and you need 5 pieces, so you should multiply them \(\frac{3}{4} \times 5 = \frac{15}{4} \). 
    
2. Education and grading: Teachers use fractions to calculate the grading and percentage. Suppose a quiz has 10 questions, and each question represents \(\frac{1}{10} \) of the total score. If a student answers 7 questions right, they will earn \(\frac{1}{10} \times 7 = \frac{7}{10} \) or 70%. This helps to assess performance clearly.
    
3. Crafts and arts: Artists and crafters often divide their materials into fractions for symmetry and balance. Let us take an example, if each decor uses \(\frac{1}{8} \) yard of ribbon and 12 decors are needed so we multiply \(\frac{1}{8} \times 12 \) which gives \(\frac{12}{8} \) ribbon is needed. By learning this concept, we can ensure precise use of supplies.
    
4. Sharing or dividing food: When we are cutting a pizza into 8 equal slices, each person can eat \(\frac{3}{8} \) of a pizza, for four people. In order to calculate the total umber of pizzas, we can use the applications of multiplying fractions with whole numbers
    
5. Travel Distance: When a car travels \(\frac{2}{3} \) km in one minute. Let's see how far it can travel in 15 minutes.
   
   \(\frac{2}{3} \times 15 = 10 \)