Improper Fractions and Mixed Numbers

What is a proper fraction?

• A proper fraction is equivalent to a mixed number.

• A proper fraction is always greater than one.

• A proper fraction represents something smaller than one whole.

• A proper fraction is an improper fraction with a negative sign.

Answer explanation

A proper fraction represents a part of a whole, where the numerator (the top number) is smaller than the denominator (the bottom number). For example, 1/2 represents half of a whole, which is less than one.

Tags

CCSS.3.NF.A.1

CCSS.3.NF.A.2B

What is an improper fraction?

• An improper fraction represents more than one whole.

• An improper fraction is always less than one.

• An improper fraction is like a piece of something smaller than one whole thing.

• An improper fraction is a whole number divided by a fraction.

Answer explanation

An improper fraction is a type of fraction where the numerator (the top number) is equal to or greater than the denominator (the bottom number), which means you have more than one whole unit. For example, 5/4 represents one whole unit plus an additional fourth, so it's more than one whole thing.

Tags

CCSS.3.NF.A.1

CCSS.3.NF.A.2B

What is a mixed number?

• A mixed number is an improper fraction with a negative sign.

• A mixed number is always equal to one.

• A mixed number is a fraction with a numerator greater than the denominator.

• A mixed number is a combination of a whole number and a fraction. 

Answer explanation

A mixed number allows you to represent a quantity that includes both a whole unit and a part of another unit. For example, 3 1/2 represents three whole units and one-half of another unit.

Tags

CCSS.3.NF.A.3C

Convert the improper fraction 7/3 to a mixed number.

• 1 2/3

• 2 1/3

• 3 1/2

• 2 3/7

Answer explanation

To convert the improper fraction 7/3 to a mixed number, divide the numerator (7) by the denominator (3): 7 ÷ 3 = 2 with a remainder of 1. The quotient (2) becomes the whole number part of the mixed number, the remainder (1) becomes the numerator of the proper fraction part, and the denominator remains the same (3). So, the mixed number equivalent of the improper fraction 7/3 is 2 1/3.

Convert the mixed number 4 2/5 to an improper fraction.

• 4/5

• 5/4

• 2/9

• 22/5

Answer explanation

To convert the mixed number 4 2/5 to an improper fraction, multiply the denominator of the fraction (5) by the whole number (4) by : 5 × 4 = 20. Then add the numerator of the fraction (2): 20 + 2 = 22. The result (22) becomes the new numerator, and the denominator remains the same (5). So, the improper fraction equivalent of the mixed number 4 2/5 is 22/5.