# Math Help—How to Work out the Product and Sum of Two Numbers

If you are asked to work out the product of two numbers then you need to multiply the two numbers together. If you are asked to find the sum of two numbers then you need to add the numbers together.

**Example 1**

Work out the product and sum of 6 and 8.

The product of 6 and 8 is 6 × 8 = 48

The sum of 6 and 8 is 6 + 8 = 14

**Example 2**

Work out the product and sum of 9 and 3.

The product of 9 and 3 is 9 × 3 = 27

The sum of 9 and 3 is 9 + 3 = 12

**Example 3**

Work out the product and sum of -7 and 9

The product of -7 and 9 is -7 × 9 = -63

The sum of -7 and 9 is -7 + 9 = 2

**Example 4**

Write down two numbers that have a product of 42.

All you need to do is look for two numbers that multiply to give 42.

There are several possible answers:

1 and 42 or 2 and 21 or 3 and 14 or 6 and 7.

You could even have:

-1 and -42 or -2 and -21 or -3 and -14 or -6 and -7.

**Example 5**

Work out the product of 2, 4 and 9.

The product means that you need to multiply the three numbers together.

2 × 4 × 9 = 72.

**Example 6**

Work out the sum of 2, 4 and 9.

This time you need to add the numbers together as you are finding the sum.

2 + 4 + 9 = 15.

So that’s all you need to know about product and sum:

**Product means multiply.**

**Sum means add.**

## Questions & Answers

- Helpful 58
Can you find two numbers which have a product of 12 and a sum of 7?

4 and 3 are a the answers.

4 multiplied by 3 is 12. 4 add 3 is 7.

Helpful 98what is the sum and product of -5 and -12?

Sum means you need to add the numbers (-5 + -12 = -5 - 12 = -17).

Product means you need to multiply the numbers (-5 multiplied by -12 = 60).

Helpful 33- Helpful 1
The product of two numbers is 72 and the sum is 18, what are that two numbers?

The two numbers are 6 and 12, because 6 times 12 is 72, and 6 added to 12 is 18.

Helpful 2

What is the product of 3 and 154?

To find the product multiply the two numbers together to give 462.

Helpful 2Can you find the product and sum of -9 and -7?

Multiply the numbers for the product, -9 times -7 is 63.

Add the numbers for the sum, -9 + - 7 is -16.

Helpful 1Can you find the product of 8 and 4?

The product can be found by multiplying the two numbers together.

8 mutliplied by 4 gives 32.

Helpful 1What are the two numbers which have a sum and product of 1 and 9?

The sum can be found by adding 1 and 9 to give 10.

The product of 1 and 9 can be found by multiplying 1 and 9 to give 9.

Helpful 5What number do you multiply 4 by and add 5 to give a square number?

The number you are looking for is 5. Since the product of 4 and 5 is 20, and 20 add 5 is 25 which is a square number.

Helpful 1What number has a product of 9 and a sum of 10?

The two numbers are 1 and 9, because 1 times 9 is 9, and 1 added to 9 is 10.

What is the sum of 2 and 7?

The two numbers needed to be added together if you are working out the sum.

So 2 + 7 = 9.

Helpful 6- Helpful 1
Can you find the product and sum of 20 and 6?

The product of 20 and 6 is 20 times 6 which is 120.

The sum of 20 and 6 is 20 plus 6 which is 26.

Helpful 1Can you find two numbers which have a product of 8 and a sum of 7?

Yes, you can but the answers are not integers (whole numbers).

You will need to solve the simultaneous equations xy = 8 and x + y = 7.

Helpful 16How can I work out the product of 18 and 4?

All you need to do is 18 multiplied by 4 which is 72.

Helpful 16Can you find two numbers which have a product of 741 and sum of 70 ?

The two number you are looking for are 57 and 13.

This is beacause 57 multiplied by 13 gives 741, and 57 added to 13 gives 70.

Helpful 11What are the two numbers that the sum is 12 and the product is 36?

Remember, sum means add and product means multiply.

The two numbers that answer this question are 6 and 6.

This is because 6 add 6 is 12, and 6 multiplied by 6 is 36.

Helpful 9The product of 5 whole numbers is 3. What is the sum of these numbers?

Product means multiply, so the 5 whole numbers that multiply together to give 3 are 1,1,1,1 and 3 (that is fours 1's and one 3).

Since "sum" means "add," then 1 + 1 + 1 + 1 + 3 gives a final answer of 7.

Helpful 9The product of 4/3 and a number is 84. What is the number?

Divide 84 by 4/3 to give 63.

Helpful 8What number pair has the sum of 5 product of 4?

Sum means add, and product means multiply.

Therefore the two numbers needed are 1 and 4, because 1 added to 4 is 5 and 1 multiplied by 4 is 4.

Helpful 7What is 1/3 the sum of six and three?

First of all, work out the sum of 6 and 3 by adding these together to give 9.

Now to find a third of something you divide by 3, so 9 divided by 3 is 3.

Helpful 7What is the pair of numbers with a sum of 5 and a product of 4?

The two numbers that solve this problem are 1 and 4.

This is because 1 + 4 gives 5 (Sum means add), and 1 multiplied 4 gives 4 (prouct means multiply).

Helpful 5What is the sum of 19 and 25 multiplied by their difference?

First, work out the sum of 19 and 25 by adding the two numbers together to give 44.

Next, find the difference of 25 and 19 by subtracting the numbers to give 6.

Now multiply 44 by 6 to give 264.

Helpful 5Can you find a number which has a product of -14 and a sum of 5?

The two numbers are -2 and 7, since -2 times 7 is -14, and -2 + 7 is 5.

Helpful 5What is the product of 1 3/ 5 and 8 1 /2 ?

Change these mixed numbers to decimals as it will be easier to work out (1 3/5 = 1.6 and 8 1/2 = 8.5). So the product is 1.6 multiplied by 8.5 which is 13.6. The sum will be 1.6 + 8.5 = 10.1.

Helpful 5From a box containing 24kg of tomatoes, a vendor sold 17 1/2kg. How much was he left with?

To work out how much left you will need to work out the difference between 24kg and 17.5kg.

24 - 17.5 = 6.5 kg.

So there are 6.5kg of tomatoes left.

Helpful 5What is the answer to halve the product of 5 and 12?

First of all work out the product of 5 and 12.

Therefore, multiply the 5 by the 12 to give 60 (since product means multiply).

Now half 60 to give a final of answer of 30.

Helpful 5Can you find two numbers which have a product of 60 and a sum of 100?

The two numbers are not integers, so there is not an obvious answer.

You will need to solve the simultaneous equations xy = 60, and x + y = 100, to give x

The two answers are 99.3963 and 0.6036 rounded to 4 decimal places.

Helpful 5What’s the product of 7/12 and 14?

Convert 7/12 into a decimal by dividing 7 by 12 to give 0.583..., now multiply this by 14 to give 8.17 rounded to 2 decimal places or 49/6 if you prefer a fraction.

Helpful 5- Helpful 1
The product of 6 and 7 is how much greater than the sum of 6 and 7?

The product of 6 and 7 is 6 times 7 which is 42.

The sum of 6 and 7 is 13.

So 42 take away 13 is 29.

Helpful 2What is the Product of 5 and (2/3n +5)?

Product means multiply so the bracket needs to be expanded.

5 multiplied by 2/3n gives 10/3n, and 5 multiplied by 5 gives 25.

So putting these terms together, the final anwer will be 10/3n + 25.

Helpful 4What is the sum of 21 and the difference of 27 and 5 ?

First of all work out the difference between 27 and 5 by subtracting 27 and 5 to give 22.

Now find the sum of 21 and 22, by adding these numbers together to give 43.

Helpful 4Can you find two numbers which have a product of 20 and a sum of 12?

The two numbers that you are looking for are 10 and 2, beacuse 10 multiplied by 2 gives 20, and 10 added to 2 gives 12.

Helpful 4Can you find a pair of numbers with a sum of 9 and a product of 20?

Product means multiply and sum means add.

So, the two numbers which solve this problem are 4 and 5 (since 4 added to 5 gives 9 and 4 multiplied by 5 is 20).

Helpful 4How can find the product of 3/5 and 42?

Probably best to convert 3/5 to a decimal first which is 0.6

0.6 multiplied by 42 is 25.2.

Helpful 4Can you find two numbers that have the sum of 35 and a difference of 15?

The two numbers that solve this problem are 25 and 10.

This is becuase 25 + 10 gives 35 (sum means add), and 25 - 10 gives 15 (difference means subtract).

Helpful 4What's the product of 6.2 and 8c?

Just multiply these together to give 49.6c.

Helpful 4What 2 integers have a sum of - 17 and a product of 52?

The two numbers that solve this problem are -13 and - 4.

This is because - 13 multiplied by - 4 gives 52, and -13 + -4 gives -17.

Helpful 4Can you find two numbers that have a product of -18 and a sum of -7?

The two numbers are -9 and 2.

This is because -9 multiplied by 2 is -18, and -9 plus 2 is -7.

Helpful 4What are a pair of numbers with a sum of 5 and a product of 4?

The numbers are 1 and 4, since 1 added to 4 gives 5, and 1 multiplied by 4 is 4.

Helpful 4What is 5 added to the product of 4 and 6?

First follow BODMAS and work out the product of 4 and 6 by multiplying these numbers together to give 24.

Next add the 4 onto 24 to give 28.

Helpful 4The square of a number is 81. Find the number?

There are two answers to this question.

The first one is 9, because 9 multiplied by 9 is 81.

The second answer is -9, because -9 multiplied by -9 is also 81 (two negatives multiplied together gives a positive answer).

Helpful 4What is the product of (3+20)(4-30)?

First, work out the brackets:

3 added to 20 gives 23, and 4 minus 30 gives - 26.

Now multiply 23 by -26 to give a final answer of -598.

Helpful 4What are two numbers that have a sum of 24 and a quotient of 3?

The two numbers are 21 and 3, becuase 21 added to 3 is 24 and 21 divided by 3 is 7.

Helpful 3The sum of a number, n, and 8 is multiplied by –4, and the result is –12. How do I solve for n?

You will need to solve:

-4(n + 8) = -12

-4n - 32 = -12

-4n = 20

n = -5

So the number is -5.

Helpful 3- Helpful 1
- Helpful 2
Eight times the sum of 5 and some number is 184. What is the number?

First divide 184 by 8 to give 23.

Next subtract 5 from 23 to give 18.

So the answer is 18.

Helpful 3How can I make 63 only using the numbers 5,2,9 and 3?

First add 5 and 2 to give 7, and then multiply the answer by 9.

Helpful 3What two numbers have the product of 20 and the quotient of 5?

Product means the two numbers need to multiply to give 20, and quotient means the two numbers must divide to give 5.

Therefore, the answers are 10 and 2, becuase 10 multiplied by 2 is 20, and 10 divided by 2 is 5.

Helpful 3What is the product of 1 and 5?

Just multiply 1 by 5 to give an answer of 5.

Helpful 3Can you find two numbers which have a sum of 13 and a product of 12?

Sum means add and product means multiply.

The two numbers are 1 and 12, as 1 + 12 = 13 and 1 multiplied by 12 gives 12.

Helpful 3Can you find the two numbers which have the product of 12 and a sum of -7?

The two numbers you are looking for are -4 and -3.

This is because -4 times -3 is 12, and -4 + -3 is -7.

Helpful 3What is The product of 48 × 9?

Product means multiply, so with a calculator type in 48 times 9.

If doing mentally, first do 40 multiplied by 9 which is 360, and then do 8 multiplied by 9 which is 72. So 360 + 72 = 432.

Helpful 3What two numbers have a product of 60 and a sum of -19?

The two numbers are -4 and -15.

This is because -4 added to -15 gives -19, and -4 times -15 gives 60.

Helpful 3What is 34 added to the product of 3 and 4?

First work out the product of 3 and 4 by multiplying the numbers together to give 12.

Now 34 added to 12 gives 46.

Helpful 3Can you find the answer for 2+3×4=?

You need to use BIDMAS or BODMAS.

First work out the multiplication to give 12.

Now 2 + 12 =14.

Helpful 3How do you find the product of 2 and 3, and then subtract that from 9?

To find the product multiply 2 by 3 to give 6.

Now subtract 6 from 9 to give an answer of 3.

Helpful 3Can you solve this: the product is 12 and the sum is 7?

The two numbers you are looking for are 4 and 3.

Since 4 multiplied by 3 is 12 and 4 added to 3 is 7.

Helpful 3What is the product of 0.009 & 2.84?

To find the product of any two numbers just multiply them.

0.009 multipled by 2.84 gives 0.02556.

Helpful 3The product of two whole numbers is 648 and their sum is 51. What are the two numbers?

The two numbers are 24 and 27.

This is because 24 multiplied by 27 gives 648.

Also, 24 added to 27 gives 51.

Remember, product means multiply and sum means add.

Helpful 3- Helpful 2
- Helpful 2
What is 72,136 more than the sum of 105 and 212?

First, find the sum of 105 and 212 to give 317.

Now add 317 and 72136 together to give 72453.

Helpful 2What two numbers have a product of 14?

2 and 7 give a product of 14, as 2 multiplied by 7 is 14.

Helpful 2What is the product of the difference between 12 and 3 and the quotient of 12 and 3?

The difference between 12 and 3 is 12 subtract 3 which is 9.

The quotient of 12 and 3 is 12 divided by 3 which is 4.

Now work out the product of 4 and 9 by multiplying them together to give 36.

Helpful 1Two numbers have a sum of 15 and a product of 26 what are they?

The two numbers are 13 and 2.

This is because 13 + 2 = 15, and 13 multiplied by 2 gives 26.

Helpful 2How can I work out the sum of 2/12 and 6/12?

To find the sum just add the two fractions together to get 8/12 which simplifies to 2/3.

Helpful 2What are two numbers that have a product of 3/8?

You need to figure out two fractions which multiply to give 3/8.

The two fractions are 3/4 and 1/2.

Helpful 2Can you find two numbers which have a product of 8 and a sum of 6?

4 and 2 are the answers, because 4 multiplied by 2 is 8 and 4 added to 2 is 6.

Helpful 2Find the product of five and ten and divide it by five. What's the answer?

First work out the product of 5 and 10 to give 50 (multiply 5 by 10).

Now divide the answer by 5 to give 10.

Helpful 2The product of two numbers is 45. Their sum is 18. What are the numbers?

The two numbers are 15 and 3, since 15 times 3 is 45, and 15 added to 3 is 18.

Helpful 1- Helpful 2
How does knowing that 2 and 9 =18 help find the product of 4 and 9 without multiplying ?

4 is double 2, so you just need to double the 18 to give 36.

Helpful 2What is the answer if you increase the sum of 5/8 and 5/8 by 14?

First work out the sum of 5/8 and 5/8 by adding these together to give 10/8.

10/8 can be simplified to 5/4 (or 1.25).

You can now increase 14 by 1.25 by adding these together to 15.25.

Helpful 1What two numbers have a sum of 15 and a product of 36 ?

The answers are 3 and 12, since 3 + 12 = 15, and 3 multiplied by 12 is 36.

Helpful 2Can you find two numbers which have a product of 9 and a sum of 10?

9 and 1 are the answers as 9 times 1 is 9, and 9 added to 1 is 10.

Helpful 2What is the product of 3(3+x)?

You just need to multiply out the bracket to give 9 + 3x.

Helpful 2- Helpful 1
What are the two numbers that have a product of 132 and sum of -23?

The two numbers are -12 and -11, because -12 times -11 is 132, and -12 + -11 = -23.

Helpful 1What is the product of three, four and five?

To find the product multiply the three numbers together in any order.

3 multiplied by 4 is 12, and 12 multiplied by 5 is 60.

Helpful 2What is the product of 3,6 and 4?

To work out the product multiply the three numbers together.

3 multiplied by 6 gives 18, now mutiply the 18 by 4 to give 72.

Helpful 2Two numbers have a sum of 5 and a product of 6 what are the numbers?

The two numbers are 3 and 2.

This is becuase 3 + 2 gives 5, and 3 multiplied by 2 gives 6.

Helpful 2Can you find two number which have a product of 42 and sum of 23?

The two number that solve the proboem are 2 and 21.

This is because 2 multiplied by 21 gives 42, and 2 added to 21 gives 23.

Helpful 2What are the two integers whose sum is 5 and product that is 4?

The two numbers are 1 and 4.

This is because 1 added to 4 gives 5, and 1 multiplied by 4 gives 4.

Helpful 2- Helpful 1
- Helpful 1
- Helpful 1
- Helpful 1
What is the product of 27 and 30?

To work out the product just multiply the two numbers together.

27 multiplied by 30 is 810.

Helpful 1Can you find two numbers that have a sum of 13 and a product of 12?

The two numbers are 1 and 12 (since 1+ 12 = 13, and 1 times 12 is 12).

Helpful 1- Helpful 1
What is the sum of 1/2, 1/4 and 2/5?

Add the fractions together to find the sum.

First make a common denominator of 20.

10/20 + 5/20 + 8/20 = 23/20.

Helpful 1- Helpful 1
How does one solve this problem: Multiply the sum of 83 and 74 by their difference, and divide the product by 15?

The sum of 83 and 74 is 157 (add them together).

The difference between 83 and 74 is 9 (take them away).

Now multiply 157 by 9 to give 1413.

Now divide 1413 by 15 to give 94.2.

Helpful 1What is the product of 27 and 45?

To work out the product multiply the numbers together, so 27 times 45 is 1215.

Helpful 1Can you find the sum of the product of 2 and 14 and the difference of 5 and 11 ?

The product of 2 and 14 is 2 times 14 which is 28.

The difference of 11 and 5 is 11 minus 5 which is 6.

Now find the sum of 28 and 6 which is 34.

Helpful 1Can you find the product of 2/9 of 90?

Just divide 90 by 9 to give 10, and multiply 10 by 2 to give 20.

However, if you have a scientific calculator type in 2/9 times 90 using your fraction button.

Helpful 1- Helpful 1
Find two numbers which have a product of 9 and a sum of 10?

The two numbers are 1 and 9.

This is because 1 times 9 is 9, and 1 add 9 is 10.

Helpful 1What two numbers have the product of 1m2? Please give your answer in cm.

1m^2 is 100cm by 100cm. So the answers are 100 and 100.

Helpful 1The sum of two numbers is −48 and their difference is 17. Can you find the numbers?

The two numbers are -15.5 and -32.5.

Helpful 1What numbers have a sum of 11 and a product of 18?

The two numbers are 9 and 2, because 9 added to 2 is 11, and 9 times 2 is 18.

Helpful 1- Helpful 1
- Helpful 1
What is the sum of 5.72 and 0.8?

Sum means add, so the two numbers must be added together.

Do this either in your head, on paper, or on a calculator.

The answer should be 6.52.

Helpful 1What two numbers have the product of 10, and sum of 11?

The two numbers are 1 and 10, because 1 multiplied by 10 is 10, and 1 added to 10 is 11.

Helpful 1The sum of two numbers is -3 and their product is -10. What are the two numbers?

The two numbers that solve this problem are -5 and 2.

This is because -5 added to 2 gives -3, and -5 multiplied by 2 is -10.

Helpful 1What are two integers whose sum is 14 and product is 33?

The two integers are 11 and 3.

This is because 11 added to 3 is 14, and 11 multiplied by 3 gives 33.

Helpful 1Can you find two numbers that have the sum of 24 and the quotient of 3?

The two number that answer this question are 18 and 6.

This is because 18 + 6 = 24 (sum means add), and 18 divided by 6 gives 3 (quotient means divide).

Helpful 1Can you write a mathematical equation for the following; the sum of two numbers is 3 more than the product?

x + y + 3 = xy

Helpful 1The sum of two numbers is 20, if you subtract it by the first number the difference is 18. What are the two numbers?

The two numbers needed are 19 and 1.

Since 19 added to 1 gives 20, and 19 minus 1 is 18. (Sum means add, and differences means subtract).

Helpful 1How much greater is the product of 4 and 3 than the sum of 4 and 3?

First, find the product of 4 and 3 by multiplying them together to give 12.

Now work out the sum of 4 and 3 by adding them together to give 7.

Now subtract 7 from 12 to give 5.

Helpful 1What is the product of 112×9?

Just multiply the numbers together to find the product, so the answer is 1008.

Helpful 1What are the two square numbers that are added to get a sum of 90?

9 and 81 because 9 is 3 squared and 81 is 9 squared and 9 added to 81 is 90.

Helpful 1Can you find the sum of 3/8 and 7/2?

Just add the two fraction together to find the sum.

Convert 7/2 to 28/8, so 3/8 + 28/8 givds 31/8 = 3 7/8.

Helpful 1What is 20 add 3 multiply 4?

First you will need to work out 3 times 4 to gives 12, as multiplication takes priority over addition (BIDMAS).

Now work out 20 plus 12 to give 32.

Helpful 19 more than 7?

Just add the two numbers together to give 16.

Helpful 1The total of a number, 9 and 12 is 32. What is the number?

Total means add to the 3 numbers must add to give 32 (? + 9 + 12 = 32)

The number is 11.

Helpful 1- Helpful 1
Can you tell me and show me how to work out 5/9×360 =?

This is the same as working out 5/9 of 360, as times means of.

Apply the rule divide by the bottom and times by the top.

360 divided by 9 gives 40, and 40 times 5 is 200.

Helpful 1What is a sum of 9 and a product of 14?

The two numbers are 7 and 2, because 7 add 2 is 9, and 7 times 2 is 14.

Helpful 1Can you find the Product of 6×7/9?

Write 6 as a fraction (6/1), and now multiply 6/1 by 7/9 to give 42/9.

This can now be changed to a mixed number as 4 2/3 .

Helpful 1Can you find two numbers which have a product of 12 and a sum of 8 ?

The two numbers are 6 and 2.

This is becuase 6 add 2 is 8, and 6 times 2 is 12.

How do you find the product of two numbers?

Just multiply the two numbers.

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