mozaMedical by Mozaik Education

Dividing fractions by natural numbers

Example 1

Ben and Adam want to divide \latex{\frac{3}{5}} of a fruit cake equally.

What proportion of the cake will Ben get?

Solution

Divide the fifths into two equal parts.

Ben will get half of the \latex{ 3 } fifths, that is, \latex{\frac{3}{5}\div2}.

Half a fifth is a tenth, so half of \latex{ 3 } fifths is \latex{ 3 } tenths, that is, \latex{\frac{3}{5}\div2=\frac{3}{10}}.

Ben will get \latex{\frac{3}{10}} of the cake.

Ben's

Adam's

When dividing a fraction by a natural number, the denominator is multiplied by the natural number and the numerator is left unchanged.

Example 2

\latex{\frac{6}{7}} of a garden was planted equally with lettuce, cabbage and pepper. What proportion of the garden was planted with lettuce?

Solution

Use a drawing to show the solution.

The third of \latex{\frac{6}{7}} is: \latex{\frac{6}{7}\div3=\frac{6\div3}{7}=\frac{2}{7}}.

The calculation can be performed this way because \latex{ 3 } is a divisor of \latex{ 6 }.

\latex{\frac{2}{7}} of the garden was planted with lettuce.

When dividing a fraction by a natural number, the numerator can be divided by the given natural number, and the denominator is left unchanged.

This method can be applied only if the natural number is a divisor of the numerator.

Example 3

Perform the following divisions.

a) \latex{2\frac{1}{5}\div3}

b) \latex{4\frac{9}{10}\div7}

Solution

Convert the mixed numbers to fraction form and perform the divisions.

a) \latex{2\frac{1}{5}\div3=\frac{11}{5}\div3=\frac{11}{15}}

b) \latex{4\frac{9}{10}\div7=\frac{49}{10}\div7=\frac{7}{10}}

Exercises

{{exercise_number}}. Perform the following operations.

a) \latex{\frac{6}{7} \div3}

b) \latex{\frac{4}{5} \div2}

c) \latex{\frac{7}{4} \div3}

d) \latex{\frac{10}{3} \div5}

e) \latex{\frac{4}{9} \div3}

f) \latex{\frac{2}{5} \div5}

g) \latex{\frac{3}{8} \div2}

h) \latex{\frac{7}{10} \div7}

i) \latex{\frac{12}{13} \div4}

j) \latex{\frac{42}{13} \div7}

k) \latex{\frac{3}{10} \div4}

l) \latex{\frac{15}{8} \div7}

{{exercise_number}}.

a) If \latex{ 10 } \latex{ litres } of oil weighs \latex{8\frac{3}{4}} \latex{ kg }, how much does \latex{ 1 } \latex{ litre } weigh?
b) If \latex{ 10 } \latex{ litres } of petrol weighs \latex{7\frac{1}{2}} \latex{ kg }, how much does \latex{ 1 } \latex{ litre } weigh?
c) If \latex{ 5 } \latex{ litres } of milk weighs \latex{5\frac{3}{20}} \latex{ kg }, how much does \latex{ 1 } \latex{ litre } weigh?
d) If \latex{ 8 } tiles weigh \latex{19\frac{1}{5}} \latex{ kg }, how much does \latex{ 1 } tile weigh?

{{exercise_number}}. What numbers should replace the letters to make the equalities true?

a) \latex{\frac{4}{7} \div{a}=\frac{4}{49}}

b) \latex{\frac{12}{11} \div{b}=\frac{3}{11}}

c) \latex{\frac{16}{3} \div{c}=\frac{4}{3}}

d) \latex{\frac{14}{3} \div{d}=\frac{14}{15}}

{{exercise_number}}. The students ate \latex{ 5 } \latex{ kg } of bread on the trip. Half a \latex{ kilogram } more was eaten at lunch than at dinner. How many \latex{ kg } of bread was eaten at lunch?

{{exercise_number}}. Perform the following operations.

a) \latex{2\frac{8}{9} \div13}

b) \latex{4\frac{4}{7} \div8}

c) \latex{4\frac{6}{13} \div2}

d) \latex{5\frac{1}{3} \div2}

{{exercise_number}}. Louis ran \latex{3\frac{1}{2}} \latex{ km } in \latex{ 15 } \latex{ minutes }, while Zack ran \latex{5\frac{1}{4}} \latex{ km } in \latex{ 21 } \latex{ minutes. }
Which one of them ran faster?

{{exercise_number}}. Which one is greater? By how much?

a) \latex{1\frac{3}{5} \times 4} or \latex{15\frac{3}{4} \div 3}

b) \latex{2\frac{6}{7} \div 5} or \latex{\frac{3}{32} \times 4}

Mathematics 5.

-