Fractions: What They Mean, and Equivalent Forms

Fractions = Parts “taken”Total (=) Parts in a Whole

“A whole” One out of two parts

2

1

Fractions = Parts “taken”Total (=) Parts in a Whole

“A whole” One out of three parts

3

1

Fractions = Parts “taken”Total (=) Parts in a Whole

“A whole” Two out of three parts

3

2So any time the numerator (top) is smaller than the denominator (bottom), the fraction has a value lower than 1.

Fractions on a Number Line

0 12

1

3

1

3

2

4

1

4

3

4

2

Equivalent FractionsTwo out of three parts

3

2

Four out of six parts

6

4is identical to

If each part of the whole is cut in two, we see why.

Equivalent Fractions

We make equivalent fractions by multiplying the numerator and denominator of any fraction BY THE SAME NUMBER.

Ex: Find a fraction equivalent to that has an 12 in the denominator. 4

3

4

33

3

Sneaky form of 1

12

9

Equivalent FractionsTwo out of three parts

3

2

Four out of six parts

6

4is identical to

If pairs of small parts are considered bigger parts, we see why.

Equivalent Fractions

We can also make equivalent fractions by dividing the numerator and denominator of a fraction by the SAME NUMBER.

Ex: Reduce to lowest terms.15

10

15

10

5

5

Sneaky form of 1

53

52

3

2

Comparing Fractions

Unit fractions can be compared by looking at the denominators…

…the bigger the denominator, the smaller the fraction.

>3

1

5

1

Comparing Fractions

Non-Unit fractions can be compared by a few different ways, for now, we’ll give them the same denominators.

In that condition, the smaller the numerator, the smaller the value.

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5

2

10

3

2

2

5

2

10

3

10

4

10

3