Fractions, decimals and percentages: Multiplying and dividing fractions. 3rd year of secondary education.

Operations with fractions

How much money would an heir inherit if he was to inherit 4/7 (four sevenths) of a total  inheritance of € 8,400,000 (eight million four hundred thousand) euros?

We are going to use the following window to solve the problem. Read the instructions carefully.

 First you need to introduce the initial quantity and the denominator at the bottom of the window. Then, click on Enter and drag point A until you reach the desired value of the numerator.

Write down the operation you had to carry out on the total QUANTITY to find out 4/7 of it.

Carry out the same operation with other quantities and fractions.

For example, find out 1/5 of 100, or 3/4 of 200 etc.

When a fraction acts as an operator on a quantity C, we get the answer by multiplying a*C and dividing the result by b.

of C = * C =

Multiplying and dividing fractions

We can use the following formulae to multiply and divide fractions:

 TO MULTIPLY FRACTIONS: TO DIVIDE FRACTIONS:

 As well as multiplying and dividing fractions in the following window, you can also cancel down the answer you get. We simplify by dividing the numerator and denominator by the same number. In div-1 you can introduce a common divisor to the multiplication of  the fractions. In div-2 you can introduce a common divisor to the division of the fractions. (Let me remind you that you can also directly introduce a common divisor and press ENTER. If the number you introduce cannot be divided exactly into the numerator or  the denominator the quotient given will not be a whole number and we will not be able to cancel the fraction down)

Exercise 7.

Multiply and divide the following fractions and cancel the answers down to the lowest terms. Then, check your results in this window:

a) 4/3 * 1/6
b) 4/3 ÷ 1/6

c) 2/5 * 3/8
d) 2/5 ÷ 3/8

e) 20/9*15/4
f)  20/9÷15/4

Exercise 8: The magic square.

This is a magic square. The reason being that the sum of all the lines (horizontal, vertical or diagonal) is always the same. We call the sum of any line of the square the magic number.

Work out the answers in each little square and calculate the magic number. Then, fill in the empty little squares with the missing number.