So my brother’s share corresponds to: 2/3 x 3/4 = 2/4 = 1/2 so, it means half of the total inheritance.

**3. In a company there are 42 executives which represents 6/11 of the employees. How many employees are there in this company?**

Answer:

We know what 6/11 represents, we are looking for how much the whole thing is 11/11 (or 1).

We will use the rule of three: we go back to the unit before going to calculate what we want.

If 6/11 is 42, then 1/11 is 6 times less so 7 (42÷6).

If 1/11 is 7, then 11/11 or the whole is 77 (11 times more)

So there are 77 employees in this company.

**4. The box of chocolate that John bought contains 450 grams, he eats 5/9 of it. How many grams of chocolate did he eat?**

Answer:

If the box of chocolate is divided into 9 equal parts and he takes 5 of those parts. Gold 450÷9 = 50 grams per slice. So 5 parts represent 250 grams.

Another method by applying the course on fractions:

John ate 5/9 of the 450 grams, hence the calculation is: 5/9 x 450

By calculating we get: 5/9 x 450=

5×450/9 = 5x9x50/9 = 5 x 50 = 250 grams

**5. What is half of four-fifths of five-sevenths of 14?**

Answer:

Keep in mind that “of” means “x” in a statement of fractions or percentages

We then obtain: (1/2 x 4/5 x5/7) x14 = 1/2 x (2×2/5) x 5/7 x 7 x 2=

2×2 = 4

**6. If Anne drank 5/6 of a bottle that contained 1.8 liters of juice. How much juice, in centilitres, is left?**

A) 10

B) 20

C) 18

D) 24

E) 30

Answer: E

If Anne has drunk 5/6 it means that there is 1/6 of the bottle left, i.e. 1/6 of 1.8 litres. It therefore remains to divide 1.8 by 6 which gives 0.3 liters or 30 cl.

**7. Maria buys a package of 84 candies. She eats 3/7 the first day and then a third of the rest the next day. How many candies will she still have two days later?**

A) 14

B) 18

C) 28

D) 32

E) 35

Answer:

Corrected exercise 6 on fractions: Answer D

If she eats 3/7 on the 1st day, she has 4/7 left. Let’s then calculate 4/7 of 84 to know the number of candies remaining after the 1st day. To do this, we divide 84 by 7 before multiplying by 4. We know that 12×7=84. So 84÷7=12. And 12×4=48.

So after the 1st day, he has 48 candies left. If she then eats 1/3 of these 48, it means that she has 2/3 left, i.e. 2/3 of 48. We proceed in the same way: 48÷3=16 and 16×2=32.

She will have 32 candies left on the 3rd day.

**8. Michael spends half of his pay on his mortgage and then a third of the rest for his various bills. He then has 900 euros left. How much is his salary?**

A) €1,800

B) €2,400

C) €2,700

D) €3,600

E) €4,500

Answer:

The key is to understand what fraction represents this €900?

After the credit, if he spends 1/3 of the rest on bills, he keeps 2/3 of the rest. But at this stage the remainder is 1/2 (half) of his pay.

So these €900 represent 2/3 of 1/2 or = 2/3 x 1/2 = 1/3 of all his pay (simplifying by 2). To determine his entire salary, we therefore multiply by 3, which gives €2,700.

**9. A master chocolatier makes three types of chocolate: milk, dark and praline. Last week of all the chocolates sold, 2/7 were milk, 1/3 dark and 96 pralines. How much chocolate did he sell last week?**

A) 192

B) 205

C) 224

D) 240

E) 252

Answer: E

In this type of question, we calculate the share, in fraction, that these 96 pralines represent before performing a rule of three to determine the total.

Let’s calculate milk + dark and then determine the remainder: 2/7 + 1/3 = 6/21 + 7/21 = 13/21. The rest is therefore what represents 96 chocolates. We will calculate what represents 1/21 before calculating the whole 21/21 = 1.

If 8/21 represents 96, then 1/21 represents 8 times month or 12 (in fact 8 × 12 = 96).

And therefore, it represents 21 times more or 21×12=252 chocolates in total.

**10. In an election, Patrick received 3/10 of the votes in the first round. What fraction of the remaining votes must he obtain to have half of all the votes?**

A) 1/5

B) 2/7

C) 3/10

D) 7/20

E) 1/2

Answer: B

The difficulty was to fully understand the question. Patrick got 3/10 of the votes, so there are 7/10 left. We are looking for what fraction of 7/10 must he obtain so that all his votes are 1/2. Keep in mind that “de” means “×”.

Method 1 of corrected exercise 9 on fractions:

The fastest was to dissect the problem. He currently has 3/10 of the votes and he wants 1/2, let’s first determine the part of the votes he lacks, 1/2 – 3/10 = 5/10 – 3/10 = 2/10 = 1/5. It must therefore obtain 1/5 of all the votes (and not the remainder) to have a majority.

Now we wonder what fraction of the remaining votes gives 1/5? That is, which proposition × 7/10 is 1/5. We test them:

A) 1/5 × 7/10 = 7/50 is not equal to 1/5

B) 2/7 × 7/10 = 2/10 and simplifying by 2 it gives 1/5.

Method 2 of corrected exercise on fractions:

we set the equation.

Let x be the desired fraction, we must solve: 3/10 + x X 7/10 x = 1/2

x X 7/10 = 1/2 – 3/10

or again: x X 7/10 = 1/5

and therefore: x = 1/5 x 10/7 = (1x2x5 / 5×7) = 2/7

Read also: Hardest Math Quiz

**11. A florist has 411 roses and 685 Columbines. In order to prepare bouquets, he wishes to distribute these flowers by using them all and obtaining the maximum number of identical bouquets.**

A) Calculate the number of bouquets.

B) Calculate the number of roses and lily in each bouquet.

Sources: PinterPandai, Davenport University, CueMath, MathIsFun

Photo credit: Ezra M. Katz (CC BY-SA 3.0) via Wikimedia Commons