Multiplying Fractions with Mixed Numbers
Multiplying fractions with mixed numbers involves the multiplication of a fraction and a mixed number. We will be studying the steps of multiplying fractions with mixed numbers along with examples in this article.
| 1. | How to Multiply Fractions with Mixed Numbers? |
| 2. | Steps of Multiplying Fractions with Mixed Numbers |
| 3. | FAQs on Multiplying Fractions with Mixed Numbers |
How to Multiply Fractions with Mixed Numbers?
To multiply fractions with mixed numbers, we first convert the mixed number into an improper fraction followed by regular multiplication of fractions where the numerators are multiplied separately and the denominators are multiplied separately and simplified to get the result. For example, (1/3) × \(1\dfrac{1}{2}\) = (1/3) × (3/2) = 3/6 = 1/2. We will be learning the steps to multiply fractions with mixed numbers in the next section in detail.
Look at the following points that will help you while multiplying fractions with mixed numbers.
- Mixed numbers are a combination of a whole number with a proper fraction such as \(1\dfrac{4}{7}\). Here 1 is the whole and 4/7 is the proper fraction.
- To convert a mixed number to an improper fraction, the whole number is multiplied by the denominator and the result is added to the numerator of the proper fraction by retaining the denominator. For example, to convert \(1\dfrac{2}{9}\) to an improper fraction, we multiply 1 and 9 i.e, 1 × 9 = 9 and the result is added to 2 i.e., 9 + 2 = 11. Thus the improper fraction is 11/9.
- To convert an improper fraction to a mixed number we will divide the numerator of the improper fraction by its denominator. The quotient becomes the whole number part, the remainder becomes the numerator of the proper fraction and the denominator remains as it is. For example, to convert 11/7 to a mixed number, we first divide 11 by 7 and get the quotient as 1 and the remainder as 4. Thus, the mixed number is \(1\dfrac{4}{7}\).
Steps of Multiplying Fractions with Mixed Numbers
Let's take an example to understand the steps of multiplying fractions with mixed numbers.
Example: Multiply the fraction 2/5 with \(3\dfrac{1}{3}\).
We have to perform (2/5) × \(3\dfrac{1}{3}\).
- Step 1: We will convert the given mixed number to an improper fraction, i.e., \(3\dfrac{1}{3}\) = 10/3.
- Step 2: We will now multiply the given fraction 2/5 with the fraction obtained in the previous step. i.e., (2/5) × (10/3).
- Step 3: To multiply (2/5) × (10/3) we will multiply the numerators and the denominators of the fractions separately, i.e., (2 × 10) / (5 × 3).
- Step 4: To simplify this, we will cancel out the common factors in the numerator and denominator that will give us (2 × 2) / 3.
- Step 5: After performing the calculation, we get 4/3 as the result.
- Step 6: If the product is an improper fraction, we will convert it into a mixed number. i.e., 4/3 = \(1\dfrac{1}{3}\).
Hence, the result of (2/5) × \(3\dfrac{1}{3}\) is equal to \(1\dfrac{1}{3}\).
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FAQs on Multiplying Fractions with Mixed Numbers
How to Multiply Fractions with Mixed Numbers?
To multiply fractions with mixed numbers, we first convert the mixed number to an improper fraction followed by multiplying the two fractions and simplifying them.
For example, let's multiply 7/8 and \(1\dfrac{4}{7}\)
= (7/8) × \(1\dfrac{4}{7}\)
= (7/8) × (11/7)
= (7 × 11) / (8 × 7)
= 11/8
How to Multiply Fractions with Mixed Numbers and Whole Numbers?
Fractions are multiplied by mixed numbers by first changing the mixed number into an improper fraction followed by multiplying them. For example, (1/2) × \(1\dfrac{1}{2}\) = (1/2) × (3/2) = 3/4. To multiply fractions with whole numbers we will write the whole number in fractional form by writing the denominator as 1 followed by multiplying the two fractions. For example, (2/5) × (7/1) = 14/5.
What are the Steps of Multiplying Fractions with Mixed Numbers?
The steps to multiply fractions with mixed numbers are given below:
- Step 1: Convert the mixed number into an improper fraction.
- Step 2: Multiply the numerators and denominators of the two fractions separately.
- Step 3: Simplify by eliminating the common factors to get the lowest form of the result.
- Step 4: If the result is an improper fraction, convert it back to a mixed number.
Example: (1/6) × \(2\dfrac{2}{3}\)
= (1/6) × (8/3)
= (1 × 8) / (6 × 3)
= (1 × 4) / (3 × 3)
= 4/9
What is the Rule of Multiplying Fractions with Mixed Numbers?
The rule of multiplying fractions with mixed numbers is that the mixed number has to be first converted into an improper fraction followed by the multiplication of the corresponding numerators and denominators of the two fractions to obtain the result in the lowest form.
How to Multiply Fractions with Mixed Numbers with Different Denominators?
Multiplying fractions with mixed numbers that are of different denominators can easily be multiplied just like regular multiplication of fractions. For this, the mixed number will have to be converted to an improper fraction initially. Next, the numerator of this improper fraction will be multiplied by the numerator of the given fraction. The denominators will also be multiplied. The result will be further simplified to obtain the result.
For example, (8/9) × \(3\dfrac{1}{3}\)
= (8/9) × (10/3)
= (8 × 10) / (9 × 3)
= 80/27
= \(2\dfrac{26}{27}\)