Table of contents
- How dividing fractions works
- How to divide fractions
- Dividing fractions examples
- How Prodigy can help you teach dividing fractions
- Dividing fractions worksheets
- Dividing fractions calculator
- Conclusion
How dividing fractions works
Teaching students how to divide fractions is part of the Common Core State Standards for Mathematical Practice. One of the most valuable things to teach your students when dividing fractions is what the answer means. Take a look at the example below:½ ÷ ⅙ = 3
Why is the solution a bigger number than the fractions involved? When you divide a fraction, you’re asking how many groups of the divisor (second number) can be found in the dividend (first number). For the above equation, we’re asking how many ⅙ appear in ½. Imagine the example equation as a cake. You’ve got half of the cake remaining. If each serving of the cake is ⅙ of the whole, how many servings do you have left?How to divide fractions
If you simply divided fractions like you were dividing a normal math problem, you’d more than likely create some complex fractions and have something that looks similar to this: [caption id="attachment_3424" align="aligncenter" width="388"]- Flip the divisor into a reciprocal
- Change the division sign to a multiplication symbol and multiply
- Simplify your answer if possible
Step 1: Flip the divisor into a reciprocal
A reciprocal is what you multiply a number by to get the value of one. If you want to change two into one through multiplication you need to multiply it by 0.5. In fraction form this looks like:²⁄₁ × ½ = 1
To find the reciprocal of a fraction you simply flip the numbers. The denominator becomes the numerator and vice versa. Take a look at the example equation again:½ ÷ ⅙ = ?
The first step to solve the problem is to turn our divisor, ⅙, into a reciprocal.⅙ → ⁶⁄₁
Step 2: Change the division sign to a multiplication symbol and multiply
Dividing and multiplying are opposites of each other. When you create a reciprocal of a number, you’re creating its opposite as well. In a division problem, when you turn the divisor into a reciprocal, you also need to change the equation from division to multiplication. Now that you’ve found the reciprocal of your divisor, you can change the equation from division into multiplication.½ ÷ ⅙ = ? → ½ × ⁶⁄₁ = ?
We’ve got an extensive guide on how to multiply fractions, but here’s a quick tutorial:- Multiply your numerators to get your new numerator
- Multiply your denominators to get your new denominator
- Simplify the final fraction, if possible
1 × 6 = 6 2 × 1 = 2 ½ × ⁶⁄₁ = ⁶⁄₂
Now you're ready to simplify to get the final answer!Step 3: Simplify your answer if possible
Fractions symbolize a part of a whole. This means many fractions represent the same value, so why not make the fraction as simple as possible? For example, you almost never say five-tenths or ⁵⁄₁₀. Instead, you simplify that to one-half or ½. To get a fraction down to its simplest form, you divide the numerator and denominator by their greatest common factor. The greatest common factor in ⁵⁄₁₀ is five. Dividing both numbers down by five leaves you with ½.Same/Different? Multiplying/dividing a fraction by 2/2. Full video at //t.co/aYmHjxOMdB #mtbos #iteachmath #samediffmath pic.twitter.com/RunWrKLQ3J
— Berkeley Everett (@BerkeleyEverett) December 16, 2018
½ ÷ ⅙ = ? → ½ × ⁶⁄₁ = ⁶⁄₂ → ³⁄₁ → 3
Dividing fractions examples
The three-step strategy is great for basic fraction problems, but what happens when you run into whole numbers, mixed fractions, improper fractions, and word-based problems? The process remains the same for the most part, but depending on the type of problem, there could be a couple more steps. Let’s look at some examples of different types of problems:How to divide improper fractions
[caption id="attachment_3342" align="aligncenter" width="395"]⅓ ÷ ⁶⁄₅ = ? → ⅓ × ⅚ = ⁵⁄₁₈
Example 2:⁷⁄₆ ÷ ¾ = ? →⁷⁄₆ × ⁴⁄₃ = ²⁸⁄₁₈ → ¹⁴⁄₉ → 1 ⁵⁄₉
No matter where the improper fraction is placed, you still flip the divisor into a reciprocal and then multiply the two fractions.How to divide mixed fractions
[caption id="attachment_3353" align="aligncenter" width="600"]3 ⅓ ÷ ⅖ = ? → ¹⁰⁄₃ ÷ ⅖ = ? → ¹⁰⁄₃ × ⁵⁄₂ = ⁵⁰⁄₆ → ²⁵⁄₃ → 8 ⅓
Example 2:¼ ÷ 2 ⅙ = ? → ¼ ÷ ¹³⁄₆ = ? → ¼ × ⁶⁄₁₃ = ⁶⁄₅₂ → ³⁄₂₆
2 ½ ÷ 1 ⅓ = ? → ⁵⁄₂ ÷ ⁴⁄₃= ? → ⁵⁄₂ × ¾ = ¹⁵⁄₈ → 1 ⅞
How to divide fractions with whole numbers
[caption id="attachment_3357" align="aligncenter" width="600"]3 → ³⁄₁
Once the whole number is turned into a fraction you can continue to solve the problem with the three-step strategy. Example:⅓ ÷ 3 = ? → ⅓ ÷ ³⁄₁= ? → ⅓ × ⅓ = ⅑
How to divide fractions with the same denominator
When you’ve got the same denominator, there’s no need to find the reciprocal or multiply. You can simply divide your fractions to get the answer. The denominators will cancel each other out and give you one. Any fraction with a denominator of one can be simplified to just the numerator. Example 1:⅘ ÷ ⅖ = ²⁄₁ → 2
Example 2:⅓ ÷ ⅔ = ½/1 → ½
Dividing fractions word problems
How Prodigy can help you teach dividing fractions
Prodigy Game helps you teach how to divide fractions, track how your students are doing, and assign specific questions to prepare your class for standardized testing – all for free.- Differentiate math practice
- Reinforce in-class concepts (like dividing fractions!)
- Deliver formative assessments and track student progress
Dividing fractions worksheets
To make sure key concepts are getting across when teaching how to divide fractions you can also use worksheets for your class. You can put an assortment of different questions in a worksheet to see what students understand and what they're struggling with.1. DadsWorksheets.com
2. Common Core Sheets
3. K5 Learning
Dividing fractions calculator
When your students are learning how to divide fractions you can show them fraction calculators. These are online tools for solving fraction problems quickly. They’re great for checking your answers, but use caution when showing these tools to your class.Final thoughts on how to divide fractions
When teaching how to divide fractions, tell your students that they're trying to find how many of the divisor can be found in the dividend. The easiest way to divide fractions is to follow three simple steps:- Flip the divisor into a reciprocal
- Change the division sign into a multiplication sign and multiply
- Simplify if possible
How do we divide mixed fractions?
To divide mixed fractions, you could first convert each to an improper fraction. Then, switch to a multiplication problem by multiply by the reciprocal of the divisor. Simplify and convert your answer back to a mixed fraction to get your answer!
How do you divide with different denominators?
To divide fractions with unlike denominators, we turn the division problem into a multiplication problem by multiplying the numerator of the division problem by the reciprocal of the denominator of the division problem, then we simplify.