The distributive property of 35 and 14 is expressed as 7(5 + 2). Here, 7 is the greatest common factor (GCF) of 35 and 14. This approach simplifies the sum 35 + 14 by factoring out that common term.
What is the distributive property of 35 50?
The distributive property of 35 and 50 is 5(7 + 10).
You get this expression by finding the greatest common factor (GCF) of 35 and 50, which happens to be 5. Factoring out the 5, you simplify the sum 35 + 50, making it much easier to calculate. It's essentially 5 times the sum of 7 and 10 (5 * 17).
What is the distributive property of 55 35?
The distributive property of 55 and 35 is 5(11 + 7).
The GCF of 55 and 35 is 5. When you apply the distributive property, you can rewrite the sum of 55 and 35 as 5 multiplied by the sum of their quotients (that's 55/5 + 35/5), which comes out to 5 * 18.
What is the distributive property of 16 and 36?
The distributive property of 16 and 36 is 4(4 + 9).
First, you need to find the greatest common factor (GCF) of 16 and 36, which is 4. Once you factor out 4, you can express the sum as 4 times the sum of (16/4) and (36/4). This simplifies 16 + 36 down to 4 * 13, which, of course, is 52.
What is the distributive property of 12 and 20?
The distributive property applied to 12 and 20 is 4(3 + 5), after factoring out their greatest common factor.
The GCF of 12 and 20 is 4. You can rewrite 12 as 4 * 3 and 20 as 4 * 5. So, 12 + 20 becomes 4 * 3 + 4 * 5. Then, using the distributive property, that becomes 4(3 + 5) or 4 * 8, which equals 32.
What is the distributive property of 15 21?
The distributive property applied to 15 and 21 is 3(5 + 7), after you factor out their greatest common factor.
The greatest common factor (GCF) of 15 and 21 is 3. You can express 15 as 3 * 5 and 21 as 3 * 7. Applying the distributive property, the sum 15 + 21 turns into 3 * 5 + 3 * 7, which simplifies to 3(5 + 7) or 3 * 12, which is 36.
What is the GCF of 55 and 35?
The greatest common factor (GCF) of 55 and 35 is 5.
To figure this out, you just list the factors of each number: factors of 55 are 1, 5, 11, 55; factors of 35 are 1, 5, 7, 35. The biggest number they share is 5. Honestly, grasping the GCF is super important if you want to use the distributive property well, as noted by Khan Academy.
What is the distributive property to factor out the greatest common factor 9 15?
To factor out the greatest common factor (GCF) from 9 and 15 using the distributive property, you get 3(3 + 5).
First, find the GCF of 9 and 15, which is 3. Next, rewrite each term using that GCF as part of a product: 9 = 3 * 3 and 15 = 3 * 5. When you apply the distributive property in reverse, you can write 9 + 15 as 3 * 3 + 3 * 5, which simplifies to 3(3 + 5).
What is the distributive property to factor out the greatest common factor of 90 27?
The greatest common factor (GCF) of 90 and 27 is 9, and applying the distributive property to factor it out, you'll get 9(10 + 3).
Once you've figured out that 9 is the GCF, you can express 90 as 9 * 10 and 27 as 9 * 3. So, 90 + 27 can be rewritten as 9 * 10 + 9 * 3. Then, using the distributive property, that's equivalent to 9(10 + 3) or 9 * 13, which equals 117.
What is the GCF of 18 and 30?
The greatest common factor (GCF) of 18 and 30 is 6.
To find this, you can list out the factors: for 18 (1, 2, 3, 6, 9, 18) and for 30 (1, 2, 3, 5, 6, 10, 15, 30). The biggest factor they share is 6. Spotting the GCF is a pretty foundational skill for applying the distributive property in reverse.
What is the GCF and distributive property of 15 36?
The greatest common factor (GCF) of 15 and 36 is 3, and applying the distributive property, you'll get 3(5 + 12).
To figure this out, you'd find the common factors of 15 (1, 3, 5, 15) and 36 (1, 2, 3, 4, 6, 9, 12, 18, 36), and 3 is the biggest one. Then, you rewrite 15 as 3 * 5 and 36 as 3 * 12. With the distributive property, 15 + 36 turns into 3 * 5 + 3 * 12, and that simplifies to 3(5 + 12).
How is the distributive property helpful?
The distributive property is helpful because it simplifies complex mathematical expressions and makes mental calculations a lot easier.
It lets you break down multiplication problems involving sums or differences into much more manageable pieces, such as a(b + c) = ab + ac. This property is pretty fundamental in algebra, letting you expand expressions and factor out common terms, as highlighted by Britannica.
What is the distributive property in math?
The distributive property in mathematics says that if you multiply a number by a sum or difference, you'll get the same answer as if you multiplied that number by each part of the sum or difference individually, and then added or subtracted those products.
In math terms, it looks like a(b + c) = ab + ac or a(b - c) = ab - ac. This foundational algebraic principle connects multiplication and addition (or subtraction), letting us expand expressions or factor out common terms. It's a cornerstone of arithmetic and algebra, really crucial for everything from basic calculations to solving advanced equations, as detailed by Cuemath.
