Chapter 05

5. Fractions, Money, Time & Measuring

Primary

Real life runs on fractions, money, time, and measurement. This chapter teaches equal parts, counting coins, reading a clock, and measuring the world around you.

At a glance
Core ideaA fraction is an equal part of a whole, written a/b.
Key termDenominator: how many equal parts the whole was cut into.
You can…Add simple fractions, count coins, read a clock and measure with units.
Watch outMore pieces means smaller pieces — 1/4 is less than 1/2.
01 · Theory

Equal parts, coins, clocks and rulers

A fraction is an equal part of a whole, written a/b: the top number (numerator) is how many parts you have, the bottom number (denominator) is how many equal parts the whole was cut into. 1/2 is a half; 1/4 is a quarter.

1/4 + 1/4 = 1/2
Two quarter-slices of a pizza make exactly the same amount as one half-slice: 1/4 + 1/4 = 1/2.

Money combines coin and bill values by adding: three 25-cent coins plus two 10-cent coins is 3 × 25 + 2 × 10 cents. Time: a clock has an hour hand (short) and a minute hand (long); 60 minutes make 1 hour, and we often read the minute hand to the nearest 5 or 15 minutes ("quarter past," "half past"). Measuring compares something to a fixed unit — a ruler for length (cm or inches), a scale for weight, a measuring cup for volume — and two measurements can only be compared directly when they use the same unit.

02 · Explanation

Fair shares, real coins, real clocks

A fraction is really about fairness: cutting a pizza into 4 equal slices means everyone gets the same amount, which is exactly what "quarter" promises. Unequal slices are not a true fraction, even if there happen to be four of them.

Money and time are fractions and place value in disguise — a quarter-dollar coin is called that because it is one quarter of a dollar, and "quarter past three" means one quarter of the hour (15 of 60 minutes) has passed since 3 o'clock. Measuring always needs a stated unit, because "5" by itself means nothing — 5 what?

03 · Practical

Worked example: fractions, coins and clock reading

Problem A — adding fractions

Add 1/4 + 1/4 (a quarter pizza slice plus another quarter slice).

  1. Same denominator (4), so keep it and add the tops: 1 + 1 = 2.
  2. Result: 2/4, which simplifies to 1/2 — two quarters make a half.
Problem B — counting money

You have 3 coins worth 25 cents each and 2 coins worth 10 cents each. What's the total?

  1. 3 × 25 = 75 cents.
  2. 2 × 10 = 20 cents.
  3. Total: 75 + 20 = 95 cents.
Problem C — reading a clock

The short hand is near 3, the long hand points at 6. What time is it?

  1. Long hand at 6 means the minute hand has gone halfway round — 30 minutes.
  2. Short hand between 3 and 4 confirms it's 3-something.
  3. Answer: 3:30, "half past three."
04 · Q&A

Test your understanding

Which is bigger: 1/2 of a pizza or 1/4 of the same pizza?

1/2 is bigger. The more pieces you cut a whole into, the smaller each piece gets — cutting into only 2 pieces gives bigger slices than cutting into 4.

A toy costs $8 and you have $5. How much more do you need?

$3, since 8 − 5 = 3. This is subtraction finding "the difference" between what you have and what you need.

How many minutes are in half an hour?

30 minutes, because a full hour is 60 minutes and half of 60 is 30.

Why can't you just say a table is "5" long without a unit?

Because 5 what? Five centimetres is tiny, five feet is a real table, and five metres is enormous. The unit gives the number its meaning — measurement is always a number and a unit together.

Concept mind map

How the ideas connect

Every key idea in this chapter, branching from the core concept — use it to see the whole picture at a glance.

Equal partsNumeratorDenominatorCoins and moneyReading a clockUsing a rulerFractions and Measures
Infographic

The key facts, visualised

1/2
One of two equal parts
1/4
One of four equal parts, a quarter
60 min
One hour on the clock
100 cm
One metre on a ruler
Solved examples

Worked problems, step by step

Follow each solution line by line, then try to reproduce it on paper before moving on.

Example 1What fraction of a pizza is one slice if it is cut into 4 equal slices?

  1. The whole is 4 equal parts
  2. One slice is 1 part out of 4
  3. Write this as 1/4

Example 2The clock shows the hour hand past 3 and the minute hand on 6. What time is it?

  1. Hour hand past 3 means 3 something
  2. Minute hand on 6 means 30 minutes
  3. So it is half past 3
Practice problem set

Now you try

Work each one out first, then tap to reveal the worked answer.

1Shade 2 of 3 equal parts. What fraction is shaded?
Two of three equal parts is 2/3.
2Which is bigger, 1/2 or 1/4?
Halves are larger pieces than quarters, so 1/2 is bigger.
3How many 20 cent coins make 1 dollar?
Five 20 cent coins make 100 cents, which is 1 dollar.
4A ribbon is 15 cm plus 8 cm long. What is its length?
15 + 8 = 23 cm long.
5What time is a quarter past 9?
A quarter past means 15 minutes, so 9:15.
6Cut a cake into 8 equal parts and take 3. What fraction is taken?
Three of eight equal parts is 3/8.