To ask about maths homework

[MissMessy12]

Could someone please help me help my son with his maths? I’m useless and have failed miserably on google. I would be very grateful if any maths teachers could help us.

1. Express 80 as a product of its prime factors. Write the prime factors in ascending order.

1. Same as above with 56

1. Same as above with 250

1. Same as as above with 60, but give answer in index form.

1. Find the lowest common multiple of 8 and 6

1. Pencils are sold in boxes of 10. Erasers are sold in boxes of 14. A teacher wants to buy the same number of pencils and erasers, work out the smallest number of boxes of each item she should buy.

1. Find the lowest common multiple of 14 and 22

1. Write 3.25 x 10(little 4) as an ordinary number

Write 6.04 x 10 (little minus 3) as an ordinary number

Write 2 400 000 in standard form

Write 0.00147 in standard form

Thank you so much

A product is when two or more numbers are multiplied together.
Factors are the numbers you multiply together to make the product.
So in 2 x 5 = 10: 2 and 5 are the factors and 10 is the product.
In this case though they only want prime factors. A prime number is a number that is only divisible by 1 and itself i.e. 1, 3, 5, 7, 11, 13.....

I think the easiest way to do this is to write a list of the prime numbers then work out what you'd need to multiply them by to get 80 and if it's a prime number that's an answer, and if it's not you "bin it".

Lowest common multiple - I would do your 6 times table and 8 times table and the lowest common multiple is the lowest value which is in both lists.
So 6, 12, 18, 24, 30, 36, 42
and 8, 16, 24, 32, 40, 48
Lowest common multiple is 24

You can work out no. 7 yourself ;)

well I am not an expert, but I can do some!

Find the factors of 80
1, 80, 2, 40, 4, 20, 5, 16, 8, 10,
which of these are prime numbers?
2, 5,

repeat for the other numbers.

I do not know what they mean by index form, which may mean I am completely wrong!

No. 6 is also a lowest common multiple question but using words to make sure you understand the concept.

Prime factors mean numbers that are prime numbers (up to 100 they are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97) that can be multiplied together to make the target number. For 80, we know that 8x10=80. 8=2x2x2 and 10=2x5, so the 80=2x2x2x2x5.

no. 6, you are looking for a number which is exactly a multiple of 10 and 14

so multioples of 10 are:
10, 20, 30, 40 , 50, 60, 70 etc
multiples of 14 are
14, 28, 42, 56, 70

so the lowest number which is an exact multiple of 10 and 14 is 70.
70 is 7 boxes of pencils and 5 boxes of erasers

No. 8 onwards
10(4) is 10 x 10 x 10 x 10
10(-3) is 10 divided 10 divided by 10
It's basically about adding zeros on the end of the number and moving the decimal place along when you divide or multiply by 10.

Then the last 2 are looking for an answer in the format of x10(number)
so it would 2.4 x 10(little number) and 1.47 x 10(minus little number)

Oh yes, lougle is right, you need to break down all the factors of 80 into prime numbers if you can.

curious to know what age he is?

For product of prime factors in index form:
First find prime factors of 60
60= 2 x 30 2 is a prime
30 = 2x15 2 is a prime
15 = 3 x5 3 and 5are prime
So 60 = 2 x2 x3 x5 (product of prime factors)
This can be written as 2² x 3 x5

2 squared makes it index form

Thank you all so much, I think we now understand prime numbers and ‘products’,
Just working now on common multiples

The best way to find the prime factors is to do a number tree.

I expect the layout will mess up, but here goes
.........….80
….8......…........10
2........4...…....2...5
2.....2...2...…..2...5

So 80 = 2x2x2x2x5 (or 2^4 x 5)

For prime factors I find it easier to start with the smallest prime and keep dividing, moving up to bigger primes as you need to

So 2 is the smallest prime
80 = 2x40 = 2x2x20 = 2x2x2x10 = 2x2x2x2x5 5 is a prime so stop

Standard form is where you take all the "place value" out of the number

So 70 = 7 x10
700 = 7 x 102 (using to represent "to the power of")
7000 = 7 x 10^3

And more complicatedly

735 = 7.35 x 10^2

This looks like Y7 ish.
The scientific notation is KS3 I’m fairly sure but the common factors are KS2.
Maybe Y8 unless they dived into scientific notation pretty early in the term.

OP, is this all the homework? If it’s not just one or two questions out of money that he doesn’t get, I think the better approach here is talking to his teacher. You can easily get the answers here, but he needs to understand the working. There are lots of great videos on YouTube.

What year is he? CGP practise books are good for Y7-Y9.

Highest Common Factor, you find the prime factors that appear in both
Lowest Common Multiple, you use all the prime factors from one, and then add in the ones you haven't yet got from the second.

24 = 2x2x2x3
30 = 2x3x5

HCF (the intersect between the two, the highest number that divides into both of them) = 2x3=6

LCM (the union of the two, the smallest number that the other two both go into) = 2x2x2x3 x 5 = 120

Common multiples are a follow on to prime factors

So if number 1 = 2 x 2 x 3 x 7 x 11

and number 2 = 2 x 2 x 2 x 7 x 13

Then you look for the factors in common which are 2, 2, 7. So the LCM is 2 x 2 x 7 = 28

There are some good videos on Corbett Maths (website) with modelled questions and answers. The topics he needs to watch are:

• prime factor decomposition
• Highest common factors/lowest common multiples (aka HCF and LCM)
• writing numbers in standard form

If they're too advanced he'll need to recap:

• factors
• multiples
• prime numbers
• powers of 10

Don't try to teach it if you don't understand it

BBC bitesize

Questions 1 - 4

factors and prime numbers
Q4 is like q 1 - 3, then look at the final questions for index form.

For Q 5, 6, 7 you need lowest common multiple
I like the Venn diagram method which is further down the page.

The final questions are about standard form

He’s 13, just gone into yr9. He does have a TA to help him, but he says the TA doesn’t know how to do it either.

Thanks Coco, I’ll look into getting CGP practise books, presumably I can get these on Amazon?

There's a method for finding LCM (and HCF) using Venn diagrams. Search for it on YouTube. My DD taught it to me and it's much easier than writing down all the multiples until one matches.

Yes, they’re in Amazon. But best for testing your knowledge once you have learned what to do - not to learn from scratch.

I’m guessing the TA is for support across the whole learning environment, not specifically maths?

White Rose is another good site to look at, the videos are well done. A lot of KS3 builds on Y6 - so don’t be afraid to take it back a level and build up his learning with simpler examples. For example, the prime factor trees - start with splitting 15 into 3 x 5, before having extra steps from starting with 60.

I find that my daughter sometimes knows how to do it, but forgets what things are called. So instead of saying - “do prime factors” when she might say, “uh?” - if she sees a tree filled out she’ll be all, “oh yeah - those”. So it might help him to make his own glossary? A simple example of each of the terms?

@MissMessy12

He’s 13, just gone into yr9. He does have a TA to help him, but he says the TA doesn’t know how to do it either.

Thanks Coco, I’ll look into getting CGP practise books, presumably I can get these on Amazon?

That doesn't sound like very effective support, tbh. There was research that shows that some TA support can actually lead to worse outcomes for students. If he's having support from someone who doesn't know what they're doing, he's actually missing out on support from his teacher, who will.