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Math 5 Reviewer First Term Examination
Topic: Convert 12-hour time to 24-hour time, and vice-versa. 12-hour clock divides the day into two periods: AM (ante meridiem) for midnight to noon and PM (post meridiem) for noon to midnight. Hours run from 1 to 12, repeating twice a day. Example: Clock A shows 10:10 am and clock B shows 4:00 pm 24-hour clock, also called military time, counts hours continuously from 00:00 (midnight) to 23:59 (11:59 PM). Example: In the clock A, instead of writing 10:10 am, you will write 10:10 only if the time is in AM while in clock B, instead of writing 4:00 pm, you will write 16:00. To convert 12-hour time to 24-hour time, and vice-versa, you will use the table: 24-hour Format 12-hour format 12:00 12:00 noon 13:00 1:00 pm Clock A Clock B
Example: a) Covert 4:50 am to 24-hour format. c) Convert 23:19 to 12-hour format. Answer: 4:50 Answer: 11:19 pm b) Convert 6:36 pm to 24-hour format. d) Convert 8:30 to 12-hour format Answer: 18:36 Answer: 8:30 am Topic: Perform three or more different operations by applying the GMDAS rules. G (group) M (multiply) D (divide) A (addition) S (subtraction) Rules: 1. Do operations inside the grouping symbol first. Multiple Grouping Symbols: 14:00 2:00 pm 15:00 3:00 pm 16:00 4:00 pm 17:00 5:00 pm 18:00 6:00 pm 19:00 7:00 pm 20:00 8:00 pm 21:00 9:00 pm 22:00 10:00 pm 23:00 11:00 pm 24-hour Format 12-hour format 00:00 12:00 midnight 01:00 1:00 am 02:00 2:00 am 03:00 3:00 am 04:00 4:00 am 05:00 5:00 am 06:00 6:00 am 07:00 7:00 am 08:00 8:00 am 09:00 9:00 am 10:00 10:00 am 11:00 11:00 am
a) parenthesis ( ) b. brackets [ ] c. Braces { } 2. Next, multiply and divide in order in which they occur. 3. Finally, add and subtract in order which they may occur. Example 1: Solve 20 + 4 x (18-9) ÷ 3 G: Perform operations inside the grouping symbol first. 20 + 4 x (18-9) ÷ 3 20 + 4 x 9 ÷ 3 MD: Multiply or divide from left to right. 20 + 4 x 9 ÷ 3 20 + 36 ÷ 3 20+ 12 AS: Add or subtract from left to right. 20+ 12 32 Therefore, 20 + 4 x (18-9) ÷ 3 is 32. Example 2: Solve 80 ÷ 10 + 5 x (7 + 4 x 5) G: Perform operations inside the grouping symbol first.
80 ÷ 10 + 5 x (7 + 4 x 5) = multiply first, then add 80 ÷ 10 + 5 x (7 + 20) 80 ÷ 10 + 5 x 27 MD: Multiply or divide from left to right. 80 ÷ 10 + 5 x 27 = divide then multiply 8 + 5 x 27 8 + 135 AD: Add or subtract from left to right. 8 + 135 143 Therefore, 80 ÷ 10 + 5 x (7 + 4 x 5) =143 Topic: Multiply fractions using models. To multiply fractions using visual models, a) Represent the first fraction bars. Shade the fraction being represented. b) Represent the second fraction by cutting the model in the opposite direction. c) Count the number of parts shaded twice. Example 1: Find the product of 1 3 x 2 5. Represent the first fraction bars. Shade the fraction being represented Represent first 1 3
It has 15 parts in all. There are 2 parts shaded twice. Represent the second fraction by cutting the model in the opposite direction. Represent 2 5 Count the number of parts shaded twice. The area shaded twice will be the numerator while the number of all the parts will be the denominator.
Therefore, 1 3 x 2 5 = 2 15 Example 2: Multiply 2 4 x 4 6 using visual model. Represent the first fraction bars. Shade the fraction being represented Represent first 2 4 Represent the second fraction by cutting the model in the opposite direction. Represent 4 6
There are 24 parts in all. Count the number of parts shaded twice. The area shaded twice will be the numerator while the number of all the parts will be the denominator. Therefore, 2 4 x 4 6 = 8 24 Topic: Multiply a fraction by a fraction. To multiply fraction, multiply the numerators and denominators to get the product. Express the product in lowest terms if possible. Example 1: 4 5 X 5 9 = 20 45 Example 2: 3 8 X 6 10 = 18÷2 80÷2 or 9 40 In multiplying a fraction and a whole number, convert the whole number to a fraction, multiply the numerators and denominators, and simplify the product. There are 8 parts shaded twice.
Example 1: Example 2: Find the product of 6 12 X 3. 6 12 X 3 1= 18 12 or 1 6 12 or 1 1 2 In multiplying other fractions, you can use cancellation or cross division to get the product easily. Example: What is the product of 15 30 x 2 3 ? Solution: 15 30 x 2 3 = 3 15 or 1 5 Topic: Solve multi-step problems involving multiplication of fractions that may or may not also involve addition or subtraction of fractions. Example: Miguel is preparing fruit salad for a party. He needs 5 6 of a kilogram of mangoes for one full bowl. He prepares 2 3 of a bowl. Later, he realizes he added too much and removes 1 4 kilogram of mangoes from the mixture. How many kilograms of mangoes are left in the bowl? 𝐷𝑖𝑣𝑖𝑑𝑒 18 𝑏𝑦 12. 3 1 1 15
Four-step in answering worded problem: 1. What is asked? The number of mangoes left in the bowl. 3. What is the number sentence? 5 6 x 2 3 - 1 4 = n 2. What are the given facts? a) 5 6 kilogram of mangoes needed for one full bowl of fruit salad. b) 2 3 fruit salad Miguel prepared in a bowl c) 1 4 kilogram of mangoes removed from the mixture Solution: a) Amount used for partial bowl 5 6 × 2 3 = 10 18 = 5 9 Miguel uses 5 9kilogram of mangoes. b) Subtract the removed amount 5 9 − 1 4 = 20 36 − 9 36 = 11 36 After removing, Miguel has 11 36 kilogram of mangoes left in the bowl. Topic: Identify the height of a parallelogram, triangle, and trapezoid, in different orientations. The height of any parallelogram, triangle, or trapezoid is always the perpendicular distance to the chosen base, even when the figure is rotated or when the height falls outside the shape.
Height (or altitude) is always perpendicular to the base. Height is not always vertical; it depends on the chosen base. Height of a Parallelogram Definition: The height is the perpendicular distance between one side (base) and the opposite parallel side. Height of a Triangle Definition: The height is the perpendicular distance from a vertex to the line containing the opposite side (base). Height of a Trapezoid Definition: The height is the perpendicular distance between the two parallel sides (bases).
Topic: Area of a Trapezoid Trapezoid- is a quadrilateral with one pair of opposite parallel sides. If two bases of different measures and a height. The area of a trapezoid is half the product of the height and the sum of the bases. A= b1 + b2 2 x h Examples: A) Given: b1= 5 cm; b2 = 7cm and h= 6cm B) A= b1 + b2 2 x h A= b1 + b2 2 x h = 5cm+7cm 2 x 6 cm = 6 cm+10 cm 2 x 7 cm = 12 cm 2 x 6 cm = 16 cm 2 x 7 cm = 6 cm x 6 cm = 8 cm x 7 cm A = 36 cm2 A = 56 cm2 Topic: Area of triangle The area of a triangle is the 2D space enclosed by its three sides, measured in square units (cm², m², in²). A rectangle cut diagonally from corner to corner always produces two identical triangles — each exactly half the rectangle's area. So, if a rectangle has area b × h, each triangle is 6 cm 10 cm 7 cm
½ × b × h. Formula: A= ½ × b × h or 𝑏𝑥ℎ 2 Example 1: A= 𝑏𝑥ℎ 2 A= 30cm² 2 A= 6𝑐𝑚𝑥5𝑐𝑚 2 A= 15 cm2 Example 2: A triangle has base length of 14 cm. The perpendicular height is 9 cm. Find the area of the triangle. Solution: A = b × h 2 A= 14 cm x 9 cm 2 A= 126 cm2 2 A= 63 cm2 Topic: Area of Rectangle The area of a rectangle is defined as the total region covered by it. It is the product of its 2 adjacent sides, i.e., length and width. We measure it in square units (cm², m², in²).
Example: A parking lot is to be constructed in a space in the shape of a rectangle. What is the area of the parking lot? Solution: A=l x w A=20 m x 12m A= 240 m2 l=20 m w=12 m