# 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:** 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:** The product of two numbers is 45. Their sum is 18. What are the numbers?

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

**Question:** What two numbers have a product of ten ?

**Answer:** There are several answers, 1 and 10 or 2 and 5 are the most obvious ones.

**Question:** What is the answer of this integer: 53-(-4) +(-6) -5?

**Answer:** This is the same as 53 + 4 -6 -5 = 46.

**Question:** What is the product of (17/9) (-3/5)?

**Answer:** Multiply the numerators to give -51 and multiply the denominators to give 45.

So the answer is -51/45 which simplifies to -17/15

**Question:** If 10 is added to the sum of 17 and 42. What is the total?

**Answer:** The sum of 17 and 42 is 59.

Now 59 add 10 is 69.

**Question:** How do you find the product of 8 and 6?

**Answer:** To find the product of 8 and 6 work out 8 multiplied by 6 which is 48.

**Question:** What is the sum and product for 7 and 18?

**Answer:** The sum is 7 plus 18 which is 25.

The product is 7 multiplied by 18 which is 126.

**Question:** What is the sum of 19 and 25 multiplied by their difference?

**Answer:** 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.

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

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

**Question:** The product of two numbers is 48. If one of the numbers is 6, what is the other number?

**Answer:** Just divide 48 by 6 to give 8.

**Question:** What is the number multiplied by 12, that product added to 6, and the sum is equal to the product of 6 and 5?

**Answer:** The product of 6 and 5 is 6 times 5 which is 30.

30 minus 6 is 24.

So the number is 2 since 2 times 12 is 24.

**Question:** What is the product of 0.009 & 2.84?

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

0.009 multipled by 2.84 gives 0.02556.

**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.

**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:** Ten is added to the sum of 17 and 42. What is the total?

**Answer:** Just add up the three numbers to give 69.

**Question:** What is the product of 3(3+x)?

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

**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:** How does knowing that 2 and 9 =18 help find the product of 4 and 9 without multiplying ?

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

**Question:** How do you find the product of two numbers?

**Answer:** Just multiply the two numbers.

**Question:** What is the product of (3+20)(4-30)?

**Answer:** 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.

**Question:** The sum of the numbers is 17, and the product is 70, what are the numbers?

**Answer:** The two answers are 7 and 10 (since 7 added to 10 is 17, and 7 multiplied by 10 is 70).

**Question:** Find the product of (-3)*(-6)*(-2)*(-1)?

**Answer:** -3 multiplied by -6 is 18.

18 multiplied by -2 is -36.

-36 multiplied by -1 is 36.

**Question:** What is 4(10+9)?

**Answer:** First work out 10 added to 9 to give 19, and then multiply 19 by 4 to give 76.

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

**Answer:** 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).

**Question:** What is the product of three, four and five?

**Answer:** 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.

**Question:** Find the sum of 5/6 and {-8/6}?

**Answer:** The answer is -3/6 or -1/2 when simplified.

**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:** 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:** 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:** 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:** 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:** 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:** What is the product of 1 and 5?

**Answer:** Just multiply 1 by 5 to give an answer of 5.

**Question:** What’s the product of 7/12 and 14?

**Answer:** 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.

**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:** Can you find two numbers which have a sum of 13 and a product of 12?

**Answer:** 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.

**Question:** The square of a number is 81. Find the number?

**Answer:** 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).

**Question:** Can you find a pair of numbers with a sum of 9 and a product of 20?

**Answer:** 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).

**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.

**© 2011 Mark**

## Comments

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

What is the product of 2,3and 4