Weekly Math Review Q1 5 Answer Key
Introduction
Welcome to the answer key for the Weekly Math Review Q1 5! In this article, we will provide you with the answers and explanations for the math problems covered in the review. Whether you are a student looking to check your work or a teacher seeking guidance for grading, this answer key will be a valuable resource for you. So let's dive right in!
Problem 1: Algebraic Expressions
Answer: The value of the expression is 22.
Explanation: To solve this problem, we substitute the given values into the expression:
2 * (3 + 5) - 4 = 2 * 8 - 4 = 16 - 4 = 12
So the value of the expression is 22.
Problem 2: Proportions
Answer: The value of x is 10.
Explanation: In a proportion, the product of the means is equal to the product of the extremes. So we can set up the equation:
5/7 = x/14
Cross-multiplying, we get:
7x = 5 * 14
7x = 70
x = 10
Therefore, the value of x is 10.
Problem 3: Geometry - Perimeter
Answer: The perimeter of the rectangle is 30 units.
Explanation: To find the perimeter of a rectangle, we add up the lengths of all its sides. In this case, we have two sides of length 7 units and two sides of length 8 units:
7 + 7 + 8 + 8 = 30
So the perimeter of the rectangle is 30 units.
Problem 4: Fractions
Answer: The sum of the fractions is 7/12.
Explanation: To add fractions, we need to find a common denominator. In this case, the common denominator is 12. We then convert each fraction to have a denominator of 12:
1/4 = 3/12
1/6 = 2/12
Now we can add the fractions:
3/12 + 2/12 = 5/12
Therefore, the sum of the fractions is 7/12.
Problem 5: Word Problems - Percentages
Answer: The discount amount is $12.
Explanation: To find the discount amount, we need to calculate 20% of the original price. We can do this by multiplying the original price by 0.2:
0.2 * $60 = $12
Therefore, the discount amount is $12.
Problem 6: Algebraic Equations
Answer: The value of x is 4.
Explanation: To solve this equation, we isolate the variable x on one side:
3x - 6 = 6
Adding 6 to both sides, we get:
3x = 12
Dividing both sides by 3, we find:
x = 4
Therefore, the value of x is 4.
Problem 7: Decimals
Answer: The product of the decimals is 0.24.
Explanation: To multiply decimals, we multiply them as if they were whole numbers and then place the decimal point in the product. In this case:
0.4 * 0.6 = 0.24
Therefore, the product of the decimals is 0.24.
Problem 8: Measurement - Volume
Answer: The volume of the cylinder is 113.04 cubic units.
Explanation: The formula for the volume of a cylinder is V = πr^2h, where r is the radius and h is the height. Substituting the given values:
V = 3.14 * 3^2 * 4
V = 3.14 * 9 * 4
V = 113.04
Therefore, the volume of the cylinder is 113.04 cubic units.
Problem 9: Word Problems - Ratios
Answer: The ratio of boys to girls is 2:3.
Explanation: To find the ratio of boys to girls, we divide the number of boys by the number of girls:
6 / 9 = 2 / 3
Therefore, the ratio of boys to girls is 2:3.
Problem 10: Algebraic Expressions
Answer: The value of the expression is 17.
Explanation: To solve this problem, we substitute the given values into the expression:
3 * (4 + 5) - 2 = 3 * 9 - 2 = 27 - 2 = 25
So the value of the expression is 17.
Problem 11: Percents
Answer: The percent increase is 20%.
Explanation: To find the percent increase, we calculate the difference between the new value and the original value, divide it by the original value, and multiply by 100. In this case:
(8 - 5) / 5 * 100 = 3/5 * 100 = 60/5 = 12
Therefore, the percent increase is 20%.
Problem 12: Geometry - Area
Answer: The area of the triangle is 12 square units.
Explanation: The formula for the area of a triangle is A = (base * height) / 2. Substituting the given values:
A = (6 * 4) / 2 = 24 / 2 = 12
Therefore, the area of the triangle is 12 square units.
Problem 13: Word Problems - Fractions
Answer: The total number of pies baked is 3.
Explanation: To solve this problem, we need to find a common denominator for the fractions. The common denominator is 12. We then convert each fraction to have a denominator of 12:
1/4 = 3/12
1/6 = 2/12
Now we can add the fractions:
3/12 + 2/12 = 5/12
Finally, we divide the total number of pies by the fraction:
15 / (5/12) = 15 * (12/5) = 15 * 12/5 = 180/5 = 36/1 = 36
Therefore, the total number of pies baked is 36.
Problem 14: Algebraic Equations
Answer: The value of x is 3.
Explanation: To solve this equation, we isolate the variable x on one side:
2(x - 1) = 6
Dividing both sides by 2, we get:
x - 1 = 3
Adding 1 to both sides, we find:
x = 3
Therefore, the value of x is 3.
Problem 15: Word Problems - Decimals
Answer: The total cost is $26.40.
Explanation: To find the total cost, we multiply the quantity by the cost per unit:
3.5 * $7.20 = $26.40
Therefore, the total cost is $26.40.
Problem 16: Geometry - Angles
Answer: The measure of angle x is 60 degrees.
Explanation: The sum of the interior angles of a triangle is always 180 degrees. We can set up the equation:
90 + 30 + x = 180
Combining like terms, we get:
120 + x = 180
Subtracting 120 from both sides, we find:
x = 60
Therefore, the measure of angle x is 60 degrees.
Problem 17: Word Problems - Measurement
Answer: The difference in temperature is 25 degrees Fahrenheit.
Explanation: To find the difference in temperature, we subtract the initial temperature from the final temperature