TranscriptFAQsPracticeWorksheets Many students have a real fear of fractions. However, if you can remember what a fraction represents and a few mathematical rules on how to work with them algebraically, you will be able to face fractions with confidence. In this
video, we will review how to multiply and divide fractions. Let’s get started. We should start by defining exactly what a fraction is. A fraction represents a ratio of a “part” to a “whole,” or part over whole. The value above the division line is referred to as the numerator, and the value below the division line is the denominator.
To multiply fractions, simply multiply “straight across,” meaning the “numerator times the numerator” divided by the “denominator times the denominator.” Let’s look at a couple of quick examples: \(\frac{2}{3} \times \frac{2}{5}\) Here, we want to multiply \(\frac{2}{3}\) by \(\frac{2}{5}\). As we said earlier, we’re going to multiply straight across. So we’re going to have 2 times 2 over 3 times 5. Which is equal to four over fifteen. So our answer is
\(\frac{4}{15}\). \(\frac{2}{3} \times \frac{2}{5}= \frac{2 \times 2}{3 \times 5}= \frac{4}{15}\) Now let’s try another one. We’re going to try \(\frac{4}{7}\) times \(\frac{3}{11}\). \(\frac{4}{7} \times \frac{3}{11}\) Again it’s the same concept. We’re going to multiply 4 times 3, divided by 7 times 11. Which gives us \(\frac{12}{77}\). \(\frac{4}{7} \times \frac{3}{11}= \frac{4 \times 3}{7 \times 11}=
\frac{12}{77}\) Pretty simple, right? Now let’s take a look at dividing fractions. Dividing fractions involves a slightly different process. Before we jump into the mechanics of the process, let’s start by looking at an intuitive example of dividing a fraction by two. The effect of dividing by 2 is simply cutting the fraction in half, or simply multiplying the fraction by 1 over 2. So, \(\frac{4}{5}\) divided by 2 is really the same as
saying \(\frac{4}{5}\) times \(\frac{1}{2}\). \(\frac{4}{5}\)\( \div \text{ } 2 \text{ }\)\( = \frac{4}{5} \times \frac{1}{2}\) Then it’s going to be multiplied across just like we did before. So we have 4 times 1 is four, over 5 times 2 is 10. Which then simplifies to \(\frac{2}{5}\). \(\frac{4}{5}\)\( \div \text{ } 2 \text{ }\)\( = \frac{4}{5} \times \frac{1}{2}= \frac{4}{10}= \frac{2}{5}\) So
in other words, \(\frac{2}{5}\) is half the size of \(\frac{4}{5}\). Similarly, dividing a fraction by 3 would result in a fraction that is one-third the size of the original: \(\frac{2}{5}\)\( \div \text{ } 3 \text{ }\)\( = \frac{2}{5} \times \frac{1}{3}= \frac{2}{15}\) So, \(\frac{2}{15}\) is
one-third the size of \(\frac{2}{5}\). Before we generalize this process, let’s review some important terminology. Consider the relationship between 2 and \(\frac{1}{2}\). These numbers are called reciprocals of one another, which means that the numerator of one number is the denominator of the other, and vice versa. Remember that 2 can be written as a fraction by writing it over 1, like this: \(\frac{2}{1}\). Therefore, \(\frac{2}{1}\) and \(\frac{1}{2}\) are reciprocals.
The same is true of 3 and \(\frac{1}{3}\), because 3 can be written as \(\frac{3}{1}\). Therefore, 3 and \(\frac{1}{3}\) are reciprocals. With this in mind, what pattern do you see in the process for dividing fractions? The process of dividing fractions is the same as multiplying the first fraction by the reciprocal of the second. A shorthand version of this wordy explanation that may help you remember the division process is “Keep, Change, Flip”: Keep the first fraction as is Once this adjustment is made, simply follow the rules for multiplying fractions by multiplying the numerators and dividing by the product of the denominators. Here is an example using the “Keep, Change, Flip” process: Say we want to divide \(\frac{3}{5}\)
by \(\frac{7}{5}\). We’ll keep the first fraction as is, change the operation from division to multiplication, and flip the second number. Now we just multiply our numerators, 3 times 5 is fifteen, over 5 times 7 is 35. And then from there, we simplify to \(\frac{3}{7}\).
I hope this video was helpful! Thanks for watching, and happy studying! Frequently Asked QuestionsQHow do you multiply fractions with whole numbers?AMultiply fractions by whole numbers by turning the whole number into a fraction by placing it over 1. Any number divided by itself is itself, so this does not change the value of the whole number. Then, multiply across as with normal fractions. QHow do you multiply mixed fractions?AMultiply mixed fractions by first turning them into improper fractions and then multiplying across as normal. If there are common factors in the numerator and denominator, cancel those out first to simplify multiplying across. To convert the fraction back to a mixed number, divide the numerator by the denominator. The number of full divisions becomes the whole number and the remainder becomes the numerator
of the fractional part over the original denominator. QHow do you divide fractions?ADivide fractions by using the phrase: “Keep, Change, Flip.” Keep the first fraction the
same. Change the division sign to a multiplication sign. Flip the second fraction. Then multiply across and simplify if necessary. QHow do you divide fractions with whole numbers?ADivide fractions by whole numbers by first turning the whole number into a fraction and then dividing the fractions as normal by flipping the second fraction and
multiplying across. Any number can be turned into a fraction by placing it over 1. QHow do you divide mixed fractions?ADivide mixed fractions by first converting them to improper fractions and then dividing the fractions as normal. Practice QuestionsQuestion #1: \(\frac{42}{9}\) \(\frac{42}{47}\) \(\frac{14}{27}\) \(\frac{14}{9}\) Show Answer Answer: The correct answer is C: \(\frac{14}{27}\). To multiply fractions, simply multiply the numerators together to
get the new numerator, and multiply the denominators together to get the new denominator. Hide Answer Question #2: \(\frac{7}{4}\) \(\frac{9}{9}\) \(\frac{14}{18}\) \(\frac{7}{2}\) Show Answer Answer: The correct answer is A: \(\frac{7}{4}\). To divide fractions, use the phrase: Keep, Change, Flip. Keep the first fraction the same. Change the division sign to a multiplication sign. Flip the second fraction so it is its reciprocal. That process looks like this: Then, multiply and simplify the fractions. Hide Answer Question #3: \(\frac{7}{108}\) \(\frac{47}{52}\) \(\frac{12}{252}\) \(\frac{27}{28}\) Show Answer Answer: The correct answer is D: \(\frac{27}{28}\). According to the Order of Operations (PEMDAS), multiplication and
division can happen at the same time. For this example, let’s work through the multiplication and division in order from left to right. So we’ll start by multiplying \(\frac{1}{4}\) and \(\frac{6}{7}\), simplifying if necessary. Then, divide \(\frac{3}{14}\) by \(\frac{2}{9}\). Therefore, \(\frac{1}{4}\times\frac{6}{7}\div\frac{2}{9}=\frac{27}{28}\). Hide Answer Question #4: \(2\frac{1}{3}\) cups \(\frac{4}{21}\) cups \(1\frac{2}{3}\) cups \(\frac{1}{7}\) cups Show Answer Answer: The correct answer is A: \(2\frac{1}{3}\) cups. The first thing that needs to happen in order to solve this problem is \(3\frac{1}{2}\) needs to be converted to an improper fraction. Then, multiply the two fractions and simplify. Finally, convert \(\frac{7}{3}\) to a mixed number. Sarah Anne needs \(2\frac{1}{3}\) cups of butter. Hide Answer Question #5: \(\frac{1}{3}\) \(\frac{3}{4}\) \(\frac{1}{4}\) \(\frac{2}{3}\) Show Answer Answer: The correct answer is C: \(\frac{1}{4}\). This question is asking us to divide \(\frac{6}{8}\) by 3. Remember, any whole number can be turned into a fraction by placing it over 1. Here’s what the division looks like: Each person gets \(\frac{1}{4}\) of the pizza. Hide Answer WorksheetsUse our free printable multiplying and dividing fractions worksheets for additional practice! Multiplying and Dividing Fractions Worksheets Multiplying and Dividing Fractions (Answer Key) Multiplying Fractions Worksheets Multiplying Fractions (Answer Key) Dividing Fractions Worksheets Dividing Fractions (Answer Key) Return to Complex Arithmetic Videos 473632150485446093300874638849 How do you divide fractions with whole numbers and fractions?To divide a fraction by a whole number, multiply the bottom of the fraction by the whole number. The denominator on the bottom of this fraction is 7. We will multiply 7 by 2. 7 × 2 = 14 and so, 6 / 7 ÷ 2 = 6 / 14 .
How do you multiply fractions with whole numbers?You can follow these steps to multiply a fraction by a whole number:. Write the whole number as a fraction with a denominator of 1.. Multiply the numerators.. Multiply the denominators.. Simplify. , if needed. If your answer is greater than 1, you may want to write your answer as a mixed number.. |