Distributive Property — Definition & Examples
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- The Distributive Property The distributive property says that if you're multiplying an expression in parentheses by a number, you have to do that operation to every number withi…
By Zora Gilbert, Alex Federspiel, Caroline K
- (Videos) The Distributive Property by Math Antics In these videos by mathantics, he goes over what the distributive property is and how you use it. Summary\large{\text{Summary}}…
By Alex Federspiel, Naomi Burgess, Zora Gilbert, Jonathan Heller, Caroline K, Joshua Siktar
- Distributive Property\textbf{Distributive Property}Distributive Property Below is a visual representation of the distributive property. Imagine two rectangles with the same heig…
By Christine, Alex Federspiel, Jonathan Heller, Caroline K
Problems 98
- Which of the following expressions are equal to x2yz3z4+x2y3x^2yz^3z^4 + x^2y^3x2yz3z4+x2y3?
- Simplify by distributing. 2(4+9x)2(4+9x)2(4+9x)
- Simplify by distributing. −4(−4x−7)-4(-4x-7)−4(−4x−7)
- Simplify by distributing. (x−7)(2)(x-7)(2)(x−7)(2)
- Simplify by distributing. (6x−y−9)(7y)(6x-y-9)(7y)(6x−y−9)(7y)
- Simplify by distributing. (2x+5)(6+5)(2x+5)(6+5)(2x+5)(6+5)
- Simplify by distributing. (−5x−2y−4z−3)(−4)(-5x-2y-4z-3)(-4)(−5x−2y−4z−3)(−4)
- Simplify by distributing. (−5x−6)(4x−9)(-5x-6)(4x-9)(−5x−6)(4x−9)
- Which of the following does the distributive property work for?
- True or False\text{True or False}True or False === A×(B×C)=(A×B)×(A×C)A \times (B \times C)=(A \times B) \times (A \times C)A×(B×C)=(A×B)×(A×C)
- Compute 3×(4+8)3\times(4+8)3×(4+8).
- Compute 6×(2+3)6\times(2+3)6×(2+3).
- Compute 4×(8+2)4\times(8+2)4×(8+2).
- Compute 9×(4+1)9\times(4+1)9×(4+1).
- Which of the following is a representation of 5×1235\times1235×123?
- Which of the following is equal to 4×3954\times3954×395?
- Compute 5×3855\times3855×385.
- Compute 3×(19−10)3\times(19-10)3×(19−10).
- Compute 20×(10−5)20\times(10-5)20×(10−5).
- Compute 9×(16−6)9\times (16-6)9×(16−6).
- Compute 8×(2−3−10)8\times(2-3-10)8×(2−3−10).
- Compute 7×(8−8−5)7\times(8-8-5)7×(8−8−5).
- Expand 7×(x−3)7\times(x-3)7×(x−3).
- Expand a×(b−c)a\times (b-c)a×(b−c).
- True or False\text{True or False}True or False === If you have a rational number pq\frac{p}{q}qp where q≠0q\neq0q=0, then pq(a+b)=paq+pbq\frac{p}{q} (a+b)=\frac{pa}{q} +\frac{…
- Simplify the expression by combining like terms. 6(x+2)+4(8−2x)6(x+2)+4(8-2x)6(x+2)+4(8−2x)
- Which property allows us to say 3x+2x=(3+2)x3x + 2x = (3 + 2)x3x+2x=(3+2)x?
- Which property allows us to multiply two expressions, so that 2x(3x+6)=6x2+12x2x(3x + 6) = 6x^2 + 12x2x(3x+6)=6x2+12x
- Which of the following products do not equal 3x2+6x43x^2 + 6x^43x2+6x4?
- You are hosting a lemonade stand to raise money for charity. If five people each bought one lemonade and two cookies, which of the following are ways can we represent the amount…
- Michelle is preparing for a fun-filled day at the park and is packing lunches for her 222 kids. In each lunch, she packs 555 carrots, 111 sandwich, and 222 cookies. Which expres…
- Distribute aaa through the following expression: a×(a+b)a\times(a+b)a×(a+b)
- Distribute aaa through the following expression: a×(a2+ab+b)a\times (a^2+ab+b)a×(a2+ab+b)
- Distribute aaa through the following expression: (1a+1)×a\bigg(\frac{1}{a}+1\bigg)\times a(a1+1)×a
- If y=4x+2y=4x+2y=4x+2, what is 3y3y3y?
- If y=x2+3x+1y=x^2+3x+1y=x2+3x+1, what is 2y2y2y?
- If y=x2−x+1y=x^2-x+1y=x2−x+1, what is −y-y−y?
- Distribute 12\frac{1}{2}21 through the expression 12(2x2−4x+8)\tfrac{1}{2}\big(2x^2-4x+8\big)21(2x2−4x+8)
- Distribute −23\frac{-2}{3}3−2 through the expression −23(−3x2+6x−1)\tfrac{-2}{3}\big(-3x^2+6x-1\big)3−2(−3x2+6x−1)
- In Michael's opinion, a complete outfit includes 111 t-shirt, 111 pair of jeans, 222 shoes, 111 hat, and 111 belt. Which expressions represent the total number of items that Mic…
- Which of the following is the correct distribution of ab2ab^2ab2 through the expression ab2(a+b+1b)ab^2\bigg(\frac{a+b+1}{b} \bigg)ab2(ba+b+1)
- Which of the following is the correct distribution of b2a\frac{b^2}{a}ab2 through the expression b2a(b−ab+a)\frac{b^2}{a}\bigg(\frac{b-a}{b}+a \bigg)ab2(bb−a+a)
- How many donuts do they need to make?
- Which property is the following: 14(23+56)=14×23+14×56\frac14\left(\frac23+\frac56\right)=\frac14\times\frac23+\frac14\times\frac5641(32+65)=41×32+41×65
- Rewrite 18+1218+1218+12 as an expression using the distributive property (select all that apply).
- Find which of the following expressions is equal to the expression 9(2+5)9(2+5)9(2+5).
- 2×(2+3×(1+5))2\times(2+3\times(1+5))2×(2+3×(1+5)) Evaluate the expression above.
- a+(b×c)=(a+b)×(a+c)a+(b\times c) = (a+b)\times (a+c)a+(b×c)=(a+b)×(a+c) Is the above correct?
- a×(b+c)=a×b+a×ca\times (b+c) = a\times b + a\times ca×(b+c)=a×b+a×c Can aaa be negative?
- 20×(45+14)20\times \left(\frac{4}{5} + \frac{1}{4}\right)20×(54+41) Evaluate the above expression.
- 13×11+10+3+13×813\times 11 + 10+3 +13\times813×11+10+3+13×8 Evaluate the expression above.
- Jack, Kaitlyn, and Francisca are having a bake sale to fund raise for their graduation trip. For every pumpkin-glazed, old-fashioned donut they sell, they make 757575 cents. Jac…
- Can you calculate 7×157\times 157×15 in your head? Which of the following expressions is it equivalent to?
- How many people in total booked a hot air balloon trip for September, October and November?
- a×(b+c)=a×b+a×ca\times(b+c)=a\times b + a\times ca×(b+c)=a×b+a×c Does this still hold if we replace ×\times× with ÷\div÷? Is it true that a÷(b+c)=a÷b+a÷ca\div(b+c)=a\div b + a\d…
- 1×13+2×13+3×13(1)1\times 13 + 2\times 13 + 3\times 13\quad\quad(1)1×13+2×13+3×13(1) 6×10+6×3(2)6\times 10 + 6\times 3\quad \quad(2)6×10+6×3(2) Is expression (1)(1)(1) equivalent…
- a−(b×c)=(a−b)×(a−c)a-(b\times c) = (a-b)\times(a-c)a−(b×c)=(a−b)×(a−c) Is the above statement true?
- We know that a×(b−c)=a×b−a×ca\times (b-c) = a\times b - a\times ca×(b−c)=a×b−a×c. Does this still hold if some (or all) of a,b,ca, b, ca,b,c are negative?
- What is 4×(13−3)4\times (13-3)4×(13−3) equivalent to?
- Keith is selling homemade, Halloween themed lollipops for a fundraiser. On average, it costs him \1.35 to make each of these lollipops. Keith is selling each for \4. In total, h…
- Anna and Casey went pumpkin picking. They got a total of 777 pumpkins and they were each 4\44. Casey paid for 444 pumpkins. How much did Anna pay?
- What is 5×(−2−3)5\times(-2-3)5×(−2−3) equivalent to?
- Above is a full milk chocolate bar. There is a total of 1×51\times 51×5 small bars. Bennie took 222 small bars. How many small bars are there left? Pick the expression that illu…
- What is 36×2336\times 2336×23 equivalent to? Choose all the right answers.
- Is there a way to expand the following? (1+2)×(4−3)(1+2)\times(4-3)(1+2)×(4−3)
- Can you calculate 50×1950\times 1950×19 in your head?
- Expand (5−2−x)×11(5-2-x)\times 11(5−2−x)×11.
- Zoe is selling some grilled cheese for a fundraiser. On average, every grilled cheese costs 1\11 to make. Zoe is selling the grilled cheese for 3.50\3.503.50 each. At the end of…
- Compute 15×615\times 615×6.
- True or False\text{True or False}True or False === The distributive property works with variables.
- True or False\text{True or False}True or False === The distributive property only works for a?(b+c)a?(b+c)a?(b+c) if ??? is a multiplication symbol.
- How can you use the distributive property to quickly calculate 49×349\times349×3?
- Which of the following is a representation of 6×43826\times43826×4382?
- True or False\text{True or False}True or False === The distributive property does not hold for fractions.
- True or False\text{True or False}True or False === The distributive property works with decimals.
- Use the distributive property to solve out (a+b)(c+d)(a+b)(c+d)(a+b)(c+d)
- You want to distribute 333 pieces of candy to all your friends. You have 444 friends in your neighborhood, 666 at school, and 555 at work. How much candy should you buy?
- Expand and simplify the following: (x+2)2×(3x2)(x+2)^2\times (3x^2)(x+2)2×(3x2)
- How can she achieve her goal? Select all possibilities.
- How can she achieve her goal? Select all possibilities below.
- How can he achieve his goal? Select all possibilities below.
- If y=2x+3y = 2x+3y=2x+3, then 2y=?2y ={?}2y=?
- −(2x+3)= ?-(2x+3) =\,?−(2x+3)=? (Select all that apply.)
- 2(x2+1)= ?2(x^2+1) =\,?2(x2+1)=? (Select all that apply.)
- Simplify 7(239−24)7(239-24)7(239−24).
- Which of the following properties apply to the set of rational numbers? Select all that apply.
- Which property states that: a(b+c)=ab+aca(b+c)=ab+aca(b+c)=ab+ac
- What is the distributive property?
- Which is an example of the distributive property?
- Simplify. 3(x+8)+11(9−x)3(x+8)+11(9-x)3(x+8)+11(9−x)
- Which of the following demonstrates the distributive property? Choose all that apply.
- Using the distributive property, calculate the following: 11×1511\times1511×15
- How can we use the distributive property to solve the following? Choose all that apply. 7×167\times167×16
- Which of the following does not demonstrate the distributive property?
- Calculate the following using the distributive property. 29×1229\times 1229×12
- What of the following does not properly use the distributive property when calculating 14×3114\times 3114×31?
- Evaluate the following: 6x×(3x+2)6x\times(3x+2)6x×(3x+2)
- Simplify the following expression: (6x)×(4x2+3)(6x) \times (4x^{2}+3)(6x)×(4x2+3)