Learn this concept that can help score AL1 in Math PSLE (Number x Value)

Not all tough problem sums involve fractions. Here is an example of a challenging problem that does not use fractions:

Cherish had twice as many $2 notes as $10 notes in her bag. She spent 3 of her $10 notes. The value of all her $10 notes remaining was $72 more than the value of all her $2 notes.

This is what we call a Number × Value Concept Question.

What is a Number × Value Concept Question?

A Number × Value concept question is a type of word problem where you know the value of each item, but you don't know how many of each item there are.

For example:

You know there are $2 notes and $10 notes (you know the values)
But you don't know how many $2 notes or how many $10 notes there are (you don't know the numbers)

The main idea is:

Total Value = Number of Items × Value of Each Item

Example:

If you have 5 ten-dollar notes, the total value = 5 × $10 = $50
If you have 8 two-dollar notes, the total value = 8 × $2 = $16

This method helps you organise information and solve problems step by step.

How to Spot a Number × Value Concept Question

You can tell it's a Number × Value concept question when you see:

Different types of items with different values (like $2 notes and $10 notes, or adult tickets and child tickets)
You know the value of each item (e.g. each note is worth $2 or $10)
You don't know how many of each item there are (that's what you need to find out)
Questions about quantities AND total value (how many of each item, and how much money in total)

If the problem tells you what each item is worth, but not how many there are, it's probably a Number × Value problem.

Example Question

Problem: Cherish had twice as many $2 notes as $10 notes in her bag. She spent 3 of her $10 notes. The value of all her $10 notes remaining was $72 more than the value of all her $2 notes. How many $2 notes did she have?

How to Solve Them

Follow these steps to solve Number × Value problems:

Step 1: Write Down What You Know

Look at the problem and write down the information using units (u).

From the question it says, "Cherish had twice as many $2 notes as $10 notes in her bag."

That means:

Number of $10 notes → 1u

Number of $2 notes → 2u

Step 2: Multiply Units with Values

Use the formula: Total Value = Number × Value per Item

Total $2 value = 2u × $2 = $4u

Total $10 value = 1u × $10 = $10u

Step 3: Apply Any Changes

From the question it says, "She spent 3 of her $10 notes."

That means → $10 notes spent = 3 × $10 = $30

$10 notes remaining = $10u - $30

Step 4: Write the Equation

The problem says: "The value of her remaining $10 notes was $72 more than the value of her $2 notes"

This means: Value of remaining $10 notes - Value of $2 notes = $72

So our equation is: (10u - 30) - 4u = 72

Step 5: Solve the Equation

10u - 30 - 4u = 72
6u - 30 = 72
6u = 102
u = 17

Step 6: Find the Answer

The question asks for the number of $2 notes:

Number of $2 notes = 2u = 2 × 17 = 34 notes

Check Your Answer

She originally had 17 ten-dollar notes
She spent 3, so she has 14 left: 14 × $10 = $140
She has 34 two-dollar notes: 34 × $2 = $68
Difference: $140 - $68 = $72 ✓

Tips to Remember

Keep number and value separate - Don't mix up "how many notes" with "how much money"
Use 1u for the smaller quantity - This makes the math easier
Read the last sentence carefully - It usually tells you what equation to write
Always check your answer - Put your numbers back into the problem to see if they work