Understanding Mixed Numbers and Like Denominators
When dealing with fractions, it’s essential to understand the concepts of mixed numbers and like denominators. Mixed numbers are a combination of a whole number and a fraction, while like denominators refer to fractions that have the same denominator. In this article, we’ll explore the concept of mixed numbers with like denominators and provide a step-by-step guide on how to work with them.
What are Mixed Numbers?
A mixed number is a number that consists of a whole number part and a fraction part. For example, 2 1⁄2 is a mixed number, where 2 is the whole number part and 1⁄2 is the fraction part. Mixed numbers are used to represent quantities that are not whole, but are not entirely fractional either.
What are Like Denominators?
Like denominators refer to fractions that have the same denominator. For example, 1⁄4 and 3⁄4 have like denominators, as both fractions have a denominator of 4. When working with fractions that have like denominators, we can perform operations such as addition and subtraction by simply adding or subtracting the numerators.
Adding Mixed Numbers with Like Denominators
Adding mixed numbers with like denominators is a straightforward process. Here’s a step-by-step guide:
- Add the whole number parts together.
- Add the fraction parts together by adding the numerators.
- If the sum of the numerators is greater than the denominator, simplify the fraction by dividing the numerator by the denominator.
- Combine the whole number part and the simplified fraction part to get the final answer.
📝 Note: When adding mixed numbers with like denominators, make sure to line up the whole number parts and the fraction parts separately.
Example:
2 1⁄4 + 1 3⁄4 =?
- Add the whole number parts: 2 + 1 = 3
- Add the fraction parts: 1⁄4 + 3⁄4 = 4⁄4 = 1
- Combine the whole number part and the simplified fraction part: 3 + 1 = 4
Subtracting Mixed Numbers with Like Denominators
Subtracting mixed numbers with like denominators is also a straightforward process. Here’s a step-by-step guide:
- Subtract the whole number parts.
- Subtract the fraction parts by subtracting the numerators.
- If the difference of the numerators is less than the denominator, simplify the fraction by dividing the numerator by the denominator.
- Combine the whole number part and the simplified fraction part to get the final answer.
📝 Note: When subtracting mixed numbers with like denominators, make sure to line up the whole number parts and the fraction parts separately.
Example:
3 1⁄4 - 2 3⁄4 =?
- Subtract the whole number parts: 3 - 2 = 1
- Subtract the fraction parts: 1⁄4 - 3⁄4 = -2⁄4 = -1⁄2
- Combine the whole number part and the simplified fraction part: 1 - 1⁄2 = 1⁄2
Multiplying Mixed Numbers with Like Denominators
Multiplying mixed numbers with like denominators involves multiplying the numerators and denominators separately. Here’s a step-by-step guide:
- Multiply the whole number parts.
- Multiply the fraction parts by multiplying the numerators and denominators.
- Simplify the fraction part by dividing the numerator by the denominator.
- Combine the whole number part and the simplified fraction part to get the final answer.
📝 Note: When multiplying mixed numbers with like denominators, make sure to multiply the numerators and denominators separately.
Example:
2 1⁄4 × 3 3⁄4 =?
- Multiply the whole number parts: 2 × 3 = 6
- Multiply the fraction parts: 1⁄4 × 3⁄4 = 3⁄16
- Combine the whole number part and the simplified fraction part: 6 + 3⁄16 = 6 3⁄16
Dividing Mixed Numbers with Like Denominators
Dividing mixed numbers with like denominators involves dividing the numerators and denominators separately. Here’s a step-by-step guide:
- Divide the whole number parts.
- Divide the fraction parts by dividing the numerators and denominators.
- Simplify the fraction part by dividing the numerator by the denominator.
- Combine the whole number part and the simplified fraction part to get the final answer.
📝 Note: When dividing mixed numbers with like denominators, make sure to divide the numerators and denominators separately.
Example:
4 1⁄4 ÷ 2 3⁄4 =?
- Divide the whole number parts: 4 ÷ 2 = 2
- Divide the fraction parts: 1⁄4 ÷ 3⁄4 = 1⁄3
- Combine the whole number part and the simplified fraction part: 2 + 1⁄3 = 2 1⁄3
In conclusion, working with mixed numbers and like denominators can be made easy by following a few simple steps. By adding, subtracting, multiplying, and dividing mixed numbers with like denominators, you can simplify complex calculations and get the right answer every time.
What are mixed numbers?
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Mixed numbers are a combination of a whole number and a fraction.
What are like denominators?
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Like denominators refer to fractions that have the same denominator.
How do I add mixed numbers with like denominators?
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Add the whole number parts together and add the fraction parts together by adding the numerators.
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