Grade 5 Geometry Study Guide

FRACTIONS STUDY GUIDE

\ A fraction is a part of a whole. A fraction is made up of two numbers: a numerator and a denominator.

numerator – the number of parts being examined

€

23 denominator – the number of parts needed to make a whole

Fractions can be represented in different ways. Fractions can be shown on a number line, as a part of a region or area, or as part of a set.

pictoral model (fraction of a region) number line

€

35

0

€

35

1

€

512

0

€

512

1

pictoral model

(fraction of a set)

€

35

✈ ✈ ✈ ✈ ✈ ✈ ✈ ✈ ✈ ✈ ✈ ✈

€

512

The denominator tells how many parts are needed to make a whole. The larger the denominator, the smaller the pieces.

€

23

€

210

€

218

When a numerator is close to a denominator, then the fraction is near 1.

€

23

€

910

€

1518

When a numerator is equal to a denominator, then the fraction is equal to 1.

€

33

€

1010

€

1818

When a numerator is grater than a denominator, then the fraction is greater than 1. This type of fraction is an improper fraction.

€

73

€

1210

Grade 5 Geometry Study Guide

To add or subtract fractions and mixed numbers with like (the same) denominators, add or subtract the numerators and keep the denominator the same.

€

47

+17

=57

€

8 710

− 3 410

= 5 310

The greatest common factor (GCF) can used to simplify fractions. You find the greatest common factor of the numerator and denominator, and use that number to simplify or reduce the fraction.

f actors of 24: 1, 2, 3, 4, 6, 8, 12, 24

€

2428

factors of 28: 1, 2, 4, 7, 14, 28 4 is the greatest common factor of 24 and 28, so you simplify by dividing the fraction by four-fourths.

€

2428

÷44

=67

Some improper fractions are renamed as mixed numbers (or mixed numerals), and vice versa.

€

73

=

= 2

€

13

mixed numeral to improper fraction

€

257 →

€

257

=217

+47

= 3 +

€

47

= 3

€

47

(3)

improper fraction to mixed numeral

5

€

14 → 5

€

14

=204

+14

=214

(5)

You can make equivalent fractions with division or multiplication. When you multiply or divide a fraction by a fraction equal to 1, the new fraction is equivalent to the original fraction.

€

23x 88

=1624

€

14x 33

=312

€

4 25x 44

= 4 820

€

912

÷33

=34

€

75100

÷2525

=14

€

9 824

÷88

= 9 13

When you divide to make an equivalent fraction with the lowest possible numerator and denominator, you are simplifying or reducing the fraction.

€

912

÷33

=34

€

34

is simplest form of

€

912

. It is also

called reduced form or lowest terms.

When fractions or mixed numbers have different denominators, you rename or convert the fractions to have the same denominator.

€

310

+12

= ? →

€

12

=510 so

€

310

+12

=310

+510

€

310

+510

=810 so

€

310

+12

=810 ( or

€

45 )

Fractions are way to express division. Because of this, you can use division to rename improper fractions into whole numbers.

€

183

= 6 (

€

183

=18 ÷ 3 and 18 ÷ 3 = 6 )

€

248

= 3 (

€

248

= 24 ÷ 8 and 24 ÷ 8 = 3 )

When adding or subtracting fractions with unlike denominators, you can use the lowest common denominator (LCD), which is the least common multiple (LCM) of the denominators. Find the multiples of the denominators, and use the lowest common multiple as the new denominator.

multiples of 4: 4, 8, 12…

€

56– 14

multiples of 6: 6, 12…

12 is the new denominator.

€

56

=1012 and

€

14

=312 so

€

56−14

=1012

−312

=712