Iota Math

IOTA MATH

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A number that is a multiple of two or more numbers.

Some multiples of 3 & 4 12, 24, 36, 48,

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The smallest common multiple of a set of two or more numbers.

4 = 4, 8, 12, 16, 20, 24, 28 5 = 5, 10, 15, 20, 25, 30

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Mixed numbers are whole numbers and fractions together.

1 3 2

Check to see if the smaller denominator divides evenly into the larger denominator. If it does, use the larger denominator for your LCD or LCM.

1 3 2 1 + 1 8

2 will divide evenly into 8, so 8 is your LCD or LCM.

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Find the multiples of each denominator.

1 3 4 = 4, 8, 12, 16, 20, 30 1 1 + 10 = 10, 20, 30, 40, 50

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Compare the lists of multiples. Circle the common multiples between the two lists.

1 3 4 = 4, 8, 12, 16, 20, 24 1 1 + 10 = 10, 20, 30, 40, 50

Use the least common multiple as the denominator. 

1 3 4 = 4, 8, 12, 16, 20, 24 1 1 + 10 = 10, 20, 30, 40, 50

This number is also called the least common denominator. 

1 3 4 = 4, 8, 12, 16, 20, 24 1 1 + 10 = 10, 20, 30, 40, 50

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Find the equivalent fractions for 1/4 & 1/10 with 20 as the denominator.

1 3 4 x 5 =20 1 1 + 10 20

Ask yourself what you multiply 4 by to get 20.

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Find the equivalent fractions for 1/4 & 1/10 with 20 as the denominator.

1 x 5 = 3 4 x 5 =20 1 1 + 10 20

That’s right 5. Since you are looking for the equivalent fraction you know the top number must also be multiplied by 5.

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Find the equivalent fractions for 1/4 & 1/10 with 20 as the denominator.

1 5 x 5 = 3 4 x 5 =20 1 1 + 10 20

To find the top number just multiply 1 x 5 to get your equivalent fraction.

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Find the equivalent fractions for 1/4 & 1/10 with 20 as the denominator.

1 5 x 5 = 3 4 x 5 =20 1 1 + 10x 2 =20

Now ask what you multiply the 10 by to get 20.

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Find the equivalent fractions for 1/4 & 1/10 with 20 as the denominator.

1 5 x 5 = 3 4 x 5 =20 1 x 2 = 2 1 + 10x 2 =20

That’s right 2. Since you are looking for the equivalent fraction you know the top number must also be multiplied by 2.

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Now just add the numerators.

1 x 5 = 5 3 4 x 5 =20 1x 2 = 2 +1 10x 2 =20 7 20

Remember! We never add the denominators.

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Now add the whole numbers.

1 x 5 = 5 3 4 x 5 =20 1x 2 = 2 +1 10x 2 =20 7 4 20

1 10 3 1 +3 6

6 6

Use the short cut to find the Least Common Denominator (LCD).

1 10 3 x 2 = 6 1 3 + 6 x 1 =6

Now find the equivalent fractions for 1/3 & 1/6.

Ask what do you multiply 3 by to get 6 and what do you multiply 6 by to get 6.

1 x 2 = 10 3x 2 = 6 1 x 1 = + 3 6 x 1 =6

Since you are writing equivalent fractions, now multiply the top numbers by the same number you did in the bottom.

1 x 2 = 2 10 3x 2 = 6 1 1 x 1 = 3 + 6x 1 =6

Now multiply across.

1 x 2 = 2 10 3 x 2 = 6 1 1 x 1 = 3 + 6x 1 =6 3 6

Add your new numerators.

1 x 2 = 2 10 3 x 2 = 6 1 1 x 1 = 3 + 6x 1 =6 3 13 6

Add your whole numbers.

3 3 1 ÷ 13 13 = 6 ÷3 2

4 11 5 1 2 + 3

15 15

Find the common multiples for 5 and 3. Write this number as your new denominator.

4 11 5 x 3 = 15 1 + 2 3 x 5 =15

Ask yourself what you multiply the bottom number by to get 15.

4 x 3 = 11 5 x 3 = 15 1 x 5 = + 2 3 x 5 =15

Multiply the top number by the same number you did in the bottom.

4 x 3 = 12 11 5 x 3 = 15 1x 5 =5 2 + 3 x 5 =15

Multiply across.

4 x 3 = 12 11 5 x 3 = 15 1 5 x 5 = 2 + 3 x 5 =15 17 15

Now add your new numerators.

4 x 3 = 12 11 5 x 3 = 15 1 5 x 5 = 2 + 3 x 5 =15 17 15

2 1 15 15) 17 15 2

1 4 x 3 = 12 11 5 x 3 = 15 1 5 x 5 = 2 + 3 x 5 =15 17 14 15

2 1 15 15) 17 15 2

1 4 x 3 = 12 11 5 x 3 = 15 1 5 x 5 = 2 + 3 x 5 =15 17 14 2 15 15

2 1 15 15) 17 15 2

1 4 x 3 = 12 11 5 x 3 = 15 1 5 x 5 = 2 + 3 x 5 =15 17 14 2 15 15

2 1 15 15) 17 15 2

1 24 5 x 4 = 20 6 x 4 = 24 5 15 x 3 = 3 + 8 x 3 =24 11 35 28 24 24

11 1 24 24) 35 24 11

Thank You