a. (69+45)+55b. 4×324×32c. 4×(16×25)4×(16×25)d. (250+86)+50

babeeb0oL 2021-01-06 Answered

a. 4u3vw=0
b. 4×324×32
c. 4×(16×25)4×(16×25)
d. (250+86)+50

You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

pattererX
Answered 2021-01-07 Author has 95 answers

To multiply and add numbers mentally using the addition and multiplication properties, we want to rearrange the numbers so we get sums or products that are multiples of 10.
a. Since 45 and 55 add to a multiple of 10, we first use the Associative Property (a+b)+c=a+(b+c)(a+b)+c to get (69+45)+55=69+(45+55) since 45+55=100
Using mental math we then get 69+(45+55)=69+100=169
b. Since 32=30+2, we can write 4×32=4×(30+2). Using the Distributive Property a(b+c)=ab+ac then gives 4×(30+2)=4×30+4×2. Using mental math we then get 4×30+4×2=120+8=128.
c. Since 4×25=100, we want to rearrange the product so 4 and 25 are next to each other. Using the Commutative Property ab=ba to switch the 16 and 25 gives 4×(16×25)=4×(25×16).
Using the Associative Property a(bc)=(ab)c then gives 4×(25×16)=(4×25)×16.
Using mental math we then get (4×25)×16=100×16=1600.
d. Since 250+50=300, we want to rearrange the sum so 250 and 50 are next to each other. Using the Commutative Property a+b=b+a to switch the 250 and 86 gives
(250+86)+50=(86+250)+50.
Using the Associative Property (a+b)+c=a+(b+c)(a+b)+c=a+(b+c) then gives (86+250)+50=86+(250+50).
Using mental math we then get 86+(250+50)=86+300=386.

Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2021-01-04

Write in words how to read each of the following out loud.
a. {xR0<x<1}
b. {xRx0 or x1}
c. {nZn is a factor of 6}
d. {nZn is a factor of 6}

asked 2021-08-11
A ball is tossed upward from the ground. Its height in feet above ground after t seconds is given by the function h(t)=16t2+24t. Find the maximum height of the ball and the number of seconds it took for the ball to reach the maximum height.
asked 2022-06-26
Let f n : R R be defined by f n ( ω ) = ω ( 1 + 1 n ) and let μ be the Lebesgue measure.
I have to show that f n does not converge in measure μ to ω.
Here's my attempt: By definition, f n converges in measure to ω if:
lim n μ ( ω : | f n ( ω ) ω | δ ) = 0.
Rewriting, it becomes that:
lim n μ ( ω : | ω | n δ ) = 0.
I realized that if δ = 1 for example, then the measure is surely 0 as n . I need to come up with a value of δ such that the measure is non-zero. I thought about letting δ = 1 n ,, but am unsure if it'll become indeterminate once I set n (because I basically get 1 ) .
Does this solution of δ = 1 n truly work as a counterexample? If not, what should I do?
asked 2022-08-07
How prove this inequality c y c a 4 a 2 + 2 b 4 1
Let a , b , c > 0 such a + b + c = 3. Show that
a 4 a 2 + 2 b 4 + b 4 b 2 + 2 c 4 + c 4 c 2 + 2 a 4 1
My attempt is to use Cauchy-Schwarz inequality. Hence, I consider
( a 4 a 2 + 2 b 4 + b 4 b 2 + 2 c 4 + c 4 c 2 + 2 a 4 ) ( a 2 + b 2 + c 2 + 2 a 4 + 2 b 4 + 2 c 4 ) ( a 2 + b 2 + c 2 ) 2
However,
( a 2 + b 2 + c 2 ) 2 ( a 2 + b 2 + c 2 + 2 a 4 + 2 b 4 + 2 c 4 )
asked 2021-08-12
The solution of the given proportion 74=f48
asked 2021-11-13
Let ​f(x)=x2 and g(x)=x2x.
Find and simplify the expression ​(fg)(b).
(fg)(b)=
​(Use integers or fractions for any numbers in the​ expression.)
asked 2021-11-13
Solve: |4x1|3. Give your answer as an interval using whole numbers, proper fractions or improper fractions. Enter DNE if the inequality does not have a solution.