Multiplying Fractions With Mixed Numbers

A fraction shows a part of something. It has two numbers: the numerator and the denominator. The numerator is the number above the fraction bar and represents the selected parts.

The number below the fraction bar is the denominator, representing the total number of equal parts. For example, if the cake is cut into 4 equal slices, and you have eaten one slice, that means you have eaten \(\frac{1}{4}\) of the cake.

Here, the numerator 1 is the slice you ate, and the denominator 4 is the total number of slices.

Here are the steps to multiply fractions with mixed numbers:

Step 1: To multiply fractions with mixed numbers, first convert the mixed number to an improper fraction

The mixed fraction is a type of number that includes a whole number and a fraction. To convert a mixed fraction to a fraction:

1. Multiply the whole number by the denominator of the fraction.

2. Add the product to the numerator of the fraction.

3. The sum is the new numerator, and keeps the denominator the same.

Step 2: Multiply the fractions

As we converted the mixed fraction to an improper fraction, we now have two fractions. So, we multiply both the fractions now. To multiply the fractions, multiply the numerators and the denominators.

Step 3: Simplify the answer 

Divide both the numerator and denominator by their greatest common factor (GCF) for simplification. 

Step 4: Convert the improper fraction to a mixed fraction
If the answer is an improper fraction, convert it to a mixed number.

To convert, follow the steps given below.

1. First, divide the numerator by the denominator.

2. The quotient is the whole number, the remainder is the new numerator, and the denominator will be the same. 

Let's look at the steps of multiplying fractions with mixed numbers by using the following example.

Example: Multiply \(\frac{1}{2} \times 2\frac{1}{4} \)

Step 1: Convert the mixed number to an improper fraction
 

• Multiply the whole number by the denominator. Here, the whole number is 2, and the denominator is 4; \(2 × 4 = 8\).
   
• Add the numerator in the fraction to the result. The numerator is 1, adding 1 to 8 gives 9.
   
• Keep the denominator the same. Therefore, the final improper fraction is \(\frac{9}{4}\).

Step 2: Multiply the fractions

Multiply \(\frac{1}{2} \times \frac{9}{4} \) 

To multiply fractions, we multiply the numerators and denominators of both fractions
 

• Multiplying the numerator, we get \(1 \times 9 = 9 \).
   
• Multiplying the denominator, we get \(2 × 4 = 8\).
   
• So the answer becomes \(\frac{9}{8}\).
   
• If there is a common factor for both the numerator and the denominator, we can simplify the fraction. As 9 and 8 have no common factor, we cannot simplify \(\frac{9}{8}\).  

Step 3: Convert it to a mixed number.
 

• Divide the numerator by the denominator. Dividing \(\frac{9}{8}\), we will get \(1 \frac{1}{8}\).
   
• The quotient becomes the whole number, the remainder becomes the new numerator, and the denominator stays the same.

The final answer is \(1 \frac{1}{8}\).

Given below are some tips and tricks that help students with the multiplication of fractions with mixed numbers and make the process easier.
 

• Always convert mixed numbers to improper fractions before multiplying.
   
• Multiply numerators together and denominators together, then simplify the result.
   
• Convert the final improper fraction back to a mixed number for easier interpretation.
   
• Use visual aids like fraction bars or number lines to understand the concept better.
   
• Practice with real-life examples like recipes, measurements, and scaling problems.

Multiplying fractions with mixed numbers is useful in many real-life situations, such as finance, healthcare, construction, etc.

• Healthcare: Doctors and medical professionals often use fractions and mixed numbers to calculate medication dosages, IV drip rates, and for treatment plans.
   
• Construction: In construction, workers use fraction measurements to calculate the amount of wood, tiles, or paint required for the work. 
   
• Finance: In finance, to calculate discounts, interest rates, and tax deductions, we multiply fractions with mixed numbers. 
   
• Cooking: Recipes often require multiplying fractions with mixed numbers to adjust ingredient quantities when changing the number of servings.
   
• Education & Learning: Teachers and students use fractions and mixed numbers in exercises, experiments, and problem-solving to develop practical math skills.