YR 7: WK 3 TOPIC: TIME 8/9/2023 10:23:54 AM EXAMPLE Calculate the number of seconds in: (a) 5 mins (b) 7 hrs 25 mins (c) 12.15 hrs SOLUTION (b) 7hrs 25mins = 7hrs + 25mins (a) 5 mins = 5 x 1min = 7 x 1hr + 25 x 1min = 7 x 60mins + 25 x 60secs = 5 x 60 secs = 7 x 60 x 1min + 25 x 60secs = 7 x 60 x 60secs + 25 x 60secs = 300 secs = 25200secs + 1500secs = 26700secs
YR 7: WK 3 TOPIC: TIME 8/9/2023 10:23:54 AM (c) 12.15hrs = 12.15 x 1hr = 12.15 x 60mins = 12.15 x 60 x 1min = 12.15 x 60 x 60secs = 43740secs
YR 7: WK 3 TOPIC: TIME 8/9/2023 10:23:54 AM EXAMPLE Express in hours and minutes: (a)(i) 150 minutes (ii) 225 minutes (b) How many minutes are in 4 hours? SOLUTION (a)(i) 150 = 2 ������������������ 30 (b) 4hrs = 4 x 1hr 60 = 4 x 60mins = 240mins = 2hrs 30mins (ii) 225 = 3 ������������������ 45 60 = 3hrs 45mins
YR 7: WK 3 TOPIC: TIME 8/9/2023 10:23:54 AM EXAMPLE Find the sum of 4 days 12 hours 20 mins, 1 day 20 hours 45 mins, 16 hours 6 mins. SOLUTION dy hr min 4 12 20 20 45 +1 16 01hr 6 0 11mins 7dys
YR 7: WK 3 TOPIC: TIME 8/9/2023 10:23:54 AM EXAMPLE Find the sum of 3hrs 40mins, 2 hrs 25 mins, 28mins , 1 hr 35mins. SOLUTION min 40 hr 25 3 28 2 35 +0 1 8hrs 8mins
YR 7: WK 3 TOPIC: TIME Evaluation 8/9/2023 10:23:55 AM Question 1 New General maths Bk 1, Pg 3, Ex 1b Nos Question 2 5a, 5b, 5c and 5d. Question 3 Question 4
YR 7: WK 3 TOPIC: TIME 8/9/2023 10:23:55 AM WORD PROBLEMS ON TIME EXAMPLE 1 A student did 3hours 35minutes studies every day in the month of June. How many hours and minutes has he done in total? SOLUTION hr min 3 35 x 30 30mins 107 hrs
YR 7: WK 3 TOPIC: TIME 8/9/2023 10:23:55 AM EXAMPLE 2 In an examination, equal time must be spent on each question. There are 3 questions altogether. If the total time allowed is 2 hours 30minutes, how much time does it take (in minutes) to solve each question? SOLUTION 2hrs 30mins = 2hrs + 30mins = 2 x 1hr + 30mins = 2 x 60mins + 30mins = 120mins + 30mins = 150mins 3 questions = 150 mins 150 1 question = 3 = 50������������������������
PHIDEL GROUP OF SCHOOLS, LAGOS Any Questions?
YR 7: WK 4 8/9/2023 10:23:56 AM LESSON OBJECTIVES: WEEK 4 TOPIC At the end of the FRACTIONS lesson, students should be able to: HOME PAGE Define fractions KEY NOTES: State and identify the fractions, magnitude types of fractions Convert improper fraction to mixed fraction and vice versa. find the equivalents of a fraction. Arrange fractions in order of magnitude
YR 7: WK 4 TOPIC: FRACTIONS 8/9/2023 10:23:56 AM FRACTIONS A Fraction is a part of a whole. A fraction has two(2) parts: a & b ������ numerator ������ denominator TYPES OF FRACTIONS Fractions are either proper, improper or mixed. (i) Proper Fractions : This is a common fraction having its denominatorE.g74 3 numerator less than its , 5 (ii) Improper Fractions : This is a common fraction having its denominatorE.g151 4 numerator greater than its , 3 (iii) Mixed Numbers: This type of fraction is in the form of an integer and a fraction i.e it has two(2) parts: a whole number, and a fraction (usually a proper fraction) E.g547 , 253
YR 7: WK 4 TOPIC: FRACTIONS 8/9/2023 10:23:56 AM CONVERSION OF IMPROPER FRACTIONS TO MIXED NUMBERS EXAMPLES Express the following improper fractions as mixed numbers (a) 8 (b) 229 5 100 SOLUTION (a) 8 = 8 ÷ 5 = 1 ������������������ 3 5 Ans = 153 (b) 229 = 229 ÷ 100 = 2 ������������������ 29 100 Ans = 2 29 100
YR 7: WK 4 TOPIC: FRACTIONS 8/9/2023 10:23:57 AM CONVERSION OF MIXED NUMBERS TO IMPROPER FRACTIONS EXAMPLES Let A������������ be the general form of a mixed number, where A = whole number part ������ = fractional part. ������ To convert to improper fraction, the following steps are followed: (1) Multiply the denominator of the fractional part by the whole number (2) Add the numerator of the fractional part to the result in (1) above. (3) Express the result in (2) above as the numerator of the improper fraction with the original denominator of the fractional part as the same denominator.
YR 7: WK 4 TOPIC: FRACTIONS 8/9/2023 10:23:57 AM ������ ������ = ������ × ������ + ������ ������ ������ EXAMPLES Express the following mixed fractions as improper fractions ������ ������ ������ 5 2 ������ 7 5 SOLUTION ������ 5 ������ = 5 × 2 + ������ ������ 7 ������ = 7 × 5 + ������ 2 2 5 5 = 10 + ������ = 35 + ������ 2 5 = = ������������ ������������ 2 5
YR 7: WK 4 TOPIC: FRACTIONS Evaluation 8/9/2023 10:23:57 AM Question 1 New General Question 2 maths Bk 1, Question 3 Pg 23, Ex 4a, Nos 1e, 1i, 1m, 1q, 2e and 2i Question 4
YR 7: WK 4 TOPIC: FRACTIONS 8/9/2023 10:23:57 AM EQUIVALENT FRACTIONS Two or more fractions are said to be equivalent if they have the same values. Equivalent fractions can be obtained by multiplying or dividing the numerator and the denominator by the same number. FINDING EQUIVALENT FRACTIONS To obtain an equivalent fraction with larger numerators and denominators, simply multiply both the numerator and the denominator of the given fraction by the same number.
YR 7: WK 4 TOPIC: FRACTIONS 8/9/2023 10:23:58 AM for example, to change 1 into 2 simply multiply the numerator and the 2 4 denominator by 2 i.e 1 = 1 × 2 = 1× 2 = 2 2 2 2 2× 2 4 To continue the sequence simply multiply by 3, 4, 5, 6, 7……..These numbers are called multipliers ×3 ×2 1 = 2 = 3 . 1 2 3 4 2 4 6 2 4 6 8 ×2 Hence: = = = … … ×3
YR 7: WK 4 TOPIC: FRACTIONS 8/9/2023 10:23:58 AM To obtain an equivalent fraction with smaller numerators and denominators, simply divide both the numerator and the denominator of the given fraction by the same number. for example, to change 6 into 3 simply divide the numerator and the 12 6 denominator by 2 i.e 6 = 6÷2 = 3 12 12 ÷ 2 6
YR 7: WK 4 TOPIC: FRACTIONS 8/9/2023 10:23:59 AM To obtain other equivalent fractions divide by 2, 3 and 6. ÷3 ÷2 6 3 2 1 12 6 4 2 6 = 3 = 2 . Hence: = = = … … 12 6 4 ÷2 ÷3
YR 7: WK 4 TOPIC: FRACTIONS 8/9/2023 10:23:59 AM EXAMPLE 1 Find the missing number 3 = 15 5 SOLUTION Divide the second denominator by the first denominator to obtain the multiplier i.e 15 ÷ 5 = 3 3×3 = 9 5×3 15 Ans = 9
YR 7: WK 4 TOPIC: FRACTIONS 8/9/2023 10:24:00 AM EXAMPLE 2 Find the missing number 4 = 16 28 SOLUTION Divide the second numerator by the first numerator to obtain the divisor i.e 16 ÷ 4 = 4 ÷4 4 = 16 7 28 ÷4 Ans = 7
YR 7: WK 4 TOPIC: FRACTIONS 8/9/2023 10:24:00 AM EXAMPLE 3 Find the missing numbers 10 = 12= 20 = 80 50 SOLUTION Use 20 as the reference fraction because both its numerator and 50 denominator are given. 20 2 i.e 50 = 5 ×2 ×6 × 16 4 = 2 12 = 2 2 = 32 10 5 30 5 5 80 ×2 ×6 × 16 The missing numbers are = 4, 30 and 32
YR 7: WK 4 TOPIC: FRACTIONS>> Evaluation 8/9/2023 10:24:00 AM Question 1 Find the missing numbers ¾ = 6/8 = 15/A = 24/B = C/28 = D/100 = E/24 Question 2 Find the missing numbers 3 48 8 = Question 3 Find the missing numbers 5 = 36 9 Question 4 Find the missing numbers 5 20 6 =
YR 7: WK 4 TOPIC: FRACTIONS 8/9/2023 10:24:01 AM ORDERING OF FRACTIONS It is much easier to compare the size of fractions, when they have the same denominator. EXAMPLE 1 Which is the larger fraction: 5 or 6 ? 7 8 SOLUTION LCM of the denominators (7 and 8) is 56 5 , 6 7 8 40 , 42 42 is greater than 40 56 ∴ 6 is greater than 5 8 7
YR 7: WK 4 TOPIC: FRACTIONS 8/9/2023 10:24:01 AM EXAMPLE 2 Arrange the following fractions in descending order 2 , 3 , 1 , 5 3 8 4 6 SOLUTION LCM of the denominators (3, 8, 4 and 6) is 24 2 , 3 , 1 , 5 3 8 4 6 16, 9, 6, 20 24 ∴ ������ℎ������ ������������������������������������������������������ ������������ ������������������������������������������������������������ ������������������������������ ������������������������������: 5 , 2 , 3 ������������������ 1 6 3 8 4
YR 7: WK 4 TOPIC: FRACTIONS>> Evaluation 8/9/2023 10:24:01 AM Question 1 Which of the following fraction is larger? 2/5 or 5/7 Question 2 Which of the following fraction is larger? 5/6 or 4/9 Question 3 Arrange the following fractions in ascending order 3/5, 8/15, 17/30 Question 4 Arrange the following fractions in ascending order 3/5, 5/8, 7/10, 13/20.
PHIDEL GROUP OF SCHOOLS, LAGOS Any Questions?
YR 7: WK 5 8/9/2023 10:24:02 AM LESSON OBJECTIVES: WEEK 5 TOPIC At the end of the FRACTIONS [contd] lesson, students should be able to: Add and subtract fractions Multiply and divide fractions Solve word HOME PAGE problems on fractions. KEY NOTES: Add , subtract , multiply and divide
YR 7: WK 5 TOPIC: FRACTIONS[contd] 8/9/2023 10:24:02 AM ADDITION AND SUBTRACTION OF FRACTIONS EXAMPLE 1 Simplify: 4 + 1 5 2 SOLUTION 4 + 1 5 2 13 3 8+5 = 10 = 1 10 10 (������������������)
YR 7: WK 5 TOPIC: FRACTIONS[contd] 8/9/2023 10:24:02 AM EXAMPLE 2 Simplify: 1 + 2 + 5 4 3 6 SOLUTION 1 + 2 + 5 4 3 6 3 + 8 + 10 = 21 = 7 = 1 3 12 (������������������) 12 4 4
YR 7: WK 5 TOPIC: FRACTIONS[contd] 8/9/2023 10:24:03 AM EXAMPLE 3 Simplify: 3 − 5 4 8 SOLUTION 3 − 5 1 4 8 8 6− 5 = 8 (������������������)
YR 7: WK 5 TOPIC: FRACTIONS[contd] 8/9/2023 10:24:03 AM EXAMPLE 4 2 3 − 1 7 Simplify: 4 10 SOLUTION ������ℎ������������������������ ������������������ℎ ������������������������������������������������ ������������ ������������������������������������������������ ������������������������������������������������ 11 − 17 4 10 55 − 34 21 1 = 20 = 1 20 20 (������������������)
YR 7: WK 5 TOPIC: FRACTIONS[contd] 8/9/2023 10:24:03 AM EXAMPLE 5 2 2 − 3 7 + 2 1 Simplify: 5 9 3 SOLUTION ������ℎ������������������������ ������������������ℎ ������������������������������������������������ ������������ ������������������������������������������������ ������������������������������������������������ 12 − 34 + 7 5 9 3 108 − 170 + 105 108+105−170 213−170 45 (������������������) = 20 = 45 = 43 45
YR 7: WK 5 TOPIC: FRACTIONS[Contd] Evaluation 8/9/2023 10:24:04 AM Simplify the following: Questi52on+1 1 + 1 2 4 Question 2 2 3 5 − 10 Question 3 5 7 6 8 4 − 3 Question 4 7 2 − 2 1 + 2 1 5 10 2
YR 7: WK 5 TOPIC: FRACTIONS[contd] 8/9/2023 10:24:04 AM MULTIPLICATION AND DIVISION OF FRACTIONS EXAMPLE 1 Simplify: 4 3 9 SOLUTIO5N × 1 3 4= 4 5 9 15 ×3
YR 7: WK 5 TOPIC: FRACTIONS[contd] 8/9/2023 10:24:04 AM EXAMPLE 2 Simplify: 3 × 4 32 7 SOLUTION 3 1 4= 3 32 7 56 × 8
YR 7: WK 5 TOPIC: FRACTIONS[contd] 8/9/2023 10:24:04 AM EXAMPLE 3 Simplify: SOLU3T15I7O×N 2 5 × 4 6 8 ������ℎ������������������������ ������������������ℎ ������������������������������������������������ ������������ ������������������������������������������������ ������������������������������������������������ 71 24 56 17 18 14 17 × 36 × = 3 1 = 4 2 3
YR 7: WK 5 TOPIC: FRACTIONS[contd] 8/9/2023 10:24:05 AM EXAMPLE 4 Simplify: 3 4 5 ÷ 9 SOLUTION 3 × (i9nverting the right hand side) 5 4 27 = 20 = 1 7 20
YR 7: WK 5 TOPIC: FRACTIONS [contd] 8/9/2023 10:24:05 AM EXAMPLE 5 Simplify: 3 2 9 6 3 ÷ 5 SOLUTION (change each term to an improper fraction) 20 ÷ 48(inverting the right hand side) 53 20 3 93 19 = 5 ×12 448 4 1 = 1 1 4
YR 7: WK 5 TOPIC: FRACTIONS[Contd] Evaluation 8/9/2023 10:24:05 AM Simplify the following: Questio4n 1 × 3 2 11 3 Question 2 334 4 1 × 9 × 1 5 Question 3 1 4 3 9 ÷ 2 5 Question 4 2 1 ÷ 2 2 10 5
YR 7: WK 5 TOPIC: FRACTIONS[contd] 8/9/2023 10:24:06 AM WORD PROBLEMS ON FRACTIONS Problems involving fractions often appear in real – life situation. EXAMPLE 1 What is the area of a rectangle of length 1232m and breadth 7¼ m? SOLUTION L = 1223m, B= 7¼m Area of rectangle, A = L x B Area = 1223 x 7¼ 19x Area = 38 29 3 42 Area = 551 6 Area = 9165m2
= (Y21R/5 7-:8/W3 )K÷ 152/5 TOPIC: FRACTIONS[contd] 8/9/2023 10:24:06 AM EXAMPLE 2 Divide the difference between 4 1 and 232 by 152. 5 . SOLUTION Interpreting the question . 4 1 − 2 2 5 3 1 2 1 5 = 23 × 5 15 7 = (251 − 38) ÷ 1 2 3 5 = 63 − 40 ÷ 7 = 23 15 5 21 = 23 ÷ 7 = 1 2 15 5 21
YR 7: WK 5 TOPIC: FRACTIONS[contd] 8/9/2023 10:24:06 AM EXAMPLE 3 What is three-quarters of 373 ? SOLUTION . Three - quarter = 43. . = 3 337 4 of . 6 = 3 × 274. 4 1 . = 18 7 = 2 4 7
YR 7: WK 5 TOPIC: FRACTIONS[contd] 8/9/2023 10:24:07 AM EXAMPLE 4 In a school, 9 of the students play sports. 32of these play football. What fraction of 10 the students play football. SOLUTION . Fraction who play sports = 9 10 Fraction that play fo.otball = 2 of 190. 3 1 2 x 93 . 13 10 5 :. 35of the students play footba.ll. .
YR 7: WK 5 TOPIC: FRACTIONS[contd] 8/9/2023 10:24:07 AM EXAMPLE 5 Three sisters share some money. The oldest gets 5 of the money. The next girl gets 11 7 12 of the remainder. What fraction of the money does the youngest girl get? SOLUTION . 1 Let the total money; be a unit = 1 = 7 × 6 = 7 12 11 22 5 5 2 1st girl gets = 11 ������������ = 1 =. 11 . 3rd girl will get = 1 − (151 + 272) Remainder = 1 - 5 = . 11−5 . = 6 . =. 1 − (102+2 7) 11 11 11 . . 2nd girl gets = 7 of th. e remainder. = 1 − (1227) = 12 ������������ . 6 . = 22−1 7 .252 7 11 22 12 ∴ ������������������������������������������������ ������������ ������ℎ������ ������������������������������ ������ℎ������ ������������������������������������������������ ������������������������ ������������������������ ������������������= .
YR 7: WK 5 TOPIC: FRACTION [Contd]>> Evaluation 8/9/2023 10:24:08 AM Question 1 A boy eats ¼ of a loaf at breakfast and 5 of it for lunch. 8 What fraction of the loaf is left? Question 2 A loaf of bread was divided into 18 e. qual slices. If 6 slices were given to Olu. What fraction is left? . Question 3 Ibrahim spends 1 of his earnings on food and 1 on clothes. He then Question 4 3 4 saves the rest. What fraction does he (a) Spend altogether (b) save . How many 5 liter bottle can be obtained from a drum holding 15 6 liters of water? .
PHIDEL GROUP OF SCHOOLS, LAGOS Any Questions?
YR 7: WK 6 8/9/2023 10:24:09 AM LESSON OBJECTIVES: WEEK 6 TOPIC At the end of the lesson, students FRACTIONS, DECIMALS AND should be able to: PERCENTAGES convert fractions to decimals Convert decimals to fractions Convert fractions HOME PAGE to percentages. KEY NOTES: Express percentages as fraction, decimal, percentages fractions.
YR 7: WK 6 TOPIC: FRACTIONS, DECIMAL AND PERCENTAGES 8/9/2023 10:24:09 AM CONVERSION OF FRACTIONS TO DECIMALS To convert a fraction into decimal first re-write the number as a decimal then divide it by the denominator. TERMINATING DECIMAL When the denominator divides exactly into numerator a terminating decimal is obtained. EXAMPLE 1 .Change ¾ into a terminating decimal number. 0.75 4 − 30 28 − 22. 00. ������������������ = 0.75
YR 7: WK 6 TOPIC: FRACTIONS, DECIMAL AND PERCENTAGES 8/9/2023 10:24:10 AM RECURRING OR REPEATING DECIMAL Sometimes when changing fractions to decimal gives the same figure or group figures repeating themselves on and on. These types of fraction are called non- terminating decimals or recurring decimals. EXAMPLE 2 Change the following into decimals . 4 6 (a) 9 (b) 11 − SOLUTION (������) 0.444 9 −4306 − 4306 40 − 36 ������������������ = 0.444 … … . 4