---
title: "Money and Measures"
book: "Primary & Middle School Mathematics"
subject: math
language: en
chapter: 12
exercises: 10
source: https://one-course.com/books/math/1/en/chapter/12-money-and-measures
---

# Chapter 12 — Money and Measures

Measuring rulers, kitchen scales, jugs, coins, clocks and calendars: this chapter is about the numbers of everyday life — how long, how heavy, how much it holds, how much it costs, and what time it is.

## 12.1 Lengths, masses, capacities

**Definition 12.1 (Everyday units).**

- *Length* : centimeter (cm) for small things, meter (m) for big ones, with $1$ m $= 100$ cm;
- *mass* : gram (g) for light things, kilogram (kg) for heavy ones, with $1$ kg $= 1000$ g;
- *capacity* (how much a container holds): liter (L).

Smaller units and their exact rules come in [Chapter 19](https://one-course.com/books/math/1/en/chapter/19-measuring#ch-g3-measure).

**Example 12.2 (Which unit?).**

A crayon: about $9$ cm. A door: about $2$ m. An apple: about $150$ g. A big bag of flour: $1$ kg. A milk bottle: $1$ L. Guess the unit before measuring — it stops silly answers like “the door is $2$ cm”.

## 12.2 Money

**Method 12.3 (Making an amount).**

With coins and bills of $1$, $2$, $5$, $10$, $20$:

1. start with the biggest that fits, then fill the rest;
2. to make $27$ : a $20$ , a $5$ , and a $2$ ;
3. there are often several ways — $27$ is also $10 + 10 + 5 +  2$ .

![Making 27 with a bill and two coins — and there are other ways, like 10 + 10 + 5 + 2.](https://one-course.com/images/onecourse/chapters/math-1/g2-measure/fig-ef1edca262bf.svg)

*Making $27$ with a bill and two coins — and there are other ways, like $10 + 10 + 5 + 2$.*

**Example 12.4 (Change).**

A book costs $14$; you pay with a $20$. The change is $20 - 14 =
6$, found by counting up: $14 \to 20$ is $6$ ([Method 9.4](https://one-course.com/books/math/1/en/chapter/9-subtraction#met-g2-subtraction-countup)).

## 12.3 Time

**Method 12.5 (Half and quarter hours).**

The long hand tells the minutes past the hour:

1. straight up ( $12$ ): on the hour — $3{:}00$ ;
2. quarter turn to the right ( $3$ ): quarter past — $3{:}15$ ;
3. straight down ( $6$ ): half past — $3{:}30$ ;
4. three-quarter turn ( $9$ ): quarter to the next hour — $3{:}45$ , “quarter to four”.

![Quarter past, half past, quarter to: the long red hand at the 3, the 6, the 9.](https://one-course.com/images/onecourse/chapters/math-1/g2-measure/fig-53004c7b1b7d.svg)

*Quarter past, half past, quarter to: the long red hand at the $3$, the $6$, the $9$.*

**Example 12.6 (The calendar).**

A year has $12$ months, in order: January, February, March, April, May, June, July, August, September, October, November, December. Most months have $30$ or $31$ days; February has $28$ (or $29$). A date names the day and the month: “the $5$th of March”.

## 12.4 Exercises

**Exercise 12.1 ★.**

Choose the unit (cm, m, g, kg or L): a pencil; the classroom length; a feather; a schoolbag; a water bottle.

**Solution of Exercise 12.1.**

Pencil: cm. Classroom length: m. Feather: g. Schoolbag: kg. Water bottle: L.

**Exercise 12.2 ★.**

Convert: $2$ m into cm; $300$ cm into m; $1$ kg into g.

**Solution of Exercise 12.2.**

$2$ m $= 200$ cm; $300$ cm $= 3$ m; $1$ kg $= 1000$ g.

**Exercise 12.3 ★.**

Make these amounts with coins and bills: $16$; $23$; $35$. Give one way for each.

**Solution of Exercise 12.3.**

For example: $16 = 10 + 5 + 1$; $23 = 20 + 2 + 1$; $35 = 20 + 10 + 5$. (Other ways are possible.)

**Exercise 12.4 ★.**

Compute the change: pay $10$ for a $6$ toy; pay $20$ for a $17$ book; pay $50$ for a $32$ game.

**Solution of Exercise 12.4.**

$10 - 6 = 4$; $20 - 17 = 3$; $50 - 32 = 18$.

**Exercise 12.5 ★.**

Read the time: long hand on $6$, short hand between $4$ and $5$; long hand on $3$, short hand just after $8$.

**Solution of Exercise 12.5.**

Long hand on $6$, short between $4$ and $5$: half past four ($4{:}30$). Long hand on $3$, short just after $8$: quarter past eight ($8{:}15$).

**Exercise 12.6 ★.**

Draw a clock showing half past two. Where does each hand point?

**Solution of Exercise 12.6.**

Half past two: the long hand points down to the $6$, the short hand sits between the $2$ and the $3$.

**Exercise 12.7 ★.**

Name the month: after May; before January; the month of your birthday.

**Solution of Exercise 12.7.**

After May: June. Before January: December. (Birthday month varies.)

**Exercise 12.8 ★.**

Lea buys a drink for $3$ and a cake for $4$. She pays with a $10$ bill. How much change?

**Solution of Exercise 12.8.**

Spent: $3 + 4 = 7$. Change: $10 - 7 = 3$.

**Exercise 12.9 ★.**

Which is heavier: a $1$ kg bag of sugar or $800$ g of apples? By how many grams?

**Solution of Exercise 12.9.**

$1$ kg $= 1000$ g, which is more than $800$ g: the sugar is heavier, by $1000 - 800 = 200$ g.

**Exercise 12.10 ★★.**

Make $40$ with exactly four coins or bills (chosen from $1$, $2$, $5$, $10$, $20$). Find two different ways.

**Solution of Exercise 12.10.**

For example $20 + 10 + 5 + 5 = 40$ and $10 + 10 + 10 + 10 = 40$ (two ways with exactly four coins or bills).