ITV News' Julie Etchingham accompanied the Prime Minister on a visit to Derby on Friday.
She spoke to him about varied topics including cuts to welfare and how best to help working families in a time of austerity.
@StressedEric72 via Twitter asked: In 50yrs (or so) when Parliament pays tribute to you, what one policy would you like them to remember and one personal quality?
David Cameron's response: Margaret Thatcher was a unique Prime Minister and so was that tribute session in Parliament. She led this country for a longer continuous period than any other Prime Minister for more than 150 years.
Any Prime Minister would aspire to a record of service and achievement like hers. I’m less than three years into the job and I’m focussed on getting on with that job in the here and now.
What I hope will be the things we really deliver, that people look back on, are reforming our economy at a time of crisis, dealing with our deficit, revitalising our schools so that all our children have a decent education...
Sorting out welfare so it pays to work and more people have structure and security of a good job, making Britain a place where if you work hard and do the right thing you get rewarded for that... So it’s impossible to choose one policy.
They’re all linked together in the vision of helping hardworking people who want to get on in life, so that together we can drive Britain forward. One personal quality? I hope it will be responsibility. That I did what was right for this country long-term, no matter what.
Yohennes Muyoyu asked via Facebook: Why are rebels in Syria called "the opposition" but not those in Mali?
David Cameron's response: The Syrian National Coalition has set out a vision of a democratic and united Syria. It offers a credible alternative to a dictator who is killing his people in their tens of thousands. That is why we have recognised it as the legitimate representative of the Syrian people.
In Mali the situation is different. Violent extremists were wreaking havoc and spreading terror among the civilian population.
The international community intervened to help the government bring stability and security to northern Mali - because in the end, this terrorism will only be defeated by full democratic rule in Mali, a proper political process and successful elections.
Adam Wilson asks via email: How will the Government be dealing with North Korea in light of recent events?
David Cameron's response: Kim Jong-un needs to make a choice about whether he wants his country to become more isolated or work positively with the rest of the world.
We have made our position very clear. We have condemned North Korea's nuclear tests and made sure the UN Security Council was strong and united in response. At the same time we hope North Korea returns to dialogue with its neighbours - and we’ll respond constructively if they do.
Casee Leigh asked via Facebook: Do you think you can live on £53 a week?
David Cameron's response: Of course no one thinks living on benefits is easy. And it appears that the person you are referring to may have actually been receiving more than that.
But what's important is that we are fixing the tax and welfare system so that it works for hardworking people. We're cutting income tax for 24 million people, taking 2.2 million out of income tax altogether and making work pay by introducing Universal Credit.
But let’s also be clear: the benefits system provides a significant range of support for people when they need it - from housing help, to financial support when people fall ill and can't work, help for people who are caring for others, help for people in work and on a low income - I could go on.
Joan Telfer asked via Facebook: Why does a country as small as the UK need Trident? Scrap Trident and our debts are cleared. Spend the money on more useful things like the NHS, creating jobs, benefits, police and education.
David Cameron's response: We’re living in an uncertain world today. Yes, the Cold War is over - but the nuclear threat has not gone away. In fact in the coming years there is a real risk of new threats emerging as countries look to develop new or better nuclear weapons.
My judgement is that it would be foolish to leave Britain defenceless against this continuing threat.
And let’s be clear about the cost. Of course, the deterrent is not cheap. But our current nuclear weapons capability costs on average around five-six per cent of the current defence budget. That is less than 1.5 per cent of our annual benefits bill.
The successor submarines are, on average, expected to cost the same once they have entered service. It is a price which I, and all my predecessors since Clement Attlee, have felt is worth paying to keep this country safe.
So the short answer is: the security of our nation is worth the price.
Lara Turner asked via email: How do you legitimise the choice to prioritise unfair cuts to the welfare bill, over boosting the economy by chasing tax avoidance, particularly by large corporations?
David Cameron's response: I don’t accept that cuts to the welfare bill are unfair. We live in a country where one pound in every three the government spends goes on pensions and benefits.
This is simply not affordable. So we are reforming welfare in a way that is sensible and fair: making sure that work pays and that help goes to those who genuinely need it.
What would be unfair is leaving another generation locked in the benefits system, leaving the taxpayer to pay for those who choose not to work, and leaving our children’s generation to pick up the rest of the bill.
And it’s not a case of prioritising welfare reform over tax avoidance – we’re doing both. In fact we’ve already committed hundreds of millions into clamping down on this – and I’ve made dealing with tax avoidance a top priority for the G8 which Britain is hosting this year.
We are getting the leaders of the world’s richest countries around a table to deal with this.
Mike Flint asked via email: Do you think it is adequate that James Crosby gives up three letters in front of his name as penance for his part in the downfall of HBOS?
David Cameron's response: This is his responsibility - and giving up his knighthood and some of his pension was the right decision.
@VicksAnne asked via Twitter: Do you think there is such a thing as society anymore?
David Cameron's response: Of course there is. Society is alive in communities up and down the country, in the huge outpouring of compassion for things like Comic Relief, and the small acts of kindness that happen every day.
Building a stronger society is why I got into politics in the first place. When I stood on the steps of Number 10 for the first time I said I wanted to build a more responsible society: where those who can, should – and those who can’t, we always help.