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Mixed Number – Definition, Example, Facts

Mixed Numbers play a vital role in the world of mathematics, especially for young learners as they advance on their mathematical journey. Here at Brighterly, we understand the importance of grasping mixed numbers and have created this comprehensive blog post to help you understand mixed numbers and their various applications in a fun and engaging way. So, let’s embark on this exciting adventure together!

What are Mixed Numbers?

At Brighterly, we believe in making complex concepts simple and easy to understand. Mixed numbers are a unique blend of whole numbers and fractions, used to represent quantities that are not whole numbers but exceed one. Picture this: you have 2 entire pizzas and half of another pizza to share with your friends. To represent this scenario, we use the mixed number 2 1/2, making it easier to communicate and visualize.

In order to better master this topic, we recommend that you pay attention to the math worksheets from Brighterly. They will allow you to learn and consolidate your knowledge of mixed numbers.

Converting Improper Fractions to Mixed Numbers

When you have an improper fraction, it means that the numerator is equal to or greater than the denominator. To convert an improper fraction to a mixed number, you’ll need to follow these steps:

1. Divide the numerator by the denominator.
2. Write down the quotient (the whole number part of the answer).
3. Write down the remainder as the new numerator over the original denominator.

For example, let’s convert the improper fraction 7/4 to a mixed number:

1. Divide 7 by 4: 7 ÷ 4 = 1 with a remainder of 3.
2. Write down the quotient: 1.
3. Write down the remainder as a new fraction: 3/4.

So, 7/4 is equivalent to the mixed number 1 3/4.

Adding Mixed Numbers

To add mixed numbers, follow these steps:

1. Add the whole numbers together.
2. Add the fractions together (you may need to find a common denominator).
3. Simplify the fraction if necessary.
4. If the resulting fraction is an improper fraction, convert it back to a mixed number.

For example, let’s add 3 1/4 and 2 3/4:

1. Add the whole numbers: 3 + 2 = 5.
2. Add the fractions: 1/4 + 3/4 = 4/4.
3. Simplify the fraction: 4/4 = 1.
4. Combine the whole numbers and the simplified fraction: 5 + 1 = 6.

So, 3 1/4 + 2 3/4 = 6.

Subtracting Mixed Fractions

Subtracting mixed fractions involves the following steps:

1. If necessary, find a common denominator for the fractions.
2. Subtract the fractions.
3. Borrow from the whole number if the fraction in the minuend is smaller than the fraction in the subtrahend.
4. Subtract the whole numbers.

For example, let’s subtract 4 1/4 from 6 3/4:

1. The fractions already have a common denominator (4).
2. Subtract the fractions: 3/4 – 1/4 = 2/4.
3. No need to borrow since the fraction in the minuend is larger than the fraction in the subtrahend.
4. Subtract the whole numbers: 6 – 4 = 2.

So, 6 3/4 – 4 1/4 = 2 2/4, which simplifies to 2 1/2.

Multiplying Mixed Fractions

To multiply mixed fractions, follow these steps:

1. Convert each mixed number to an improper fraction.
2. Multiply the numerators together to get the new numerator.
3. Multiply the denominators together to get the new denominator.
4. Simplify the resulting fraction if necessary.
5. Convert the result back to a mixed number if necessary.

For example, let’s multiply 2 1/2 and 1 3/4:

1. Convert the mixed numbers to improper fractions: 2 1/2 = 5/2 and 1 3/4 = 7/4.
2. Multiply the numerators: 5 × 7 = 35.
3. Multiply the denominators: 2 × 4 = 8.
4. The resulting fraction is 35/8, which is already simplified.
5. Convert the improper fraction back to a mixed number: 35 ÷ 8 = 4 with a remainder of 3, so 35/8 = 4 3/8.

So, 2 1/2 × 1 3/4 = 4 3/8.

Converting Mixed Numbers to Decimals

To convert a mixed number to a decimal, follow these steps:

1. Convert the fraction part of the mixed number to a decimal by dividing the numerator by the denominator.
2. Add the whole number part to the decimal result.

For example, let’s convert 3 1/2 to a decimal:

1. Convert the fraction to a decimal: 1 ÷ 2 = 0.5.
2. Add the whole number part: 3 + 0.5 = 3.5.

So, 3 1/2 is equal to 3.5 as a decimal.

Converting Mixed Numbers to Improper Fractions

To convert a mixed number to an improper fraction, follow these steps:

1. Multiply the whole number by the denominator of the fraction.
2. Add the result to the numerator of the fraction.
3. Write the new numerator over the original denominator.

For example, let’s convert 4 3/8 to an improper fraction:

1. Multiply the whole number by the denominator: 4 × 8 = 32.
2. Add the result to the numerator: 32 + 3 = 35.
3. Write the new numerator over the original denominator: 35/8.

So, 4 3/8 is equivalent to the improper fraction 35/8.

Parts of a Mixed Number

A mixed number consists of two parts:

1. Whole Number: The integer part of the mixed number.
2. Fraction: The fractional part of the mixed number, consisting of a numerator and a denominator.

For example, in the mixed number 5 3/4, the whole number is 5, and the fraction is 3/4.

Properties of Mixed Numbers

Mixed numbers have several important properties:

1. Mixed numbers are greater than 1: By definition, mixed numbers consist of a whole number and a fraction, so they are always greater than 1.
2. Mixed numbers can be represented as improper fractions and vice versa: As shown earlier, mixed numbers can be converted to improper fractions, and improper fractions can be converted to mixed numbers.
3. Mixed numbers can be represented as decimals: Mixed numbers can be converted to decimal form, which is useful for various calculations and comparisons.

Real Life Examples of Mixed Numbers

Mixed numbers are used in various real-life situations, such as:

1. Measuring lengths and distances: Mixed numbers are often used to represent measurements, like the length of a room or the distance between two points.
2. Cooking and baking: Recipes often use mixed numbers to indicate the required ingredients’ quantities.
3. Time management: Mixed numbers can be used to represent elapsed time or the duration of events.

Practice Questions on Mixed Numbers

1. Convert the mixed number 3 1/3 to an improper fraction.
2. Add the mixed numbers 2 1/2 and 4 1/6. 3. Subtract the mixed numbers 5 2/3 from 8 1/2.
3. Multiply the mixed numbers 3 1/4 and 2 2/3.
4. Convert the mixed number 6 5/8 to a decimal.

Conclusion

Here at Brighterly, we understand the significance of mastering mixed numbers in a child’s mathematical education. Gaining a solid understanding of mixed numbers and learning how to perform various operations with them enables children to tackle real-life problems and enhance their overall mathematical abilities. As always, we are committed to making learning enjoyable and accessible, empowering young minds to reach their full potential. So keep exploring, keep learning, and keep shining with Brighterly!

Frequently Asked Questions on Mixed Numbers

What is the difference between a mixed number and a fraction?

A mixed number is a combination of a whole number and a fraction, while a fraction consists of just a numerator and a denominator without a whole number part.

Can mixed numbers be negative?

Yes, mixed numbers can be negative. You can represent a negative mixed number by placing a negative sign in front of the whole number.

Why are mixed numbers important?

Mixed numbers are important because they help us represent quantities that are not whole numbers but are greater than one. They are also useful in various real-life applications, such as measuring lengths, cooking, and time management.

Information Sources

1. Adding and subtracting mixed numbers (Wikihow)
2. Multiplying and dividing mixed numbers (ThoughtCo)
3. Converting mixed numbers to decimals (Homeschool Math)