Mixed number facts for kids

A mixed number is a special way to write a number that combines a whole number and a fraction. It shows you have full units and also a part of another unit. For example, if you have two whole pizzas and half of another pizza, you have 2 1/2 pizzas.

Mixed numbers are often used in everyday life. You might see them in recipes, when measuring things, or when talking about time. They help us describe amounts that are more than a whole but not quite the next whole number.

What Are Mixed Numbers?

A mixed number has two main parts:

• A whole number: This is a regular counting number like 1, 2, 3, and so on. It tells you how many full units you have.
• A fraction: This is a part of a whole, like 1/2, 3/4, or 1/3. It tells you how much of the next unit you have.

For example, in the mixed number 3 1/4, the '3' is the whole number, and '1/4' is the fraction. This means you have three full items and one-quarter of another item.

Why Do We Use Mixed Numbers?

Mixed numbers make it easier to understand quantities that are between whole numbers. Imagine you are baking and a recipe calls for "one and a half cups of flour." It's much clearer to write this as 1 1/2 cups rather than trying to use an improper fraction like 3/2 cups, which might be harder to picture. They help us describe real-world measurements more naturally.

How Are Mixed Numbers Different from Improper Fractions?

Mixed numbers and improper fractions represent the same value, but they look different.

• An improper fraction is a fraction where the top number (the numerator) is larger than or equal to the bottom number (the denominator). For example, 7/3 is an improper fraction.
• A mixed number combines a whole number and a proper fraction. For example, 2 1/3 is a mixed number.

Both 7/3 and 2 1/3 mean the same amount. They are just different ways to write it.

Converting Improper Fractions to Mixed Numbers

It's easy to change an improper fraction into a mixed number. Here's how:

1. Divide the numerator by the denominator. The quotient (the answer to the division) will be your whole number.
2. The remainder from the division becomes the new numerator of your fraction.
3. The denominator stays the same as in the original improper fraction.

Let's convert 7/3:

• Divide 7 by 3: 7 ÷ 3 = 2 with a remainder of 1.
• The whole number is 2.
• The new numerator is 1 (the remainder).
• The denominator is still 3.

So, 7/3 becomes 2 1/3.

Converting Mixed Numbers to Improper Fractions

You can also change a mixed number back into an improper fraction:

1. Multiply the whole number by the denominator of the fraction.
2. Add this result to the numerator of the fraction. This sum becomes the new numerator for your improper fraction.
3. The denominator stays the same as in the original mixed number.

Let's convert 2 1/3:

• Multiply the whole number (2) by the denominator (3): 2 × 3 = 6.
• Add this to the numerator (1): 6 + 1 = 7.
• The new numerator is 7.
• The denominator is still 3.

So, 2 1/3 becomes 7/3.

Working with Mixed Numbers

You can add, subtract, multiply, and divide mixed numbers, just like other numbers. Often, it's easiest to convert them to improper fractions first, do the math, and then convert the answer back to a mixed number if needed.

Adding Mixed Numbers

To add mixed numbers:

1. Add the whole numbers together.
2. Add the fractions together.
3. If the sum of the fractions is an improper fraction, convert it to a mixed number and add its whole part to the sum of the whole numbers.

Example: 1 1/2 + 2 1/4

• Add whole numbers: 1 + 2 = 3.
• Add fractions: 1/2 + 1/4 = 2/4 + 1/4 = 3/4.
• Combine: 3 3/4.

Subtracting Mixed Numbers

To subtract mixed numbers:

1. If the first fraction is smaller than the second fraction, you might need to "borrow" from the whole number.
2. Subtract the whole numbers.
3. Subtract the fractions.

Example: 3 1/2 - 1 1/4

• Convert to improper fractions: 7/2 - 5/4 = 14/4 - 5/4 = 9/4.
• Convert back to mixed number: 9/4 = 2 1/4.

Multiplying Mixed Numbers

To multiply mixed numbers, it's usually best to convert them to improper fractions first:

1. Convert both mixed numbers to improper fractions.
2. Multiply the numerators together.
3. Multiply the denominators together.
4. Simplify the resulting fraction and convert it back to a mixed number if needed.

Example: 1 1/2 × 2 1/3

• Convert: 3/2 × 7/3.
• Multiply: (3 × 7) / (2 × 3) = 21/6.
• Simplify: 21/6 = 7/2 = 3 1/2.

Dividing Mixed Numbers

To divide mixed numbers:

1. Convert both mixed numbers to improper fractions.
2. "Flip" the second fraction (find its reciprocal).
3. Multiply the first fraction by the flipped second fraction.
4. Simplify the result and convert back to a mixed number if needed.

Example: 3 1/2 ÷ 1 1/4

• Convert: 7/2 ÷ 5/4.
• Flip the second fraction: 7/2 × 4/5.
• Multiply: (7 × 4) / (2 × 5) = 28/10.
• Simplify: 28/10 = 14/5 = 2 4/5.

Mixed numbers are a useful part of mathematics that help us describe quantities more clearly in many real-world situations.