What Is the Distributive Property? A Grade 6 Guide

The distributive property lets you multiply one number by a sum by multiplying it by each part first. For 3 × (4 + 5), you work out 3 × 4 and 3 × 5, then add: 12 + 15 is 27. I call it sharing the outside number out, because every term inside the brackets gets its fair share.

I first saw the need for it in a boy who wrote 2(x + 5) = 2x + 5 and looked hurt when I marked it wrong. He had shared the 2 with the x and forgotten the 5, so his answer was short by 5. Once he saw the 2 visit every term inside, he never made that slip again.

What Is the Distributive Property?

The distributive property says multiplying one number by a sum gives the same answer as multiplying that number by each part and then adding. In symbols, a(b + c) equals ab + ac, so 3 × (4 + 5) equals 3 × 4 + 3 × 5, which is 27.

Think of a bag with two pockets. The number outside the brackets must visit both pockets, not just the first one. If it visits only one pocket, part of the sum never gets multiplied, and the answer comes out too small.

The property also runs in reverse. When two products share a factor, you can pull that factor out: 12 + 18 becomes 6 × (2 + 3), which is 6 × 5, or 30. Children meet this reverse move later as factoring, but the sharing idea stays the same.

How Do You Use It, Step by Step?

Use the distributive property in three steps: spot the number outside the brackets, multiply it by every term inside, and add or subtract the results. Never skip a term, because 2(x + 5) equals 2x + 10, not 2x + 5, and the check is simple: work it both ways.

I teach the steps with a real story first. Six bags hold 4 apples and 3 bananas each, so the total fruit is 6 × (4 + 3). Share the 6 out: 6 × 4 is 24 apples and 6 × 3 is 18 bananas, and 24 + 18 is 42. The direct check agrees, because 6 × 7 is also 42.

With letters, the steps do not change. For 4(x + 6), multiply 4 by x to get 4x, then multiply 4 by 6 to get 24, and write 4x + 24. The letter part stays put while the number part gets shared out, just like the apples and bananas.

Does It Work With Subtraction and Negative Numbers?

Yes, the distributive property works with subtraction and negative numbers in the same way, because subtraction is adding a negative. For 7 × (9 − 4), multiply 7 by 9 and 7 by 4, then subtract: 63 − 28 is 35, and the direct check, 7 × 5, is also 35.

Signs cause the most slips here, so I slow children down at this step. For 3 × (−4 + 6), share the 3 out: 3 × (−4) is −12 and 3 × 6 is 18, so −12 + 18 is 6. The direct check agrees, because 3 × 2 is 6, and that agreement builds trust in the method.

Watch the sign on every product. A negative times a positive stays negative, and a negative times a negative turns positive, so each shared-out product needs its own sign check before you add.

How Does It Help With Mental Maths?

The distributive property turns hard multiplications into easy ones by breaking a number into tens and ones. For 6 × 48, split 48 into 40 + 8, then 6 × 40 is 240 and 6 × 8 is 48, so the answer is 288, and children can do it without a method.

I use this trick at the shops with my own children. For 7 × 29, split 29 into 30 − 1, then 7 × 30 is 210 and 7 × 1 is 7, so 210 − 7 is 203. The hard sum becomes two easy sums, and the answer arrives before anyone reaches for a pencil.

Breaking numbers apart is the same skill children use when they group like terms, because both skills rest on seeing parts inside a whole. The grouping like terms guide shows the sorting half of this habit, and the distributive property shows the sharing half.

Common Mistakes I See With the Distributive Property

The first mistake is sharing with only the first term. In 2(x + 5), the 2 must reach the 5 as well, or the answer loses 5. I make children point at each term inside and say its product out loud before they write anything.

The second mistake is dropping the sign when sharing over subtraction. In 5 × (8 − 3), the products are 40 and 15, and the sign between them stays minus, so the answer is 25. Children who add instead get 55, and the direct check, 5 × 5, catches the slip at once.

The third mistake is using the property where it does not belong. It shares multiplication over addition and subtraction only, so it never applies to exponents or to division in the same way. Standard 6.EE.A.3 asks children to apply the properties of operations to make equivalent expressions, and knowing the limits of each property is part of that skill.

Practise With the Free Worksheet

The laws of integers worksheet gives your child six pages of practice with the commutative, associative and distributive laws, including the sharing step in every section. It moves from naming each law to using it in short answers and real-life problems, so the distributive habit builds one step at a time.

Try These Three Yourself

1. Use the distributive property: 8 × (5 + 3). (Answer: 64, because 8 × 5 is 40 and 8 × 3 is 24, and 40 + 24 is 64.)
2. Expand 3(y + 4). (Answer: 3y + 12, because 3 × y is 3y and 3 × 4 is 12.)
3. True or false: 2(x + 5) = 2x + 5? (Answer: False. The 2 must multiply both terms, so the answer is 2x + 10.)

Share one sum out tonight. Pick a number outside the brackets, visit every term inside, and let the distributive property turn one hard multiplication into two easy ones. Find more Grade 6 guides on the Grade 6 hub.