Unit 4 Flashcard

A fraction represents a part of a whole and is expressed as $$\frac{a}{b}$$ , where 'a' is the numerator and 'b' is the denominator.

To find the total, divide the number of items by the fraction. For example, if $$\frac{3}{5}$$ of a book is 75 pages, the total pages are $$75 \div \frac{3}{5} = 125$$ .

Dividing a quantity into equal parts means splitting it into smaller sections that are all the same size. For example, if 6 cups of jam are divided into 4 containers, each container gets $$\frac{6}{4} = \frac{3}{2}$$ cups.

To find the number of batches, divide the total amount of the ingredient by the amount needed for one batch. For example, if 5 $$\frac{1}{3}$$ cups of sugar are used and each batch requires $$\frac{2}{3}$$ cup, then the number of batches is $$5\frac{1}{3} \div \frac{2}{3} = 8$$ .

To divide fractions, multiply the first fraction by the reciprocal of the second fraction. For example, to divide $$\frac{3}{4}$$ by $$\frac{1}{8}$$ , calculate $$\frac{3}{4} \times \frac{8}{1} = 6$$ .

The reciprocal of a fraction $$\frac{a}{b}$$ is $$\frac{b}{a}$$ . It is used in division of fractions.

To convert a mixed number to an improper fraction, multiply the whole number by the denominator and add the numerator. For example, $$5\frac{1}{3} = \frac{5 \times 3 + 1}{3} = \frac{16}{3}$$ .

The formula is: Total = Part ÷ Fraction. For example, if 75 pages is $$\frac{3}{5}$$ of a book, then Total = $$75 \div \frac{3}{5} = 125$$ .

Simplifying a fraction means reducing it to its lowest terms by dividing the numerator and denominator by their greatest common divisor (GCD).

To add fractions with different denominators, find a common denominator, convert the fractions, and then add the numerators.