Lesson 3: Fractions and Mixed Numerals
Fractions
Sept. 26th
A fraction is a whole divided into some number of equal parts. The
denominator of the fraction is the bottom number. It tells you how many
equal parts the whole is divided into. The numerator of the fraction is the
top number. It tells you how many equal parts of the whole you have.
Numerator
⅔
Denominator
The fraction above tells you that a whole was divided into 3 equal parts,
and that you have 2 of those parts!!
Jenny has 8 balls. She has 5 basketballs and 3 soccer balls. What fraction of the balls are
basketballs?
In this problem, the whole is the total number of balls. Therefore the denominator of the fraction is
8.
The numerator of the fraction is the number of basketballs, which is 5.
Five out of the 8 balls are basketballs. The fraction form is ⅝.
PRACTICE:
1. Mr. Devono has 4 pens, 3 pencils, and 5 erasers. What fraction of Mr. Devono’s objects are
erasers? _________
2. Justin had 10 hits. Seven of the hits were singles. What fraction of the hits were NOT singles?
__________
3. Brittany has 2 brothers and 3 sisters. What fraction of Brittany’s siblings are boys? _______
Draw a shape that represents each of the first four fractions. Name the fraction that is
represented in the last four shapes.
EQUIVALENT FRACTIONS Sept. 27th
Equivalent Fractions are fractions that represent the same amount. If Tom ate ½ of a pizza and
Bonita ate 3/6 of the same-sized pizza, who ate more? Neither of them---they ate the same
amount. The fractions ½ and 3/6 are equivalent!\
One way to find whether fractions are equivalent is to draw pictures of them:
1/10
1/10
1/5
1/10
1/10
1/10
1/5
1/10
1/10
1/5
1/10
1/5
1/10
1/10
1/5
You can see from the picture that 3/5 = 6/10
When both the numerator and the denominator are the same, the fraction is equal to 1.
5/5 = 1
7/7 = 1
a/a = 1
cat/cat = 1
Practice:
For the next problem, write the equivalent fractions to describe the shaded parts of the figures.
Multiplying/ Dividing to find EQUIVALENT FRACTIONS
Sept 28th
You can rename an equivalent fraction by multiplying or dividing both the numerator and
denominator with the same number.
EXAMPLE: Find two fractions that are equivalent to 4/10
4 x 3 = 12
4÷2=2
10 x 3 = 30
10 ÷ 2 = 5
Two Fractions that are equivalent to 4/10 are 12/30 and 2/5.
Practice:
1. Circle all the fractions that are equivalent to ¾.
4/5
Complete the sheet:
6/8
9/12
21/24
½
Fractions in Lowest Terms
A Fraction is in lowest terms when its numerator and denominator have a greatest common factor
(GCF) of 1. In other words, the biggest number that will go into the numerator and denominator
is 1. If there is a bigger number than 1, then you can divide the top and the bottom with that
number.
Example
Write the following fractions in lowest terms:
6/8
7/14
8/11
6/8: the biggest number that goes into 6 and 8 is 2, so divide the top and bottom by 2
6 ÷ 2 = 3 and 8 ÷ 2 = 4 so the answer is ¾
7/14: the biggest number that goes into 7 and 14 is 7, so divide the top and bottom by 7
7 ÷ 7 = 1 and 14 ÷ 7 = 2 so the answer is ½
8/11: the biggest number that goes into 8 and 11 is 1, so 8/11 is in lowest terms
Practice:
For questions 1 through 6, write the fraction in lowest terms.
1. 4/10 = _________________
2. 9/12 ____________________
3. 6/8 ____________________ 4. 9/19 ____________________
5. 5/30 ___________________ 6. 12/28 ___________________
Comparing and Ordering Fractions with Like Denominators
Fractions with like denominators can be compared and ordered by looking at their numerators.
The fraction with the greater numerator is the greater fraction.
⅜<⅝
⅔>⅓
⅕<⅖
⅚ >⅙
EXAMPLE:
Order the fractions from least to greatest.
4/9, 3/9, 8/9, 1/9
1/9, 3/9, 4/9, 8/9
PRACTICE
Directions: For questions 1 through 4, compare the fractions. (use >, <, or =.)
1. 1/8 _______2/8
2. 7/10 ______6/10
3. 4/11 ______1/11
4. 5/12 ______5/12
Directions: For questions 5 through 6, order the fractions from least to greatest.
5. 6/8, 4/8, 7/8, 2/8 ____________________________________________
6. 20/25, 23/25, 19/25, 21/25 ____________________________________
Comparing and Ordering Fractions with Unlike
Oct. 10th
Denominators
To compare fractions with unlike denominators, you need to find equivalent
fractions with a common denominator. Change the fractions so the least common
denominator (LCD) is the denominator for the fractions.
For example: ¾ and 4/6
LCD = 12…change ¾ to 9/12…change 4/6 to 8/12…compare 9/12 with 8/12…
9/12 > 8/12 so ¾ > 4/6
Order: 4/9, 2/3, 2/6, 2/9 from least to greatest
The LCD of 3, 6, and 9 is 18…change all the fractions so they have an 18 on the
bottom….4/9 changes to 8/18…2/3 changes to 12/18…2/6 changes to 6/18…and 2/9
changes to 4/18…order 8/18, 12/18, 6/18, 4/18…..they become 4/18, 6/18, 8/18,
12/18….so the answer is 2/9, 2/6, 4/9, 2/3
PRACTICE:
Use the <, =, > to make the statement true
1. 2/7____ 3/5
2. 7/9 ____ 5/8
3. 6/9 ____ 4/6
4. 7/8 ____ 6/7
5. ½ ____ ⅔
6. ¾ ____8/12
Order from GREATEST to LEAST
7. ¾, 2/3, 5/6, 11/12 ________________
8. ½, 5/8, 7/12, 1/6 _________________
9. 4/9, ¼, 2/3, 5/12 _________________
Improper Fractions
The numerator is greater than the denominator. An improper fraction can be
written as a Mixed Numeral by dividing the numerator by the denominator. Write
the remainder as a fraction using the remainder as the numerator and keeping the
denominator the same. Also, make sure fractions are in lowest terms!
For Example: 28/8 is an improper fraction. Write it as a mixed numeral.
28 ÷ 8 = 3 R4…3 is the whole number…4 is the new numerator…..8 is the
denominator……the answer is 3 4/8…DON’T forget to reduce 4/8…the real answer is
3½
35/7?
Practice: For questions 1 through 4 write the improper fraction as a whole number
or mixed numeral.
1. 81/23
2. 40/8
3. 17/5
Fractions on a Number Line
.
0
. . .
½
1
4. 14/6
Oct. 17th
Adding and Subtracting Like-Fractions Oct. 18th
Like-Fractions: fractions with the same denominator
*ADD (SUBTRACT) the numerators
*LEAVE the denominator the same
*Change to Mixed Numeral (if possible)
*Reduce (lowest terms) the fraction
EXAMPLES:
3/5 + 4/5 = 7/5 = 1 2/5
5/8 – 3/8 = ¼
HW: 16 Problems
1. 5/9 + 2/9
2. 5/10 – 2/10
3. 10/11 – 6/11
4. 7/8 – 5/8
5. 1/3 + 1/3
6. 11/12 – 8/12
7. 7/8 + 5/8
8. 2/5 + 2/5
9. 5/8 + 3/8
10. 2/5 + 4/5
11. ¾ + ¾
12. 8/9 – 3/9
13. 11/12 + 8/12
14. 9/12 – 1/12
15. 4/5 – 1/5
16. 9/12 – 9/12
Adding and Subtracting Unlike-Fractions Oct. 19th
Unlike-Fractions: fractions with different denominators
*Change the Fractions so the denominators are the same
*ADD (SUBTRACT) the numerators
*LEAVE the denominator the same
*Change to Mixed Numeral (if possible)
*Reduce (lowest terms) the fraction
EXAMPLES:
⅓ + ½ LCD = 6 Change the ⅓ to 2/6 and change the ½ to 3/6. Add 2/6
and 3/6. It equals 5/6.
5/6 – 1/4 LCD = 12 Change the 5/6 to 10/12 and change the 1/4 to 3/12.
Add 10/12 and 3/12. It equals 13/12. Which can be converted to 1 1/12.
HW: 16 Problems
1. 2/5 + 1/4
2. 1/2 – 1/4
3. 5/6 – 1/12
4. 8/9 – 5/6
5. 2/3 - 4/9
6. 1/5 + 5/10
7. 2/5 + 5/9
8. 4/5 - 4/10
9. 3/8 + 5/6
10. 1/2 + 1/6
11. 4/7 + 1/3
12. 3/5 + 4/7
13. 5/8 – ¼
14. 2/3 + 3/12
15. 3/5 – 4/10
16. 7/8 – 2/3