6th Grade Adding and Subtracting Multi-Digit Decimals
What is 5.67 + 8.34?
14.01
What is 3.2 × 2.5?
8.0
What is 12.6 ÷ 3?
4.2
Estimate the quotient of 365 ÷ 12.
About 30 (since 360 ÷ 12 = 30)
Sarah bought 2.5 pounds of grapes at $3.20 per pound. How much did she pay in total?
$8.00
What is the sum of 15 and 27? (Show using a number line)
42
You have 10 dollars. You buy a book for 4 dollars. How much money do you have left?
6 dollars
What is the sum of -4 and 9?
5
What is 1/4 + 3/4?
1
What is the sum of the interior angles in any triangle?
180 degrees
What is the sum of the interior angles of any triangle?
180°
What is an exterior angle in a triangle?
An angle formed by extending one side of a triangle
What postulate is used to determine if two triangles are similar by using only two angles?
Angle-Angle (AA) Similarity Postulate.
What are alternate interior angles?
Angles that lie between two parallel lines on opposite sides of a transversal and are congruent.
If the exterior angle of a triangle measures 110° and one of the opposite interior angles is 50°, what is the measure of the other interior angle?
60°.
What is 12.58 - 6.79?
5.79
4.7 by 1.3.
6.11
Divide 24.48 by 6.
4.08
What is the estimated quotient of 75.3 ÷ 4?
About 19 (since 76 ÷ 4 = 19)
A book costs $12.99. If you buy 3 books, how much will it cost?
$38.97
What is 58 - 32? (Show using a number line)
26
You are planning a party and need 24 cupcakes. You already have 10 cupcakes. How many more cupcakes do you need?
14 cupcakes
What is -12 + (-8)?
-20
What is 2/5 - 1/5?
1/5
You have $15, but you spend $25. How much money do you have now?
-$10
In a triangle, if two angles are 45° and 75°, what is the measure of the third angle?
60°
The measure of an exterior angle is 100°, and one of the opposite interior angles is 60°. What is the measure of the other opposite interior angle?
40°
How can you tell if two triangles are similar based on their angles?
If two angles of one triangle are congruent to two angles of another triangle, the triangles are similar.
True or False: Same-side interior angles are supplementary
True
Solve for x if two alternate interior angles are given as x + 15° and 75°
x = 60°.
If you add 4.5 and 12.75, what is the result?
17.25
What is 6.05 × 3.6?
21.78
What is 45.6 ÷ 4?
11.4
Estimate the quotient of 150 ÷ 9.
About 17 (since 153 ÷ 9 = 17)
A truck travels 70.5 miles in 3 hours. How many miles does it travel per hour?
23.5 miles per hour
Add 123 and 59. What is the result? (Show using a number line)
182
You have 35 yards of fabric. You use 22 yards to make a dress. How much fabric is left?
13 yards
If the temperature is -3 degrees and it drops by 6 degrees, what is the new temperature?
-9 degrees
Add 1/2 and 3/4. What is the sum?
5/4 or 1 1/4
A car is traveling 60 miles south. After 30 minutes, it travels 40 miles further south. How far south is the car now?
100 miles
Explain why the sum of the interior angles of a triangle is always 180°
The angles add up to form a straight line when extended
True or False: The measure of an exterior angle in a triangle is equal to the sum of the two opposite interior angles.
True.
If two triangles have angle measures of 40°, 60°, and 80°, are they similar?
Yes, because they have identical sets of angles.
If two parallel lines are cut by a transversal, and one of the alternate exterior angles measures 120°, what is the measure of the other alternate exterior angle?
120°.
In a triangle, if one angle measures x, another angle is 2x, and the third angle is 3x, what are the values of the angles?
30°, 60°, and 90°.
What is the result of 15.642 - 9.503?
6.139
12.36 × 1.9.
23.444
15.75 by 5.
3.15
If you divide 67.8 by 5, what is the estimated quotient?
About 14 (since 70 ÷ 5 = 14)
A package weighs 5.25 pounds. If the shipping cost is $1.50 per pound, how much will the shipping cost?
$7.88
If you have 45 apples and you give away 17, how many do you have left? (Show using a number line)
28
A train travels 48 miles per hour. How far will it travel in 3 hours?
144 miles
What is -7 - 4?
-11
What is -3/8 + 1/2?
1/8
You need to climb to a height of 50 feet, but you're currently 10 feet below the ground. How many feet do you need to climb?
60 feet
True or False: In any triangle, the sum of the angles can be less than 180 degrees
False
Find the measure of an exterior angle if one of the interior opposite angles is 50° and the other is 70°.
120°.
Two triangles are similar. The first triangle has side lengths 3 cm, 4 cm, and 5 cm. The second triangle has a side length of 6 cm for the corresponding side of 3 cm. Find the lengths of the other two sides of the second triangle.
The scale factor between the triangles is 63=2\frac{6}{3} = 236=2.
The second triangle's corresponding sides will be 2 times the lengths of the first triangle:
4×2=84 \times 2 = 84×2=8 cm
5×2=105 \times 2 = 105×2=10 cm
The side lengths of the second triangle are 6 cm, 8 cm, and 10 cm.
What type of angle pairs are formed when two parallel lines are cut by a transversal?
Corresponding, alternate interior, alternate exterior, and same-side interior angles.
f a linear pair includes angles measuring (2x + 10)° and (3x - 20)°, find the value of x.
x = 38°.
13.005 + 7.89?
20.895
What is the product of 2.75 × 4.12?
11.33
What is the quotient of 48.24 ÷ 3?
16.08
What is the estimated quotient of 101.25 ÷ 8?
About 13 (since 104 ÷ 8 = 13)
Tom needs to divide 225.75 gallons of paint equally into 5 cans. How many gallons of paint will go into each can?
45.15 gallons
What is 202 + 456?
658
You earn $50 per week. How much will you earn in 8 weeks?
$400
What is -15 + 20?
5
What is -2/3 - 4/9?
-10/9 or -1 1/9
The temperature was -5°C in the morning and rose 12°C during the day. What is the temperature now?
7°C
A triangle has angles measuring 45°, 2x + 20°, and 3x - 10°. Find the value of x and the measure of each angle.
The sum of the angles is 180°: 45+(2x+20)+(3x−10)=18045 + (2x + 20) + (3x - 10) = 18045+(2x+20)+(3x−10)=180
Simplifying: 45+2x+20+3x−10=18045 + 2x + 20 + 3x - 10 = 18045+2x+20+3x−10=180
5x+55=1805x + 55 = 1805x+55=180
5x=1255x = 1255x=125
x=25x = 25x=25
The angles are: 45°, 70°, and 65°.
In a triangle, one exterior angle is 120°, and one of the interior opposite angles is 50°. The other two interior angles of the triangle are in the ratio of 2:3. Find the measure of all three interior angles.
The exterior angle is 120°, so the sum of the two interior opposite angles is 180°−120°=60°180° - 120° = 60°180°−120°=60°.
The two remaining angles are in a 2:3 ratio, so let the angles be 2x2x2x and 3x3x3x.
2x+3x=602x + 3x = 602x+3x=60, so 5x=605x = 605x=60, thus x=12x = 12x=12.
The two angles are 24° and 36°
The interior angles of the triangle are 50°, 24°, and 36°.
Name a real-world example where similar triangles are used
Answers may vary: e.g., shadow measuring to find the height of a tree or building.
If two parallel lines are cut by a transversal, and one of the corresponding angles measures 75°, what is the measure of the alternate interior angle, same-side interior angle, and alternate exterior angle?
Corresponding angles are congruent, so the alternate interior angle is also 75°.
Same-side interior angles are supplementary, so 180°−75°=105°180° - 75° = 105°180°−75°=105°.
Alternate exterior angles are congruent, so the alternate exterior angle is also 75°.
Solve for x in the following equation: 2x+15=3x−102x + 15 = 3x - 102x+15=3x−10. Then, use the value of x to find the measure of the unknown angle in a triangle where the other two angles are (2x+15)°(2x + 15)°(2x+15)° and (3x−10)°(3x - 10)°(3x−10)°.