Question
Write the number two million two thousand and two in figures.
▶️Answer/Explanation
$2002002$
- Two million → This is 2,000,000
- Two thousand → This is 2,000
- Two → This is 2
write them as a single number
$2,002,002$
Question
Write the number $31072 000$ in words.
▶️Answer/Explanation
Thirty-one million[s] [and]
seventy-two thousand[s]
- Millions group: 31
- Thousands group: 072 (or just 72)
- Ones group: 000
Put groups together
$\text{Thirty-one million seventy-two thousand}$
Question
34 55 76 83 111 121
From this list of numbers, write down all the multiples of 11.
▶️Answer/Explanation
55 121
Multiples of 11 are numbers that can be divided by 11 leaves 0 as remainder.
- $34 ÷ 11 ≈ 3.09 →$ Not a multiple
- $55 ÷ 11 = 5 →$ Multiple of 11
- $76 ÷ 11 ≈ 6.91 →$ Not a multiple
- $83 ÷ 11 ≈ 7.55 →$ Not a multiple
- $111 ÷ 11 = 10.09 →$ Not a multiple
- $121 ÷ 11 = 11 →$ Multiple of 11
Question
Zaid has a non-calculator method for working out if a number is a multiple of 11. He shows his method for the number 919281.
Show that the number 918271937 is a multiple of 11 by using Zaid’s method.
▶️Answer/Explanation
$9 − 1+ 8 -2 +7 -1 +9 − 3+ 7$
$33=3 \times 11$
Question
The highest common factor (HCF) of two numbers is 6.
The lowest common multiple (LCM) of the two numbers is 90.
Both numbers are greater than 6.
Work out the two numbers.
▶️Answer/Explanation
18 30
$
\text{HCF} \times \text{LCM} = \text{Number 1} \times \text{Number 2}
$
$
6 \times 90 = \text{Number 1} \times \text{Number 2}
$
$
540 = \text{Number 1} \times \text{Number 2}
$
$(6\times 90)=540$ → Not valid (one number is 6, but both should be greater than 6)
$(10\times 54)=540$
$(18\times 30)=540$
As given HCF $= 6$
HCF$(10, 54) = 2$
HCF$(18, 30) = 6 $
Question
Find the greatest odd number that is a factor of 140 and a factor of 210.
▶️Answer/Explanation
Ans: 35
Prime factorization of 140:
$
140 = 2^2 \times 5 \times 7
$
Prime factorization of 210
$
210 = 2 \times 3 \times 5 \times 7
$
The odd common factors powers of 2.
Common odd factors: 5 and 7.
The greatest odd factor is:
$35$
Question
Write the number thirty thousand and fifty in figures.
▶️Answer/Explanation
30 050
Detailed Solution:
The number is thirty thousand and fifty.
Thirty thousand $= 30,000.$
Fifty $= 50.$
add these
$30,000 + 50 = 30,050$
Question
(a) Write 326.413 correct to 2 significant figures.
(b) Find the square root of one million.
(c) Calculate
\(\frac{64.3+7.465}{5.2-3.65}.\)
▶️Answer/Explanation
(a) To round 326.413 to 2 significant figures, we first need to identify the two most significant digits. In this case, they are 3 and 2. The third significant digit is 6, which is greater than or equal to 5. Therefore, we need to round up the second significant digit (2) to 3. So, rounding 326.413 to 2 significant figures gives us:
326.413 ≈ 330
(b) The square root of a number is a value that, when multiplied by itself, gives the original number. In other words, if we take the square root of a number “x”, the result is another number “y” that satisfies the equation \(y^2 = x.\)
\(\therefore\) The square root of one million is 1000.
This is because \(1000^2 = 1,000,000\)
(c)we first need to add the numbers inside the parentheses in the numerator:
64.3+7.465 = 71.765
we need to subtract the numbers in the denominator:
5.2-3.65=1.55
Finally, we can divide the numerator by the denominator to get the final answer:
\(\frac{71.765}{1.55}= 46.29\)
Therefore,\(\frac{64.3+7.465}{5.2-3.65}.\)=46.29
Question
(a) Write down all the factors of 15.
(b) Factorise completely.
15p2 + 24pt
▶️Answer/Explanation
(a)\(1\times 15\)
\(3\times 5\)
The factors of 15 are 1, 3, 5, and 15.
(b)To factorize \(15p^{2}+24pt\), we first need to takr common the greatest common factor, which is 3p:
\(\therefore\) \(15p^{2}+24pt=3p(5p+8t)\).
Now, this cant be factorized fuirther ,so final answer will be \(3p(5p+8t)\).
Question
(a) Write down a 2-digit odd number that is a factor of 182.
(b) Find all the prime factors of 182.
▶️Answer/Explanation
(a)We can find the factors of 182 by checking which integers dividing 182 .
\(182=1\times 182=2\times 91=7\times 26=13\times 14\)
Out of these, the odd factors are 13 and 7. Therefore, one possible 2-digit odd factor of 182 is 13.
(b)We can find the prime factors of 182 by dividing it successively by prime numbers until the result is a prime number.
\(182=2\times 91\)
\(182=2\times 7\times 13\)
Therefore, the prime factors of 182 are 2, 7, and 13.