**Table: Analysis of PSLE Maths β Marks Distribution 7 years**

This table shows the analysis of the PSLE Math paper over 7 years from 2016 to 2022. There are two trends that we have observed. The first trend is the topic βNumbers, Measurements and Ratio and Percentageβ comprising about 60% of the PSLE Math paper.

Ratio and percentage makes up on average about 11% of the PSLE Math paper. Today we will be discussing 2 questions from the 2021 PSLE Math paper on Ratio and percentage.

**PSLE Paper 1 Q29 (2 Marks)**

29) Susan had a box of blue beads and red beads in the **ratio** 7 : 13. **She removed an equal number of blue beads and red beads from the box.** The ratio of the number of of blue beads and red beads left in the box became 1 : 3. What **percentage** of the beads were left in the box?

**Step 1:**

Read the question and identify the concept of this maths question, by looking at the keyword βratio, percentageβ, this tells you that this is a ratio and percentage question.

We also see the sentence that βShe removed an equal number of blue beads and red beads from the box.β. This tells us that the difference between the red and blue beads is constant, since the same number was removed. The sentence also shows us that a change is involved, so we should use the tic tac toe table to solve the question.

**Step 2:**

The tic tac toe table is a method used to show information presented in a question when there is a starting scenario, a change, and an ending scenario, we call this start change end. For this question we can identify the start, change, end as follows:

(START) Susan had a box of blue beads and red beads in the ratio of 7 : 13. (CHANGE) She removed an equal number of blue beads and red beads from the box. (END) The ratio of the number of blue beads and red beads left in the box became 1 : 3.Β What percentage of the beads were left in the box?

So we can fill up the table according to that:

Now the key to the question is to understand that the difference between the number of blue and red beads is the same at the start and also at the end, since the same number of beads were taken out. So we also need a column to show the difference between the red and blue beads, to show that the difference is constant, since the same number of beads were removed.

At the moment the difference at the start is 6u, while the difference at the end is 2u. So the next thing would be to change the units at the end to 6u, so that the difference in units is the same. All the units at the end would then be multiplied by 3.

Complete the rest of the table to check that the **change in units** is the same for both blue and red.

In the change row, we can confirm that 4 units worth of beads was taken out for both blue and red beads.

**Step 3:**

Lastly, the last step of Bluetreeβs SOLVE technique is to βRead the math question again to solve the mysteryβ. Solve the question to find the percentage of beads left in the box, this can be done by adding the units for blue and red beads at the end and dividing that by the total number of units at the start.

**Percentage left:**

Now we have solved that the percentage of beads left in the box at the end is 60% of the original number at the start.

### PSLE Paper 2 Q11 (3 marks)

11) The number of boys and girls taking part in a quiz are in the ratio 7:4. These students are put into two groups. 30% of the boys and 60% of the girls are in Group P. The rest of the students are in Group Q.

(a) What is the ratio of the number of students in Group P to Group Q?

(b) The number of boys in Group P is fewer than 70. What is the largest possible total number of students taking part in the quiz?

**Step 1:**

First read the question and **identify the concept of this Maths question**, by looking at the keyword **βratio, 30%,60%β**, this tells you that this is a **ratio and percentage question.**

**Step 2:**

The number of boys and girls taking part in a quiz are in the ratio 7:4. These students are put into two groups. 30% of the boys and 60% of the girls are in Group P. The rest of the students are in Group Q.

(a) What is the ratio of the number of students in Group P to Group Q?

We can start by writing out what we know from the question by using read and write, writing the information down sentence by sentence and see if we can find the percentage of the units of the boys and girls that are in Group P.

**NOTE:**

Students find it confusing to work with decimals, hence we will always change it to a number that is easier for students to work with. The advance students who are comfortable with decimals can always stick to decimals as the answers will be the same.

**Step 3:**

So the next step would be to find the lowest common multiple for 7 and 10, and 4 and 10, so that the percentage of units can be whole numbers. The lowest common multiple for 7, 4 and 10, will be 70 and 40 respectively.

### Step 4:

Now we find the ratio of units in Group Q

πππ‘ππ π π‘π’ππππ‘π = 70π’ + 40π’ = 110π’

ππ‘π’ππππ‘π ππ πΊπππ’π π = 110π’ β 45π’ = 65π’

Finally we simplify the ratio of Group P to Group Q in the simplest form

πΊπππ’π π βΆ πΊπππ’π π = 45 βΆ 65 = 9 βΆ 13

Now we have found the ratio of the number of students in Group P to Group Q in simplest form is 9:13.

### 11b.

### Step 1:

The number of boys and girls taking part in a quiz are in the ratio 7:4. These students are put into two groups. 30% of the boys and 60% of the girls are in Group P. The rest of the students are in Group Q.

(a) What is the ratio of the number of students in Group P to Group Q?

(b) The number of boys in Group P is fewer than 70. What is the largest possible total number of students taking part in the quiz?

Part B states the number of boys in Group P is fewer than 70, and asks what is the largest possible total number of students taking part in the quiz? This means the question is asking us to suggest the largest possible number of boys in Group P that is less than 70.

Since there are 21 units of boys in Group P, the number of actual boys represented by the units must be a multiple of 21, and that multiple has to be smaller than 70.

ππ’ππ‘πππππ ππ 21 = 21, 42, 63, 84β¦

From here we can tell that the largest possible multiple of 21, that is less than 70, is 63.

**Step 2:**

Now knowing that 21 units is equal to 63, we can find the value of 1 unit, and subsequently the total number of students represented by 110 units found earlier.

21π’ = 63

1π’ = 3

110π’ = 330

Hence we have solved the question that the largest possible total number of students taking part in the quiz is 330.

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