Question

Приведи к общему наименшиму знаменателю . а) 1/12 , 1/35. б) 17/96 ,. 41/72​

Answer 1

12 = 2² · 3;  35 = 5 · 7;  НОК = 2² · 3 · 5 · 7 = 420

420 : 12 = 35 - доп. множ. к 1/12 = 35/420

420 : 35 = 12 - доп. множ. к 1/35 = 12/35

Ответ: 1/12 и 1/35 = 35/420 и 12/420.

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96 = 2⁵ · 3;  72 = 2³ · 3²;  НОК = 2⁵ · 3² = 288

288 : 96 = 3 - доп. множ. к 17/96 = 51/288

288 : 72 = 4 - доп. множ. к 41/72 = 164/288

Ответ: 17/96 и 41/72 = 51/288 и 164/288.

Answer 2

Finding the Least Common Denominator

To find the least common denominator (LCD) for the given fractions, we need to determine the smallest multiple that both denominators share. Once we have the LCD, we can convert the fractions to equivalent ones with the same denominator.

Calculating the Least Common Denominator

a) 1/12, 1/35:

The least common denominator for 1/12 and 1/35 is 420. To find this, we can list the multiples of each denominator and find the smallest number they have in common:

Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 180, 192, 204, 216, 228, 240, 252, 264, 276, 288, 300, 312, 324, 336, 348, 360, 372, 384, 396, 408, 420, ...

Multiples of 35: 35, 70, 105, 140, 175, 210, 245, 280, 315, 350, 385, 420, ...

Therefore, the least common denominator for 1/12 and 1/35 is 420.

b) 17/96, 41/72:

The least common denominator for 17/96 and 41/72 is 288. Similarly, we can list the multiples of each denominator and find the smallest number they have in common:

Multiples of 96: 96, 192, 288, ...

Multiples of 72: 72, 144, 216, 288, ...

Therefore, the least common denominator for 17/96 and 41/72 is 288.

Converting Fractions to Equivalent Fractions with the LCD

Now that we have the least common denominators, we can convert the fractions to equivalent ones with the same denominator.

a) 1/12, 1/35:

1/12 = 35/420, 1/35 = 12/420

b) 17/96, 41/72:

17/96 = 36/288, 41/72 = 144/288

By finding the least common denominators and converting the fractions to equivalent ones with the same denominator, we can compare and perform operations on the fractions more easily.