Numbers and operations · Ages 12–13

Working with numbers worksheet

Covers: Divisibility by 4, 6, 8 and 9, Powers, Prime factorisation, H.C.F. and L.C.M., Brackets inside brackets, Fractions and decimals mixed

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Numbers and operations · Ages 12–13

Numsprite
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Name:Date:Score:／48

Write each answer in the space. For word problems, show your working and write a sentence answer.

1.The four-digit number 470 is divisible by 9. What is the smallest digit that can go in ?
Answer:
2.9 × 10² =
Answer:
3.5 × 4 × 5 × 4 × 4 × 5 × 5 × 4 × 4 = 4^□ × 5^□
Fill in each blank
Answer:
4.Write 240 as a product of prime factors: 240 = 2^□ × 3^□ × 5^□
Fill in each blank
Answer:
5.Break 12 × 30 into prime factors: 12 × 30 = 2^□ × 3^□ × 5^□
Fill in each blank
Answer:
6.24 = 2³ × 3¹ and 216 = 2³ × 3³. Their H.C.F. = 2^□ × 3^□
Fill in each blank
Answer:
7.The L.C.M. of 8, 20 and 9 is .
Answer:
8.Work out 146 − [17 + (7 − 1) × 3]. Put the steps in order.
- A. 7 − 1 = 6
- B. 17 + 18 = 35
- C. 146 − 35 = 111
- D. 6 × 3 = 18
Write the letters in the right order
Answer:
9.35 + 34 × 6 = (as a fraction in its simplest form)
Answer in simplest form
Answer:

13.8399 is a five-digit number divisible by 6. What is the largest digit that can go in ?
Working:
Answer:
14.A city uses about 100,000 cubic metres of water a year. Write 100,000 as a power of 10: 10^□.
Working:
Answer:
15.A cube-shaped box holds 1728 cm³. How long is each edge?
Working:
Answer:
16.Three alarms ring together, then every 4, 10 and 18 minutes. At least how many minutes later do all three ring together again?
Working:
Answer:
17.Ka-yan has $300, buys 3 notebooks at $16 each and a pencil case for $10, then shares the money left equally among 2 younger brothers and sisters. How many dollars does each get?
Working:
Answer:
18.Ming reads a 80-page book: 0.3 of it on day one and 18 of it on day two. How many pages in the two days?
Working:
Answer:

Show the answers and working

Working with numbers worksheet: Answers and working

1. 7
The known digits add up to 4 + 7 + 0 = 11. With □ added the sum must be a multiple of 9, so the least is 7.
2. 900
10² is 1 followed by 2 zeros, so 9 × 10² = 900.
3. 5, 4
4 appears 5 times and 5 4 times: 4⁵ × 5⁴.
4. 4, 1, 1
240 divides by 2 4 times, then by 3 1 times, then by 5 1 times. So 240 = 2⁴ × 3¹ × 5¹.
5. 3, 2, 1
No need to multiply out 360 first: break 12 and 30 into primes separately, then add up how many of each prime there are.
6. 3, 1
For the H.C.F., take each prime's smaller index: 2 to the 3, 3 to the 1.
7. 360
Break all three into primes and multiply each prime to its largest index: 360.
8. A → D → B → C
Inside out: the round brackets, then inside the square ones (times before plus), and the subtraction outside last.
9. 5110
Multiply first: 34 × 6 = 92; then add 35: 5110.

10. False
Only the last two digits matter: 59 ÷ 4 leaves 3. The whole number is divisible by 4 only when they make a multiple of 4 (remainder 0).
11. B. 30
Brackets first, 16 − 1; then times and divide from left to right, 6 × (16 − 1) ÷ 5; add 12 last: 30.
12. False
Dividing by a fraction is multiplying by its reciprocal: 16 ÷ 38 = 16 × 83.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. 4
For 6, □ must be even and 29 + □ a multiple of 3. Trying even digits down from 8, the largest is 4.
14. 5
100,000 is 1 followed by 5 zeros, 5 tens multiplied: 10⁵.
15. 12 cm
In 1728's prime factors every index is a multiple of 3; divide each by 3 for the edge: 12 cm.
16. 180 minutes
It must be a multiple of 4, 10 and 18: the least is their L.C.M., 180.
17. 121 dollars
As one calculation: [300 − (3 × 16 + 10)] ÷ 2 = 121.
18. 34 pages
80 × (0.3 + 18) = 34 pages. Both are parts of the whole book, so add them first.

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