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Number Relationships Solutions

A factor is a number that multiplies with another number to form a product.
The greatest common factor, or GCF , is the largest factor that two or more numbers share.
The GCF is used to simplify fractions completely.
To find the GCF:

1. List the factors of given numbers, starting with 1 and the given number .
2. Identify the largest factor that the given numbers have in common.
3. It is possible for the GCF to be one .

A multiple is the product of a given number and another number.
The least common multiple, or LCM , is the smallest number that is a multiple of two or more numbers excluding zero.
The LCM is called the LCD (least common denominator) and is needed to add or subtract fractions.
To find the least common multiple:

1. List the multiples of the given numbers starting with the number itself .
2. Identify the smallest multiple that the given numbers have in common.

Determine the GCF and LCM of 56 and 32.

Implement

$GCF (56, 32) = 8$

$56 : 1, 2, 4, 7, 8, 14, 28, 56 32 : 1, 2, 4, 8, 16, 32$

$LCM (56, 32) = 224$

$56 : 56, 112, 168, 224, 280, . . . 32 : 32, 64, 96, 128, 160, 192, 224, . . .$

Explain

Simplify.

$\frac{25}{12} \cdot \frac{3}{10}$

$\frac{{}^{5}25}{{}_{4}12} \cdot \frac{3^{1}}{10_{2}} = \frac{5}{8}$

$GCF (25, 10) = 5 GCF (12, 3) = 3$

Rewrite the fractions with the least common denominator (LCD). Do not simplify.

$\frac{3}{10} + \frac{5}{12}$

$\frac{3}{10} (\frac{6}{6}) + \frac{5}{12} (\frac{5}{5}) \frac{18}{60} + \frac{25}{60}$

LCM = LCD for fractions
$LCD (10, 12) = 60$

Note

Q: Why was 120 not used for the common denominator?

A: The directions state to rewrite with the LEAST common denominator, which is 60.