Fractions and mixed numbers are essential concepts in mathematics, and understanding how to perform operations with them is crucial. In this blog post, we’ll focus on dividing a fraction by a mixed number, specifically 3/4 divided by 1 1/2. We’ll break down the steps and provide clear explanations to help you master this mathematical skill.
What is 3/4 / 1 1/2?
3/4 divided by 1 1/2 is equal to 2/3. To calculate this, first convert 1 1/2 to an improper fraction, which is 3/2. Then, invert and multiply: (3/4) ÷ (3/2) = (3/4) × (2/3) = 6/12. Simplify to 1/2. So, 3/4 divided by 1 1/2 equals 2/3.
Understanding Fractions and Mixed Numbers
Before diving into division, let’s briefly review what fractions and mixed numbers are.
- Fractions: Fractions represent parts of a whole or a ratio. They consist of a numerator (the top number) and a denominator (the bottom number). For instance, in the fraction 3/4, 3 is the numerator, and 4 is the denominator. This fraction represents three parts out of four equal parts.
- Mixed Numbers: Mixed numbers combine whole numbers and fractions. For example, 1 1/2 consists of the whole number 1 and the fraction 1/2. It represents one whole unit and one-half of another.
Step 1: Convert the Mixed Number to an Improper Fraction
To divide a fraction by a mixed number, we first need to convert the mixed number into an improper fraction. Here’s how you can do it:
- Multiply the whole number by the denominator of the fraction part.
- Add the numerator of the fraction part to the result.
In our example, for 1 1/2:
- Multiply 1 (the whole number) by 2 (the denominator): 1 * 2 = 2.
- Add the numerator (1) to the result from step 1: 2 + 1 = 3.
So, 1 1/2 as an improper fraction is 3/2.
Step 2: Invert and Multiply
Once we have both fractions, we can proceed with division. To divide a fraction, we use the “invert and multiply” method. Here’s how it works:
- Keep the first fraction (3/4) as it is.
- Invert (reciprocate) the second fraction (3/2) by swapping the numerator and denominator. This gives us 2/3.
Now, we have 3/4 divided by 3/2, and we can multiply instead of dividing:
- Multiply the fractions together: (3/4) × (2/3).
Step 3: Multiply the Numerators and Denominators
To multiply fractions, multiply the numerators (top numbers) together and the denominators (bottom numbers) together. Here’s the calculation:
- Numerator: 3 × 2 = 6.
- Denominator: 4 × 3 = 12.
So, (3/4) × (2/3) equals 6/12.
Step 4: Simplify the Fraction
It’s important to simplify the fraction to its simplest form. To do this, we find the greatest common divisor (GCD) of the numerator and denominator, and then divide both by the GCD.
- GCD of 6 and 12 is 6.
- Divide the numerator (6) by the GCD: 6 ÷ 6 = 1.
- Divide the denominator (12) by the GCD: 12 ÷ 6 = 2.
The simplified fraction is 1/2.
Step 5: Understand the Result
So, 3/4 divided by 1 1/2 is equal to 1/2. This means that if you divide three-quarters by one and a half, the result is half.
FAQs
What is the sum of 2 3 and 1 4 in fraction? The sum of 2 3 and 1 4 is 11/4 when expressed as an improper fraction.
How to solve a fraction? To solve a fraction, you can perform various operations like addition, subtraction, multiplication, or division depending on the problem. Understanding the rules for each operation and simplifying fractions to their simplest form is essential.
How do you add fractions? To add fractions with the same denominator, you simply add the numerators and keep the denominator unchanged. For fractions with different denominators, you need to find a common denominator first.
How do you multiply fractions? To multiply fractions, multiply the numerators together to get the new numerator and multiply the denominators together to get the new denominator. Simplify the resulting fraction if necessary.
What is the sum of 1 4 and 1 4 in fraction? The sum of 1/4 and 1/4 is 2/4, which can be further simplified to 1/2.
How do you sum mixed fractions? To add mixed fractions, first add the whole numbers together if they are different. Then, add the fractions using the same denominator, and simplify the result if needed.
What’s the easiest way to do fractions? The easiest way to work with fractions is to have a good understanding of the basic operations (addition, subtraction, multiplication, and division) and to simplify fractions whenever possible. Practice and familiarity with fraction arithmetic will also make it easier.
How to calculate fractions without a calculator? You can calculate fractions manually using paper and pencil. For addition and subtraction, find a common denominator if necessary and perform the operation. For multiplication, multiply the numerators and denominators directly. For division, multiply by the reciprocal of the second fraction.
How do you solve fractions on a calculator? On a calculator, you can enter fractions by using the “/” symbol (e.g., 1/2) and perform operations like you would with regular numbers. Many calculators also have specific fraction buttons or functions.
How do you teach kids to add fractions? Teach kids to add fractions by explaining the concept of a common denominator for addition. Use visual aids like diagrams to illustrate the process. Start with simple fractions and gradually introduce more complex ones as they gain confidence.
How do you add fractions for dummies? For beginners, start with fractions that have the same denominator. Add the numerators and keep the common denominator. For fractions with different denominators, find a common denominator and then add. Simplify the result when possible.
Can you teach me how to add fractions? Certainly! To add fractions:
- Ensure they have a common denominator.
- Add the numerators together.
- Keep the common denominator.
- Simplify the result if needed.
How do you simplify fractions with whole numbers? To simplify fractions with whole numbers, express the whole number as a fraction with the same denominator as the fraction part, then add or subtract as usual. Finally, simplify the result if necessary.
How do you find the common denominator? To find the common denominator for two or more fractions, identify the least common multiple (LCM) of their denominators. The LCM is the smallest number that all the denominators can divide evenly into.
What is in a fraction? A fraction consists of two parts: the numerator (the top number), which represents the part you have, and the denominator (the bottom number), which represents the total number of equal parts the whole is divided into. Fractions are used to represent parts of a whole or ratios.
Conclusion
Dividing fractions by mixed numbers may seem challenging at first, but by converting the mixed number to an improper fraction, using the “invert and multiply” method, and simplifying the result, you can easily tackle such problems. In the case of 3/4 divided by 1 1/2, the answer is 1/2, demonstrating that with a clear understanding of fraction operations, you can solve complex mathematical problems with confidence. Keep practicing, and you’ll continue to improve your math skills!
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