Why does the 1 rule help me?
Some multiplication problems have a 1 in them, like 1 × 9 or 6 × 1. When you know the 1 rule, you know the answer at once. You do not need to count. The rule works for every number, even very big ones. First, see why the rule is true.
What does 1 × 4 mean?
1 × 4 means 1 tray with 4 cookies on the tray. Look at the tray. Count the cookies.
One tray of 4 cookies
1 tray of 4 cookies.
Check the explanation and answers
There is 1 tray. It has 4 cookies, and there is no other tray to add: 1 × 4 = 4. The answers are 1 tray, 4 in each tray, and 4 in total.
There is only 1 tray. The cookies on that tray are all the cookies.
Does 1 group work with a bigger number?
Here is 1 box of crayons.
One box of 8 crayons
There is 1 box. The box has 8 crayons. How many crayons are there in all?
It works with any number. Think of 1 box of 100 crayons. You have 100 crayons: 1 × 100 = 100.
What does 5 × 1 mean?
Now the 1 comes last. 5 × 1 means 5 baskets with 1 apple in each basket. Count the baskets. Count the apples. Then press Add 1 more basket. What changes? and count again.
Five baskets with 1 apple in each
5 baskets. 1 apple in each basket.
Check the explanation and answers
There are 5 baskets with 1 apple in each basket: 1 + 1 + 1 + 1 + 1 = 5, so 5 × 1 = 5. The answers are 5 baskets, 1 in each basket, and 5 in total. Add 1 more basket, and there are 6 baskets with 1 apple in each: 6 × 1 = 6. The total is always the number of baskets.
Each basket has 1 apple. So you count 1 apple for each basket. The number of apples is always the number of baskets.
Is 1 × 5 the same as 5 × 1?
Take the 5 apples out of the 5 baskets. Put them all in 1 basket.
The same 5 apples in 1 basket
1 basket of 5 apples.
Check the explanation and answers
All 5 apples are in 1 basket: 1 × 5 = 5. Before, there were 5 baskets with 1 apple in each basket: 5 × 1 = 5. They are the same 5 apples, so 1 × 5 = 5 × 1. The answers are 1 basket, 5 in each basket, and 5 in total.
You did not add an apple or lose an apple. The 1 can come first or last. The answer is the other number.
What is the identity property of multiplication?
Any number times 1 is that same number. And 1 times any number is that same number. This rule is the identity property of multiplication.
Your identity is who you are. When you multiply a number by 1, the number stays what it is. It keeps its identity. That is why the rule has this name.
The rule works for every number, small or big: 9 × 1 = 9, 1 × 25 = 25, and 1,000 × 1 = 1,000.
How is times 1 different from times 0 and plus 1?
Do not mix up these three. Each one starts with 5.
Times 1 keeps the number. 5 baskets with 1 apple in each basket: 5 × 1 = 5.
Times 0 gives 0. 5 baskets with 0 apples in each basket: 5 × 0 = 0.
Plus 1 makes the number 1 bigger. 5 apples and 1 more apple: 5 + 1 = 6.
To learn why times 0 gives 0, see the zero property of multiplication.
Can I use the 1 rule with new numbers?
Try these 3 problems. Read each one with care. One of them does not have a 1.
One nest
A hen has 1 nest. The nest has 10 eggs. How many eggs does the hen have?
Nine plates
There are 9 plates. Each plate has 1 cupcake. How many cupcakes are there in all?
Eight pots
There are 8 pots. Each pot has 0 seedlings. How many seedlings are there in all?
Why is 7 × 1 not 8?
A common mistake is 7 × 1 = 8. That adds 1. But 7 × 1 means 7 bags with 1 ball in each bag. Count the balls: 1 + 1 + 1 + 1 + 1 + 1 + 1 = 7. So 7 × 1 = 7.
Another mistake is 7 × 1 = 1. The 1 tells how many balls are in each bag. It does not tell how many balls there are in all. There are 7 bags, so there are 7 balls.
Where can I get an identity property of multiplication worksheet with answers?
Print 8 questions: a tray and baskets to count, quick facts, missing numbers, facts with 1 and 0, a mistake to fix, a picture to draw, and a story problem. Each PDF has a student page and a separate answer key.
Download the worksheet and answer key (US Letter PDF)
Download the worksheet and answer key (A4 PDF)
Print at actual size. Try all 8 questions first, then check your work with the answer key.
Plan short multiplication practice
Use the Math Builders quiz to plan practice for your child or class.
Notes for parents and teachers
Start with real objects. Put out 3 plates with 4 crackers on each plate. Ask three questions: How many plates? How many on each plate? How many in all? Take 1 plate away and ask again. Do it one more time, so that 1 plate is left.
Then teach the other meaning. Put out 5 plates with 1 cracker on each plate. A child who answers 6 for 5 × 1 has added 1. Say the full phrase each time: 5 plates of 1.
Let your child say the rule in their own words before you name it. The term identity property of multiplication can come later. For older students: the number 1 is the multiplicative identity. Addition has a different identity, 0, because 5 + 0 = 5.
Review equal rows in multiplication arrays, or connect facts with multiplication and division fact families. For short recall practice, go back to the multiplication fact fluency guide.
More rules of multiplication: the distributive property of multiplication and the zero property of multiplication.
Teaching connections: Common Core 3.OA.A.1 and 3.OA.B.5. This lesson supports work with equal groups and with properties of multiplication.