Write each number as a product using the GCF as a factor, and apply the Distributive Property.

Mathematics

1 answer:

Rasek [7]4 years ago

6 0

The distributive property: a(b + c) = ab + ac.

Factors of 38: 1, 2, 19, 38

Factors of 57: 1, 3, 19, 57

GCF(38, 57) = 19

38 + 57 = 19 · 2 + 19 · 3 = 19(2 + 3)

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DerKrebs [107]

Answer:

3000 girls
38 fishes
37 points
115 marbles
19 gray coloured cars

Step-by-step explanation:

Let the unknown values be x

30 class mates = 1 class room

18 girls in 1 classroom

18 girls in 30 classmates

x girls in 5000 class mates

$18\:girls= 30\:students\\x\:girls = 5000\:students\\\\Cross\:Multiply\\\\30x = 90000\\\\Divide\:both\:sides\:by\:30\\\frac{30x}{30} = \frac{90000}{30}\\ \\x = 3000\\= 3000 girls$

$2.5\:miles = 12 \:fishes\\8\:miles = x\:fishes\\\\Cross\:Multiply\\2.5x = 96\\\\Divide\:both\:sides\:of\:the\:equation\:by\:2.5\\\\\frac{2.5x}{2.5}=\frac{96}{2.5}\\ \\x = 38.4\\Approximately \: =38\:fishes$

$8\:minutes = 14\: points\\21 \:minutes = x \:points\\\\Cross\:Multiply\\8x = 294\\\\\mathrm{Divide\:both\:sides\:by\:}8\\\frac{8x}{8}=\frac{294}{8}\\\\Simplify\\x=\frac{147}{4}\\\\x = 36.75\\\\Approximately\:= 37\:points$

$32\:marbles = 5\:inches\\x\:marbles = 18\:inches\\\\Cross\:Multiply\\5x = 576\\\\\mathrm{Divide\:both\:sides\:by\:}5\\\frac{5x}{5}=\frac{576}{5}\\\\x=\frac{576}{5}\\\\x =115.2\\= 115=\:marbles$

$2 \: gray\:colour= 15\:cars\\x\:gray= 140\:cars\\\\Cross\:Multiply\\\\15x = 280\\\\\mathrm{Divide\:both\:sides\:by\:}15\\\frac{15x}{15}=\frac{280}{15}\\\\Simplify\\x=\frac{56}{3}\\\\x =18.666\\Approximately ;\\19$