Download Ch. 6 Benchmark Assessment Tuesday, February 19th 6

Ch. 6 Benchmark Assessment
Tuesday, February 19th
6-1 Estimating Fractions
- Use the benchmarks 0, ½, and 1 to round fractions
- Round mixed numbers to the nearest whole number
Examples:
Estimate. 4
7
1
+2 .
8
3
Estimate
3 9
+ .
8 10
7
1
4  2  5 2  7
8
3
3
1
9
is about , and
is about 1.
8
2
10
3 9
1
1
So,    1  1
8 10
2
2
The sum is about 7.
The sum is about 1
1
.
2
Practice:
1
 19 =
6
7 5
 =
9 6
11 1
- =
12 8
6-2 Adding and Subtracting Fractions
- Like fractions have a common denominator
- Unlike fractions have do not have a common denominator
- When adding/subtracting like fractions add or subtract the numerators and
put it over the denominator.
- When adding/subtracting unlike fractions, find a common denominator,
rename the fractions with a common denominator, add or subtract the
numerators and put it over the denominator.
Examples:
Subtract
11 4
 . Write in simplest form.
12 12
11 4 11  4
 
12 12
12
=
Add
7
12
Subtract the numerators.
Write the difference over the denominator.
1 1
+ . Write in simplest form.
4 12
The least common denominator of 4 and 12 is 12.
1 1 3 3


4 4  3 12
1
Rename 4 using the LCD.
3
1 4
1
or
+
=
12 12 12
3
Practice:
2 1
 =
3 4
3 1
+
8 8
MAGAZINES In Monday’s mail, Dave received a stack of magazines measuring
Tuesday, he received magazines measuring
5
inch in height. On
8
2
inch in height. What is the total height of the stack of
3
magazines Dave received on Monday and Tuesday?
6-3 Adding and Subtracting Mixed Numbers
- To add mixed numbers, add the fractions and whole numbers separately.
Rename the fractions if necessary and simplify.
- To subtract mixed numbers, make sure the first fraction is larger than the
second fraction. If it is not, rename the fraction by writing an improper fraction
using the whole number.
Examples:
7
1
+ 3 . Write in simplest form.
12
12
7
1
8
2
6 3  9
or 9
Add the whole numbers and fractions separately. Simplify.\
12
12
12
3
1
3
Find 5  2 .
4
4
1
Rename 5 before subtracting.
4
1
4 1
5
1
5
Rename 5 as 4 .
5  4  or 4
4
4 4
4
4
4
5
3
2
1
4  2  2 or 2
First subtract the whole numbers and then the fractions. Simplify.
4
4
4
2
1
3
1
So, 5  2  2 .
4
4
2
Add 6
Practice:
1
1
8 6 =
5
2
Danielle needs 3
7
3
7 3
8
4
2
3
feet of trim to complete the blouse she is making and 1 feet of the same trim to
3
4
complete the matching skirt. What is the total amount of trim Danielle needs to complete the outfit?
6-4 Multiplying Fractions and Mixed Numbers
- To multiply fractions, multiply the numerators and multiply the denominators.
Then simplify.
- To multiply mixed numbers, rewrite your mixed number as an improper
fraction then multiply.
Examples:
1 1
 . Write in simplest form.
4 5
1 1 1 1
Multiply the numerators and multiply the denominators.
 
4 5 45
1
=
Simplify.
20
1
2
Find  2 . Write in simplest form.
3
5
Multiply
4
1
2 1 12
2  
3
5 3 5
Rename 2
2
12
as an improper fraction,
.
5
5
1
1 4
=
1 5
4
=
5
Multiply.
Simplify.
Practice:
3
2
=
5
James uses
he need?
3 2

4 7
2
×
×4
cups flour to make one pie. If he is making four pies for a bake sale, how much flour will
6-5 Solving Equations with Fractions
- Two numbers whose product is 1 are called multiplicative inverses or
reciprocals
- Multiplication Property of Equality: If you multiply each side of an equation by
the same nonzero number, the two sides remain equal.
Examples:
3
.
8
3
8
3 8
Multiply by to get the product 1.
 1
8
3
8 3
3
8
2
The multiplicative inverse of is , or 2 .
8
3
3
Find the multiplicative inverse of
d
Solve 6 = 4. Check your solution.
d
4
6
d
6  46
6
d = 24
The solution is 24.
Write the equation.
Multiply each side of the equation by 6.
Simplify.
Practice:
Solve.
5
x = −10
8
=2
=3