Multiples
EXAMPLES
1
How many numbers are multiples of 3 from 1 to 300?
Solution:
Let’s first consider multiples of 3 from 1 to 30.
3, 6, 9, 12, 15, 18, 21, 24, 27, 30
There are 10 multiples of 3 from 1 to 30.
By the same logic,
10 × 10 = 100
100 numbers are multiples of 3 from 1 to 300.
2
A book has 200 pages.
How many digits are used for the page numbers in the book?
Solution:
Page 1 to page 9 → 9 digits
From page 10 to page 99, there are 90 numbers.
Since each number has 2 digits,
90 × 2 = 180
there are 180 digits from page 10 to page 99.
From page 100 to page 200, there are 101 numbers.
Since each number has 3 digits,
101 × 3 = 303
there are 303 digits from page 100 to page 200.
9 + 180 + 303 = 492
492 digits are used for the page numbers in the book.
Adapted:
Maths Olympiad – Unleash The Maths Olympian In You! (Junior 2)
© Singapore Asia Publishers Pte Ltd & Terry Chew. All rights reserved.
Reproducible for home/classroom use only.
STRICTLY NOT FOR SALE.
Look for other useful resources: www.sapgrp.com
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PRACTICE
1
How many numbers from 1 to 800 are multiples of 4?
2
A book has 175 pages. How many digits are used for the page numbers in the book?
3
432 digits are used for the page numbers of a book. How many pages does the book have?
Adapted:
Maths Olympiad – Unleash The Maths Olympian In You! (Junior 2)
© Singapore Asia Publishers Pte Ltd & Terry Chew. All rights reserved.
Reproducible for home/classroom use only.
STRICTLY NOT FOR SALE.
Look for other useful resources: www.sapgrp.com
2
Solutions to:
Multiples
1.
From 1 to 40, there are 10 multiples of 4.
800 ÷ 40 = 20
20 × 10 = 200
There are 200 multiples of 4 from 1 to 800.
2.
page 1 to page 9 → 9
page 10 to page 99 → 90 × 2 = 180
page 100 to page 175 → 76 × 3 = 228
9 + 180 + 228 = 417
417 digits are used for the page numbers in the book.
3.
page 1 to page 9 → 9
page 10 to page 99 → 180
432 – 9 – 180 = 243
243 digits are used for 3-digit numbers.
243 ÷ 3 = 81
81 + 99 = 180
The book has 180 pages.
Adapted:
Maths Olympiad – Unleash The Maths Olympian In You! (Junior 2)
© Singapore Asia Publishers Pte Ltd & Terry Chew. All rights reserved.
Reproducible for home/classroom use only.
STRICTLY NOT FOR SALE.
Look for other useful resources: www.sapgrp.com
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