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Maths years 5–7: free practice, theory and problems

A fraction shows a part of a whole. of a pizza means the pizza is cut into 4 equal slices, and you have 3 of them.

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Fractions
Decimals
Percent
Area and perimeter
Measurement and units
Statistics
Simple equations

1. Fractions

What is it about?

A fraction shows a part of a whole. $\frac{3}{4}$ of a pizza means the pizza is cut into 4 equal slices, and you have 3 of them.

Key points

The number below the line is the denominator: how many equal parts the whole is split into.
The number above is the numerator: how many parts you have.
Equivalent fractions: $\frac{1}{2} = \frac{2}{4} = \frac{4}{8}$ . Multiply (or divide) top and bottom by the same number.
Simplifying: $\frac{6}{8} = \frac{3}{4}$ (divide both by 2).
A fraction of a number: $\frac{3}{4}$ of 20 – divide by the denominator and multiply by the numerator: $20 : 4 \cdot 3 = 15$ .
Same denominator: add the numerators. $\frac{1}{5} + \frac{2}{5} = \frac{3}{5}$ .

Example

What is $\frac{2}{3}$ of 12? $12 : 3 = 4$ , and $4 \cdot 2 = 8$ .

The bigger the denominator, the smaller each piece:

\frac{1}{8}

is less than

\frac{1}{4}

Practise fractions in the app →

2. Decimals

What is it about?

Decimals have digits after the decimal point. They show parts of a whole, just like fractions.

Key points

The first digit after the point is tenths, the next is hundredths. 0.7 = $\frac{7}{10}$ , 0.25 = $\frac{25}{100}$ .
When you add or subtract: line up the decimal points.
Multiplying by 10 moves the point one step right: $3.4 \cdot 10 = 34$ . By 100: two steps.
Dividing by 10 moves the point one step left: $56 : 10 = 5.6$ .
Rounding: look at the next digit. 5 or more – round up. 4 or less – round down. $3.6 \approx 4$ .

Example

$2.5 + 1.75 = 4.25$ . Write 2.50 so both have the same number of decimals.

0.5 is the same as a half, and 0.25 is a quarter.

Practise decimals in the app →

3. Percent

What is it about?

Percent means "out of a hundred". 30 % means 30 out of 100. Percentages are used for discounts, scores and statistics.

Key points

100 % is the whole. 50 % is half. 25 % is a quarter. 10 % is a tenth.
10 % of a number: divide by 10. 10 % of 250 is 25.
Build other percentages from 10 %: 30 % is three times 10 %. 5 % is half of 10 %.
Discount: new price = old price $-$ the discount.
Percent as a decimal: 35 % = 0.35.

Example

A jumper costs 400 kr. There is a 25 % discount. 25 % of 400 is 100, so it costs $400 - 100 = 300$ kr.

Find 10 % first – then you can work out almost any percentage in your head.

Practise percent in the app →

4. Area and perimeter

What is it about?

The perimeter is the distance around a shape. The area is how big the surface inside is.

Key points

Perimeter: add up all the sides. Measured in cm, m …
Area of a rectangle: length · width. Measured in square centimetres (cm²) or square metres (m²).
Area of a square: side · side.
Area of a triangle: $\frac{\text{base} \cdot \text{height}}{2}$ – half of a rectangle.
1 cm² is a square of 1 cm by 1 cm.

Example

A room is 4 m long and 3 m wide. Area: $4 \cdot 3 = 12$ m². Perimeter: $4 + 3 + 4 + 3 = 14$ m.

Area has "²" in the unit because we multiply two lengths.

Practise area and perimeter in the app →

5. Measurement and units

What is it about?

We measure length, weight, volume and time. The unit tells us what we measured with.

Key points

Length: 1 km = 1000 m, 1 m = 100 cm, 1 cm = 10 mm.
Weight (mass): 1 kg = 1000 g. 1 tonne = 1000 kg.
Volume: 1 litre = 10 dl = 1000 ml.
Time: 1 hour = 60 min, 1 min = 60 s.
From a big unit to a small one: multiply. From small to big: divide.

Example

2.5 m in cm: $2.5 \cdot 100 = 250$ cm.

"Kilo" means thousand: kilometre = 1000 metres, kilogram = 1000 grams.

Practise measurement and units in the app →

6. Statistics

What is it about?

Statistics is collecting numbers and describing them briefly. What is typical? How big is the spread?

Key points

Mean: add all the numbers and divide by how many there are.
Median: the middle number when you sort from smallest to largest.
Mode: the number that occurs most often.
Range: largest $-$ smallest.
A bar chart shows how many there are in each group.

Example

The numbers 2, 4, 4, 5, 10. Mean: $\frac{25}{5} = 5$ . Median: 4. Mode: 4. Range: $10 - 2 = 8$ .

One very large number pulls the mean up, but the median hardly changes.

Practise statistics in the app →

7. Simple equations

What is it about?

An equation is a sum with a number you do not know, often called $x$ . Solving the equation means finding $x$ .

Key points

Think of scales in balance: what is on each side of $=$ weighs the same.
Do the same thing on both sides and the balance holds.
$x + 5 = 12$ : subtract 5 on both sides. $x = 7$ .
$3x = 15$ : divide by 3 on both sides. $x = 5$ .
Check the answer: put it back in. $7 + 5 = 12$ ✓.

Example

$2x + 3 = 11$ . Subtract 3: $2x = 8$ . Divide by 2: $x = 4$ . Check: $2 \cdot 4 + 3 = 11$ ✓.

3x

means

3 \cdot x

Practise simple equations in the app →

Example problems with solutions

Here are some of the problems in maths years 5–7. In the app, calculation problems get new numbers every time, so you can practise until it sticks – and take a graded practice exam before the real one.

Fractions: What is the denominator in

\frac{3}{7}

Answer: 7

The denominator is the number below the line: 7.

Decimals: What is 0.5 as a fraction?

Answer: $\frac{1}{2}$

0.5 = $\frac{5}{10} = \frac{1}{2}$ .

Percent: What does 50 % mean?

Answer: Half

50 out of 100 is half.

Area and perimeter: Which unit fits for area?

Answer: cm²

Area is measured in square units, for example cm².

Practise all the problems →

Maths years 5–7: free practice, theory and problems

Contents

1. Fractions

What is it about?

Key points

Example

2. Decimals

What is it about?

Key points

Example

3. Percent

What is it about?

Key points

Example

4. Area and perimeter

What is it about?

Key points

Example

5. Measurement and units

What is it about?

Key points

Example

6. Statistics

What is it about?

Key points

Example

7. Simple equations

What is it about?

Key points

Example

Example problems with solutions