joke for the day! “do you want that cut into six slices or eight slices?” a man orders a cheese...
TRANSCRIPT
Joke for the Day!
“Do you want that cut into six slices or eight slices?”
A man orders a cheese pizza.
“Six slices. I’m not hungry enough to eat
eight.”
Fractions, Mixed Numbers, and Decimals
Convert, rewrite, and compare fractions and decimals
Suppose you had a box of red and green marbles and there are twice as many red marbles as green ones. What possibilities are there for the number of marbles in your box?
green marbles
red marbles
Equivalent fractions are different expressions for the same number.
To create equivalent fractions, you must multiply/divide the numerator and the denominator by the same number.
Example 1 Find a fraction equivalent to the given fraction
5
7 5 2
27
10
14
18
24
18
2
3
34
6
8
Since the numerator
and denominator
are prime you should
multiply by a number
Since the numerator and denominator are not prime you can either multiply or divide by a
new number.
5 10 and are equivalent
7 14
18 6 and are equivalent
24 8
Example 2 Determine Whether Fractions are Equivalent
Write the fractions with a common denominator. Then determine if they are equivalent.
4 28
6 42 and
2
3
24
6 2
28
42
14
1
2
34
Since the fractions both express the same number, the fractions are equivalent.
6 20
10 25 and
5
5
0
10 0
6 3
5
20
25
2 0
52
4
0
Since the fractions do not express the same number they are not equivalent.
Thoughts for Review
8 31
5 5
Is an improper fraction because its numerator is larger than its denominator.
Is a mixed number because it contains both a whole number and a fraction.
Convert Improper Fractions to Mixed Numbers
13
5
Divide the numerator by
the denominator
5 1310
03
2Use the quotient
and the remainder to write the mixed
number
2
3
5
Convert Mixed Number to Improper fraction
72
37 23
3
23
3
Fractions <to> Decimals
To write a fraction as a decimal, divide the numerator by the denominator.
1
4 4 1.00
.2
8
20
5
200
.25
You try it!
9
5 1.8
5 9.01.8 2
3
.
.66
3 2 00.66
This is called a terminating
decimal because it
ends
This is called a repeating decimal because it repeats the same pattern
Decimals to FractionsTo write a decimal as a fraction, use the place value furthest to the right as your denominator. Simplify if necessary
0.018 = 18 9
1000 500
-0.6 = 6 3
10 5
1.55 = 55 11
1 1100 20
You try it!
0.45
-0.25
5.09
9
20
1
4
95
100
Compare and Order Rational Numbers
• To compare fractions you must first convert them to the same denominator– Then compare the numerators
• To compare decimals, line up the decimal points.
• To compare a fraction to a decimal, write the fractions as decimals and then compare the decimals.
Compare the fractions. Write < or >.
7 5
9 8
Write both fractions with a common denominator.
7 7 8 56
9 9 8 72
5 5 9 45
8 8 9 72
56 45 7 5Since is greater than , > .
72 72 9 8
Compare the fractions. Write < or >.
2 3
5 7 Write both fractions with a
common denominator. Put the negative signs in
the numerators
2 2 7 14
5 5 7 35
3 3 5 15
7 7 5 35
14 15 2 3, so
35 35 5 7
Compare the decimals. Write < or>.
Line up the decimal points. The tenths and hundredths are the same. Compare the thousandths: 7 > 5
Ordering Fractions and Decimals
Order the numbers from least to greatest.
First convert all fractions to decimals.
Put decimals in order from least to greatest.
Therefore…