In this lesson, we solve problems where we find the product of a fraction and a whole number. Show
Rules for finding the product of a fraction and a whole number
Example Multiply $\frac{5}{4}$ × 8 Solution Step 1: First, we write the whole number 8 as a fraction $\frac{8}{1}$ Step 2: $\frac{5}{4}$ × 8 = $\frac{5}{4}$ × $\frac{8}{1}$ Step 3: As 4 and 8 are multiples of 8, cross cancelling 4 and 8, we get $\frac{5}{4}$ × $\frac{8}{1}$ = $\frac{5}{1}$ × $\frac{2}{1}$ Step 4: Multiply the numerators and denominators of both fractions as follows. $\frac{5}{1}$ × $\frac{2}{1}$ = $\frac{(5 × 2)}{(1 × 1)}$ = $\frac{10}{1}$ = 10 Step 5: So $\frac{5}{4}$ × 8 = 10 Multiply $\frac{4}{5}$ × 15 SolutionStep 1: First, we write the whole number 15 as a fraction $\frac{15}{1}$ Step 2: $\frac{4}{5}$ × 15 = $\frac{4}{5}$ × $\frac{15}{1}$ Step 3: As 5 and 15 are multiples of 5, cross cancelling 5 and 15, we get $\frac{4}{5}$ × $\frac{15}{1}$ = $\frac{4}{1}$ × $\frac{3}{1}$ Step 4: We multiply the numerators and denominators of both fractions as follows. $\frac{4}{1}$ × $\frac{3}{1}$ = $\frac{(4 × 3)}{(1 × 1)}$ = $\frac{12}{1}$ = 12 Step 5: So $\frac{4}{5}$ × 15 = 12 Multiply $\frac{3}{7}$ × 14 SolutionStep 1: First, we write the whole number 14 as a fraction $\frac{14}{1}$ Step 2: $\frac{3}{7}$ × 14 = $\frac{3}{7}$ × $\frac{14}{1}$ Step 3: As 7 and 14 are multiples of 7, cross cancelling 7 and 14, we get $\frac{3}{7}$ × $\frac{14}{1}$ = $\frac{3}{1}$ × $\frac{2}{1}$ Step 4: Multiply the numerators and denominators of both fractions as follows. $\frac{3}{1}$ × $\frac{2}{1}$ = $\frac{(3 × 2)}{(1 × 1)}$ = $\frac{6}{1}$ = 6 Step 5: So $\frac{3}{7}$ × 14 = 6 For multiplying fractions with whole numbers, the whole number is written in the fraction form and then multiplied with the given fraction using the rules of multiplication of fractions. While multiplying fractions with whole numbers, it should also be remembered that the given fractions should be in the form of a proper fraction or an improper fraction. Let us learn more about multiplying fractions with whole numbers, along with some examples. What is Multiplying Fractions With Whole Numbers?Multiplying fractions with whole numbers is similar to repeated addition where the fraction is added the same number of times as the whole number. For multiplying fractions, we first multiply the numerators, then multiply the denominators, and finally, reduce the resultant fraction to its lowest terms. However, when we need to multiply fractions with whole numbers, we write the whole number in the form of a fraction by writing 1 as its denominator. After this step, we can multiply it using the same rules. For example, when we multiply the fraction a/b × c/d, we get (a × c) / (b × d). This rule is applicable while multiplying fractions with whole numbers as well. How to Multiply Fractions With Whole Numbers?Multiplying fractions with whole numbers is an easy concept. We just need to convert the whole number into a fraction by writing 1 as the denominator and writing the whole number as the numerator. Then it is multiplied by the given fraction. After multiplying these, the final result should be in the form of a proper fraction or a mixed fraction. If the result is in an improper fraction, we convert it to a mixed fraction. Let us understand the steps with the help of an example. Example: Multiply 1/8 × 5 Solution: Here, 1/8 is the fraction and 5 is the whole number.
Let us look at another example to understand this better. Example 2: Multiply 5 × 3/10. Solution: Here, 5 is the whole number and 3/10 is the proper fraction.
How to Multiply Mixed Fractions with Whole Numbers?In order to multiply mixed fractions with whole numbers, we convert the mixed fraction to an improper fraction and then multiply it with the whole number. Example: Multiply \(1\dfrac{2}{5}\) with 10. Solution: Let us see how to multiply the given mixed fraction with a whole number.
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FAQs on Multiplying Fractions With Whole NumbersWhat is Meant by Multiplying Fractions With Whole Numbers?Multiplying fractions with the whole numbers is considered as repeated addition where the fraction is added the same number of times as the whole number. The multiplication of fractions with whole numbers is done using the same multiplication rules, where the numerators are multiplied together, then the denominators are multiplied together and then they are reduced to get the product. How to Multiply Fractions With Whole Numbers?In order to multiply fractions with whole numbers, we use the following steps.
How to Multiply Mixed Fractions with Whole Numbers?The following steps show how to multiply mixed fractions with whole numbers:
How to Multiply Improper Fractions with Whole Numbers?For multiplying improper fractions with whole numbers, we use the same rules of multiplication. This means the whole number is written in the form of a fraction and then multiplied with the improper fraction. The numerators are multiplied together, then the denominators are multiplied together and then they are simplified, if needed. How to Multiply 3 Fractions with Whole Numbers?In order to multiply 3 fractions with whole numbers, we use the following steps. Let us multiply 4/5 × 10/6 × 1/4 × 25.
How to Multiply Negative Fractions with Whole Numbers?For multiplying negative fractions with whole numbers, we use the same rules of multiplication. This means the whole number is written in the form of a fraction and then multiplied with the negative fraction. The numerators are multiplied together, then the denominators are multiplied together and then they are simplified if needed. However, it should be remembered that the product will have the sign according to the sign given in the fraction. This means if a negative fraction is multiplied with a positive whole number, the product will have a negative sign. For example, -6/4 × 5 = -6/4 × 5/1. Now we can multiply the numerators and denominators to get -30/4 which will be further reduced to -15/2. What is the Rule of Multiplying Fractions?There are two simple steps for multiplying fractions. First, multiply the numerators, and then the denominators of both the fractions to obtain the resultant fraction. Then, we need to simplify the fraction obtained, to get the product. This can be further reduced, if required. This can be understood by a simple example. 2/6 × 4/7 = (2 × 4)/(6 × 7) = 8/42 = 4/21. How do you multiply fractions with whole numbers and different denominators?To multiply two mixed numbers, follow these steps:. Change each mixed number to an improper fraction.. Multiply the numerators.. Multiply the denominators.. Simplify, if needed. You may want to write your answer as a mixed number.. |