# How to Find the Product and Sum of Two (Or More) Numbers

*Mark, a math enthusiast, loves writing tutorials for stumped students and those who need to brush up on their math skills.*

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

Below, we will work through several examples together.

**What are** 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**

**What are** the product and sum of 9 and 3?

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**

**What are** 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**

### 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
- 2 and 21
- 3 and 14
- 6 and 7
- -1 and -42
- -2 and -21
- -3 and -14
- -6 and -7

**What are** the product and sum of 2, 4 and 9?

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

The sum means that you need to add the three numbers together.

2 + 4 + 9 = 15

## Questions & Answers

**Question:** What do you get if you double 15?

**Answer:** Just multiply the number by 2 to give 30.

**Question:** Can you find two numbers which have a product of 12 and a sum of 7?

**Answer:** 4 and 3 are a the answers.

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

**Question:** How do you multiply the sum of 12 and 8 by their difference?

**Answer:** The sum of 12 and 8 is 12 add 8 which is 20.

The difference between 12 and 8 is 12 minus 8 which is 4.

Now 20 times 4 is 80.

**Question:** what is the sum and product of -5 and -12?

**Answer:** 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).

**Question:** What two numbers have a sum of 15 and a product of 36 ?

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

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

**Answer:** 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).

**Question:** Which two numbers have a sum of -4 and a product of -45?

**Answer:** The two numbers are -9 and 5 since -9 add 5 is -4, and -9 times 5 is -45.

**Question:** What are two numbers that have a sum of 24 and a quotient of 3?

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

**Question:** What is the product of 3, 6, and 8?

**Answer:** 3 times 6 is 18 and 18 times 8 is 144.

**Question:** What is the product of 7 and 2?

**Answer:** Just multiply 7 by 2 to give 14.

**Question:** What is the product of 5 and 8?

**Answer:** Just multiply 5 by 8 to give 40.

**Question:** Multiply the sum of 5 and 3 and the sum of 8 and 9?

**Answer:** The sum of 5 and 3 is 5 + 3 = 8.

The sum of 8 and 9 is 8 + 9 = 17.

Now multiply 17 by 8 to give 136.

**Question:** What two numbers make the product of 13?

**Answer:** 1 and 13 will give a product of 13.

These are the only whole numbers as 13 is a prime number,

**Question:** The product of two whole numbers is 648 and their sum is 51. What are the two numbers?

**Answer:** 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.

**Question:** What is the Product of 5 and (2/3n +5)?

**Answer:** 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.

**Question:** What is the product of 14 and 21?

**Answer:** To work out the product multiply 14 by 21 to give 294.

**Question:** What is the sum of 3, 7 and 10?

**Answer:** To find the sum add the three numbers up to give 20.

**Question:** Brandy added 27 to the product of 255 and 18. What is the sum?

**Answer:** 255 times 18 is 4590.

4590 + 27 is 4617.

**Question:** Two numbers have a sum of −15 and a product of −100. What are the numbers?

**Answer:** The two numbers are -20 and 5, since -20 + 5 is -15 and -20 multiplied by 5 is -100.

**Question:** What is the sum of 1 and 1?

**Answer:** Just add the two numbers together, 1 add 1 is 2.

**Question:** The sum of two numbers is 68. If one number is 12 more than the other number, what are the numbers?

**Answer:** Half 68 to give 34, and half 12 to give 6.

34 add 6 is 40, and 34 minus 6 is 28.

Therefore the two numbers are 28 and 40.

**Question:** What times 2 equals 11?

**Answer:** Just divide 11 by 2 to give 5.5.

**Question:** What is 34 added to the product of 3 and 4?

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

Now 34 added to 12 gives 46.

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

**Answer:** 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.

**Question:** What 2 integers have a sum of - 17 and a product of 52?

**Answer:** 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.

**Question:** What are the two integers whose sum is 5 and product that is 4?

**Answer:** The two numbers are 1 and 4.

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

**Question:** What is a sum of 9 and a product of 14?

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

**Question:** Find the product of 3/5 with the quotient of 9/5 and 8/7?

**Answer:** The quotient of 9/5 and 8/7 is 9/5 divided by 8/7 which is 63/40.

The product of 3/5 and 63/40 is 3/5 times 63/40 which is 189/200.

**Question:** What is the product of 3,6 and 4?

**Answer:** 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.

**Question:** Can you find two numbers that have the sum of 24 and the quotient of 3?

**Answer:** 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).

**Question:** What are a pair of numbers with a sum of 5 and a product of 4?

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

**Question:** What's the product of 6.2 and 8c?

**Answer:** Just multiply these together to give 49.6c.

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

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

**Question:** What is the sum of (-5)-(-2)?

**Answer:** This is the same as work out -5 + 2 which is -3.

**Question:** Can you find two numbers which have a product of 8 and a sum of 7?

**Answer:** 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.

**Question:** How can I work out the product of 18 and 4?

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

**Question:** The product of 5 whole numbers is 3. What is the sum of these numbers?

**Answer:** 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.

**Question:** Can you find two numbers which have a product of 741 and sum of 70 ?

**Answer:** 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.

**Question:** The product of 4/3 and a number is 84. What is the number?

**Answer:** Divide 84 by 4/3 to give 63.

**Question:** What are the two numbers that the sum is 12 and the product is 36?

**Answer:** 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.

**Question:** What is 1/3 the sum of six and three?

**Answer:** 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.

**Question:** What number pair has the sum of 5 product of 4?

**Answer:** 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.

**Question:** What is the sum of 2 and 7?

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

So 2 + 7 = 9.

**Question:** What are the two numbers which have a sum and product of 1 and 9?

**Answer:** 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.

**Question:** Can you find two numbers that have a product of -18 and a sum of -7?

**Answer:** The two numbers are -9 and 2.

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

**Question:** The product of two numbers is 72 and the sum is 18, what are that two numbers?

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

**Question:** Can you find a number which has a product of -14 and a sum of 5?

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

**Question:** How can I work out the sum of 2/12 and 6/12?

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

**Question:** What is the answer to halve the product of 5 and 12?

**Answer:** 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.

**Question:** Can you find two numbers which have a product of 60 and a sum of 100?

**Answer:** 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.

**© 2011 Mark**

## Comments

**Rachel Simpson** on April 30, 2020:

What is the product of 2,3and 4