Dividing Fraction Word Problems (R)

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

To divide a fraction by a whole number, multiply the denominator by that whole number. For example, $$\frac{a}{b} \div c = \frac{a}{b \times c}$$ .

Simplifying a fraction means reducing it to its lowest terms, where the numerator and denominator have no common factors other than 1.

Divide both the numerator and denominator by their greatest common divisor (GCD), which is 10. So, $$\frac{40 \div 10}{50 \div 10} = \frac{4}{5}$$ .

To find the fraction each person receives, divide the total fraction by the number of people. For example, $$\frac{2}{7} \div 4 = \frac{2}{7 \times 4} = \frac{2}{28} = \frac{1}{14}$$ .

To find how many items can be made, divide the total amount by the amount needed for one item. For example, if you have 10 yards and each bandana requires $$\frac{1}{3}$$ yard, then $$10 \div \frac{1}{3} = 10 \times 3 = 30$$ .

To divide fractions, multiply by the reciprocal of the divisor. For example, $$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$$ .

'Each' refers to the individual amount that every person or item receives when a total is divided.

To find the fraction of a whole used, divide the part used by the total amount. For example, if $$\frac{4}{9}$$ of ice cream is used for 6 sundaes, each sundae uses $$\frac{4}{9} \div 6 = \frac{4}{54} = \frac{2}{27}$$ .

The numerator indicates how many parts are being considered, while the denominator indicates how many equal parts the whole is divided into.