Unit Rates and Fraction Operations

A unit rate is a comparison of two different quantities when they are combined together. It shows how much of one quantity corresponds to one unit of another quantity.

To find the unit rate, divide the first quantity by the second quantity. For example, if you have 60 miles in 2 hours, the unit rate is 60 ÷ 2 = 30 miles per hour.

A fraction represents a part of a whole. It consists of a numerator (top number) and a denominator (bottom number). For example, in $$\frac{3}{4}$$ , 3 is the part and 4 is the whole.

Dividing fractions means multiplying by the reciprocal of the second fraction. For example, to divide $$\frac{1}{2}$$ by $$\frac{3}{4}$$ , you multiply $$\frac{1}{2}$$ by $$\frac{4}{3}$$ .

An equivalent fraction is a fraction that represents the same value as another fraction, even though the numerator and denominator are different. For example, $$\frac{1}{2}$$ is equivalent to $$\frac{2}{4}$$ .

To simplify a fraction, divide the numerator and the denominator by their greatest common factor (GCF). For example, $$\frac{4}{8}$$ simplifies to $$\frac{1}{2}$$ .

A ratio is a comparison of two quantities. It can be written in three ways: as a fraction, with a colon, or with the word 'to'. For example, the ratio of 2 to 3 can be written as $$\frac{2}{3}$$ , 2:3, or '2 to 3'.

A part-to-part ratio compares two parts of a whole. For example, if there are 5 boys and 3 girls in a class, the part-to-part ratio of boys to girls is 5:3.

A part-to-whole ratio compares one part to the entire whole. For example, if there are 5 boys in a class of 23 students, the part-to-whole ratio of boys to the whole class is 5:23.

To convert a mixed number to an improper fraction, multiply the whole number by the denominator and add the numerator. For example, $$1\frac{1}{3}$$ becomes $$\frac{4}{3}$$ .