MATH / Foundations

Number and place value

Place value gives a digit its size. Integers, fractions and decimals describe the same number line in different ways; a negative sign indicates a position below zero.

Learning objectives

Explain number and place value using a concrete example.
Apply the worked method and justify each step.
Recognise the limitation described in the final check.

The big idea

Place value gives a digit its size. Integers, fractions and decimals describe the same number line in different ways; a negative sign indicates a position below zero.

Estimate first, then use the order of operations. Fractions require a common denominator for addition, but multiplication combines numerators and denominators directly.

Equations and relationships

\frac ab+\frac cb=\frac{a+c}{b}

Add equal-sized fractional parts.

Worked example

Find 3/4 + 1/8.

Follow the solution

Convert 3/4 to 6/8, then add 1/8 to obtain 7/8.

Investigate and explain

Predict the worked result before calculating. Change one input, record the new result, and explain which assumptions still hold.

Related interactive model. Compare its assumptions with the explanation; it is not a complete syllabus lesson.

Open the interactive investigation

Check your understanding

1. Which is larger: −2 or −5?

−5
−2
They are equal

Check the answer and reasoning

−2

−2 lies farther right on the number line.

2. Find 3/4 + 1/8.

4/12
1/2
7/8

Check the answer and reasoning

7/8

Convert 3/4 to 6/8, then add 1/8 to obtain 7/8.

3. What is 2 + 3 × 4?

Check the answer and reasoning

Multiplication is performed before addition unless brackets specify otherwise.