5. Fractions, Money, Time & Measuring
PrimaryReal life runs on fractions, money, time, and measurement. This chapter teaches equal parts, counting coins, reading a clock, and measuring the world around you.
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.
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.
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?
Worked example: fractions, coins and clock reading
Add 1/4 + 1/4 (a quarter pizza slice plus another quarter slice).
- Same denominator (4), so keep it and add the tops: 1 + 1 = 2.
- Result: 2/4, which simplifies to 1/2 — two quarters make a half.
You have 3 coins worth 25 cents each and 2 coins worth 10 cents each. What's the total?
- 3 × 25 = 75 cents.
- 2 × 10 = 20 cents.
- Total: 75 + 20 = 95 cents.
The short hand is near 3, the long hand points at 6. What time is it?
- Long hand at 6 means the minute hand has gone halfway round — 30 minutes.
- Short hand between 3 and 4 confirms it's 3-something.
- Answer: 3:30, "half past three."
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.
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.
The key facts, visualised
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?
- The whole is 4 equal parts
- One slice is 1 part out of 4
- Write this as 1/4
Example 2The clock shows the hour hand past 3 and the minute hand on 6. What time is it?
- Hour hand past 3 means 3 something
- Minute hand on 6 means 30 minutes
- So it is half past 3
Now you try
Work each one out first, then tap to reveal the worked answer.