Acme Mathematics-4 151G. Proper and improper fractionProper fraction : Fractions in which the numerator is less than the denominator are called proper fractions.For example : 35 , 27 , 910 etc are proper fractions.Improper Fraction : Fractions in which the numerator is greater than the denominator are called improper fractions.For example : 75 , 43 , 127 etc are improper fractions.H. Mixed fraction (mixed number)Consider the improper fractions 323 half is shaded. 12121222 = 1 122 half is whole.22 = 1 (whole)3 half = 1 whole and 12 = 1 and 12 = 112112 is called mixed number. 1 is whole number. 12 is fraction.ClassworkStudy the given figure and express as proper fraction and mixed fraction.Figures Fraction Mixed Fraction52 2 12+ + = +
152 Acme Mathematics-4132Exercise 2.301. List the proper fractions from the given fractions:12, 34, 128 , 1520, 32,53, 911, 76, 97, 172. List the improper fractions from the given fractions:32, 13, 1110, 85, 83, 27, 34, 1253. List the mixed number (fractions) from the given fractions:35, 234, 110, 314, 2030, 313, 1015, 179 257, 516Remember!Numerator and denominator
Acme Mathematics-4 1532.4 DecimalWrite the decimal and fraction of each shaded part.Fraction : ............Decimal : ............Fraction : ............Decimal : ............Fraction : ............Decimal : ............Fraction : ............Decimal : ............Fraction : ............Decimal : ............Fraction : ............Decimal : ............Fraction : ............Decimal : ............Fraction : ............Decimal : ............Fraction : ............Decimal : ............Fraction : ............Decimal : ............Fraction : ............Decimal : ............Fraction : ............Decimal : ............Activity
154 Acme Mathematics-4A. TenthsThere are ten equal parts. One part is shaded.The shaded part is 110. 110 is represented as 0.1 in decimal. It is read as zero point one.Similarly, the shaded parts of the strip is written as 310. It is expressed as 0.3 in decimal and is read as zero point three. Observe the location of these decimal numbers in the number line.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 11102103104105106107108109101010Classwork1. Write the fractions for the following shaded parts and express them in decimal:(a) 310 = 0.3 (b)=(c)=(d) =2. Fill in the missing decimal numbers on the number line.7.4 7.9Exercise 2.311. Express the following fractions as decimal numbers:(a) 310 = (b) 710 = (c) 110 = (d) 410 = (e) 810 = (f) 910 = 2. Write the following decimal numbers into fractions:
Acme Mathematics-4 155(a) 0.4 = (b) 0.3 = (c) 0.7 = (d) 0.6 = (e) 0.2 = (f) 0.9 = 3. Fill the missing numbers in the number line:(a) 0 1102101010(b) 0 0.2 0.5 1.04. Fill in the missing decimal numbers on each number line.0.2 0.4 1.22.6 3.0 3.2 3.84.1 4.2 4.5 4.65. What decimal numbers do the letters on each number line represent?5.0 C 5.2 5.3 A 5.5 5.6 B 5.8 5.9 6.0A = ......... B = ......... C = .........9 Q 9.2 9.3 R 9.5 9.6 9.7 PP = ......... Q = ......... R = .........1.9 2.1 X 2.5 Z 2.9 Y 3.3X = ......... Y = ......... Z = .........
156 Acme Mathematics-41. Match the following.12100 410 310 20100 610 910 66100 45100B. HundredthsOne hundredthThere are 100 equal parts. 12 parts are shaded.The shaded part is 12100 in fraction. In decimal system, it is written as 0.12 and is read as zero point one two.Classwork
Acme Mathematics-4 1571. Determine the amount shaded of the whole. Write their answer as a decimal.Exercise 2.32
158 Acme Mathematics-42. Write in decimal numbers.1.1
Acme Mathematics-4 159_____ = _____ _____ = __________ = _____ _____ = _____3. Study the given figure and write in fraction as well as decimal number._____ = __________ = _____ _____ = _____1100 = _____ 0.01• If the number after decimal is of single digit, divide it by 10.• If the number after decimal is of two digit, divide it by 100.Remember
160 Acme Mathematics-4D. Decimal number on the number line0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.30 0.61 0.62 0.63 0.64 0.65 0.66 0.67 0.68 0.69 0.70 0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49 0.50 0.81 0.82 0.83 0.84 0.85 0.86 0.87 0.88 0.89 0.90 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.40 0.71 0.72 0.73 0.74 0.75 0.76 0.77 0.78 0.79 0.80 0.51 0.52 0.53 0.54 0.55 0.56 0.57 0.58 0.59 0.60 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.20How far is 1 from 0?
Acme Mathematics-4 161Classwork1. Match the following:(a) 0.7 (i) 0.1(b) 110 (ii) 75100(c) 0.82 (iii) 0.09(d) 0.75 (iv) 710(e) 9100 (v) 821002. Write the decimal and fraction number represented by these figures in the blanks:Decimal Fraction(a) .......................... ..........................(b) .......................... ..........................(c) .......................... ..........................(d) .......................... ..........................(e) .......................... ..........................(f) .......................... ..........................Exercise 2.331. Shade to represent the given decimal number:(a) 0.3
162 Acme Mathematics-4(b) 0.7(c) 0.5(d) 0.8(e) 0.92. Write the decimal and fraction numbers represented by the following graphs :(a) (b)(c) (d)3. Change to the fractions:(a) 0.4 = (b) 0.3 = (c) 0.5 =
Acme Mathematics-4 163(d) 2.4 = (e) 7.4 = (f) 1.1 =4. Change to the decimal number:(a) 710 = 0.7 (b)410 = _____ (c)80100 = _____(d)18100 = _____ (e)310 = _____ (f)610 = _____(g)36100 = _____ (h)46100 = _____ (i)910 = _____(j)86100 = _____ (k)52100 = _____ (l)69100 = _____5. Colour the square room to represent the following decimal number.(a) (b)(c) (d)210051002510065100Let's draw:
164 Acme Mathematics-45.18 PercentageLook at the given figure.One part out of 10 parts is shaded.It is 110.In the figure alongside out of 100 squaresone square is shaded. It is 1100.1100 is a special fraction. Its denominator is 100.1100 is also called 1 per hundred.1100 = 1 per hundredPer hundred = percentage (%)I got 98% marks in the exam.Remember2100 = 2%3100 = 3%9100 = 9%I know! Percentage is a fraction with denominator 100.A. Conversion of percentage into fractionExample 1 : Convert 8% into fraction..Solution : Here, 8% = 8100Example 2: In the class there are 100 students out of them 60 students are boys. How many percentage are boys? And how many percentages are girlsSolution : (a) out of 100, 60 are boys.60100 are boys, so 60% are boys% is symbol for per hundred.
Acme Mathematics-4 165(b) Out of 100, (100-60) are girls. Out of 100, 40 are girls. or 40100 are girls, so 40% are girls.Classwork1. Express as percentage:(a) The red colored part.(b) The blue colored part(c) The green colored part.(d) The white colored part.2. (a) Write in percentage : 0.31 = ...........(b) Write 5100 in percentage : ..........(c) Tick () the percentage : (i) 0.3 (ii) 310(iii) 3100 (iv) 100(d) Study the figure and express in percentage.(e) Express in decimal : 30%3. Measure the given line segments. How long is AB more than XY?BYAX
166 Acme Mathematics-4Exercise 2.341. Change to percentage:(a) 3100 = (b) 7100 = (c) 11100 =(d) 9100 = (e) 20100 = (f) 25100 =2. Change to fractions:(a) 2% = (b) 3% = (c) 13% = (d) 7% = (e) 67% = (f) 99% = 3. Match the following:3 out of 100 13 out of 10010 out of 100 7 out of 1007100 10%13100 3%15% 5010050% 151004. Colour the correct one:3100 = 50% 7100 = 17% 5% = 1201% = 1100 3% = 30100100100 = 100%5. Convert the following percentage into the fraction.(a) 2 % (b) 3 % (c) 5 % (d) 8 %(e) 10 % (f) 25 % (g) 40 % (h) 50 %(i) 100 % (j) 105 % (k) 115 % (l) 200 %
Acme Mathematics-4 1676. In class 4, there are 75 boys out of 100 students.(a) fraction of boys = ................... (b) fraction of girls = ......................(c) Precentage of boys = .............. (d) Percentage of girls = .................B. Conversion of percentage into decimal numberStudy the given examples:Example 1 : Convert 13% as decimal number.Solution : Here, 13% = 13100 = 0.13Example 2 : Convert 9% as decimal number.Solution : Here, 9% = 9100 = 0.09C Conversion of decimal number into percentageStudy the given examples.Example 3 : Convert 0.12 as percentage.Solution : Here, 0.12 = 012100= 12100 = 12%Example 4 : Convert 0.4 as percentage.Solution : Here, 0.4 = 0.40 = 40100 = 40%D. Conversion between percentage, decimal and fraction.Fraction Decimal Percent35100 0.35 35% Fraction Decimal Percent70100 0.70 70% After decimal, 2 numbers are needed.
168 Acme Mathematics-4Fraction Decimal Percent47100 0.47 47% Fraction Decimal Percent19100 0.19 19% Exercise 2.351. Convert the following percentage into decimal number.(a) 5% (b) 8% (c) 10% (d) 12%(e) 15% (f) 30% (g) 40% (h) 60%2. Colour the correct one.5% = 0.5 0.2 = 25% 3% = 0.50.5 = 50% 0.51 = 51% 0.99 = 99%3. Change into decimal numbers.(a) 4 % = (b) 12 % = (c) 19 % =(d) 22 % = (e) 35 % = (f) 90 % =4. Convert the following decimal number into percentage.(a) 0.11 (b) 0.15 (c) 0.20(d) 0.25 (e) 0.30 (f) 0.55(g) 0.75 (h) 0.88 (i) 0.98(j) 0.4 (k) 0.8 (l) 0.9
Acme Mathematics-4 1691. Study the given figure alongside.(a) Write the fraction of the shaded part.(b) Write the numerator and denominator of the obtained fraction.(c) Write the obtained fraction in words.2. (a) Add : 217 + 327 + 437(b) Sagar spent 58 of his income to buy clothes and his wife spent 18 of her income to buy saree and kurta. How much did they spend altogether?(c) Write '25 tenths' in decimal form.(d) Express 71100 in percentage.3. Observe the given figure alongside.(a) Write the coloured part in decimal.(b) Write the obtained decimal number in words.(c) Express the obtained fraction into percentage.4. (a) Convert into decimal.(i) 7100 (ii) 45100(b) What is the decimal value of 9100?(i) 0.9 (ii) 0.09 (iii) 9(c) Write the following fractions in words.(i) 38 (ii) 255. (a) Simplify : 78 + 18 – 38(b) Simplify : 12 421 + 6 321 – 5 121Mixed Exercise
170 Acme Mathematics-46. Do the following:(a) Subtract : 2810 – 1710(b) Express the 120% into fraction.(c) Write the decimal for 50%.7. Tick () the correct answers.(a) Number 37 is greater than .................i.27 ii. 57 iii. 37(b) The decimal number zero point zero three is ............ .i. 0.003 ii. 0.3 iii. 0.038. Study the given figure alongside.(a) Write the shaded part in fraction and decimal.(b) Write the obtained decimal in word.(c) Write the decimal form : 85 hundredths9. (a) Study the decimal number 0.14 and answer the following questions.i. Write the place value of 4 of the given number.ii. Write the given number in percentage.iii. Write the given number in words.(b) Write in decimal numberi. 5610 ii. 35100
Acme Mathematics-4 17110. Marks obtained by Kanchan is given alongside by shading.(a) Write the full marks.(b) Express the marks obtained by Kanchan in fraction.(c) Express the Kanchan's marks in decimal.(d) Kriti got 710 marks, compare the marks of Kanchan and Kriti who got more marks?11. (a) Convert 5678 to the nearest hundred.(b) A soap cartoon contain 60 soaps. Ritesh has 123 such cartoons. What is the process to get total number of soaps?(c) Calculate the number of soap that Ritesh has.12. Mother cuts a bread into 6 equal slices. Brother ate 2 slices and sister ate 2 slices.(a) What fraction of the bread did brother eat?(b) What fraction of the bread did sister eat?(c) What fraction of the bread did brother and sister eat altogether?13. The teacher divides a sheet of paper into 10 equal parts. He shades 4 parts with red colour and 5 parts with green colour.(a) Write the fraction for red shaded parts and convert into decimal.(b) Write the fraction for green shaded parts and convert into decimal.(c) Write the total of the shaded parts in decimal.14. Hari spent 34 of his income and Shyam spent 24 of his income.(a) Who spent more? Compare it.(b) If monthly income of Hari has Rs. 1200, how much has Hari spent?
172 Acme Mathematics-4EvaluationTime: 60 minutes Full Marks: 251. (a) Fill in the blanks. In the fraction, a quarter is written as……. . [1] (b) Write in words: 0.65 [1] (c) Convert 0.25 into fraction. [2] (d) Write 45 % into fraction. [1]2. The figures in right side showed Melina’s mark secured in the annual exam.(a) Write the Melina’s marks in fraction. [1] (b) Write the Melina’s marks in decimal number. [1] (c) How much percentage did Melina receive in exam ? [1] (d) Melina’s friend Sabina receive the marks 710 in fraction then, who receive more marks ? [2] 3. (a) Which is the fraction for the shaded parts ? [1] (i) 2 (ii) 3 (iii) 4 6 6 6(b) Which is the decimal representation of 110 ? [1] (i) 0.01 (ii) 0.1 (iii) 0.001 (c) Convert 1520 in to percentage. [2]4. (a) The figure shows Hari's mark secured in the second terminal exam. (i) Write the Hari's marks in fraction. [1](ii) Write the Hari's marks in decimal number. [1](iii) Write the Hari's marks in percentage. [1](b) If Hari's friend Bikash receive the marks in fraction as 410, find out who receive more marks by how much ? [2]5. (a) Convert into decimal: 25100 [1] (b) Write one-third in fraction. [1] (c) Sabina ate 14 cake from 34 cake. How much cake is left? [2] (d) Simplify: 710 + 610 - 310 [2]
Acme Mathematics-4 173MEASUREMENT CHAPTER3Warm-up:1. Write the time:It is .......... O' clock It is .......... O' clock It is .......... O' clock2. Put am or pm:(a) 8 o'clock (morning) .................. (b) 6 o'clock (evening)..................c) 11 o'clock (night) .................. (d) 10 o'clock (morning)..................3. Fill in the blanks:(a) 7 days = ........... week (b) 30 days = ........... month(c) 2 weeks = ........... days (d) 1 hour = ........... minutes(e) ........... months = 1 year (f) ........... days = 1 year4. Study the given calender:Now, answer the following questions:(a) Which month is in the calender?(b) How many Saturdays are there?(c) How many days are there in the month?5. Write in short form:(a) 8th Baishakh 2080 = 08/01/2080 (b) 10th Jestha 2069 = ........................(c) 30th Asar 2070 = ..................... (d) 22nd Falgun 2065 = .....................3.1 TimecfOtjf/Sunday;f]djf/Mondayd+unjf/Tuesdaya'wjf/Wednesdaylalxjf/Thursdayz'qmjf/Fridayzlgjf/Saturday! @ # $ % ^& * ( !) ! ! !@ !#!$ !% !^ !& !* !( @)@ ! @@ @# @$ @% @^ @&@* @( #) # !efb| @)*# Aug/Sep 202617 18 19 20 21 2223 24 25 26 27 28 2930 31 SEPT. 1 2 3 4 56 7 8 9 10 11 1213 14 15 16
174 Acme Mathematics-4Relation between day, week, month and yearA. Days and week7 days = 1 week1 week = 7 daysConversion of days and weekExample 1 : Convert 8 weeks into days.Solution: 1 week = 7 days8 weeks = 7 × 8 days= 56 daysExample 2 : Convert 84 days into week.Solution : 7 days = 1 week84 days = 84 ÷ 7 weekNow,So, 84 days = 12 weeksExample 3 : Convert 3 month into days.Solution : 1 month = 30 days3 month = 3 × 30 days= 90 daysB. Days and monthExample 4 : Convert 120 days into months.Solution : 30 days = 1 month120 days = (120 ÷ 30) months= 4 monthsWeeks× 7÷ 7days 7) 8 4 (12 – 71 4 – 1 4 ×Number of weeks30) 1 2 0 (4– 1 2 0 ×Months× 30÷ 30days30 days = 1 month1 month = 30 daysI remember.Quotient is weeks.Remainder is days.
Acme Mathematics-4 175C Days and yearExample 5 : Convert 3 years into days.Solution : 1 year = 365 days3 years = 3 × 365 days= 1095 daysExample 6 : Convert 730 days into years.Solution : 365 days = 1 year730 days = (730 ÷ 365) years= 2 yearsD. Month and yearExample 7 : Convert 10 years into months.Solution : 1 year = 12 months10 years = 10 × 12 months= 120 monthsExample 8 : Convert 156 months into years.Solution : 12 months = 1 year156 months = (156 ÷ 12) years= 13 yearsExample 9 : Convert 169 months into years and months.Solution : 12 months = 1 year169 months = (169 ÷ 12) yearsNow,So, 169 months = 14 years and 1 month.365 days = 1 year1 year = 365 days 1 2 × 1 0 0 0 1 2 1 2 0 12) 1 5 6 (13 – 1 2 3 6 – 3 6 ×it is yearsit is month 12) 1 6 9 (14 – 1 2 4 9 – 4 8 11 year = 12 months12 months = 1 year
176 Acme Mathematics-4To convert larger to smaller unit we should multiply.Week × 7 daysMonths × 30 daysYears × 12 monthsYears × 365 daysTo convert smaller to larger unit we should divide.Days ÷ 7 weekDays ÷ 30 monthsMonths ÷ 12 yearsDays ÷ 365 yearsClasswork1. Fill in the blanks:(a) 21 days = ............... weeks(b) 2 weeks = ............... days(c) 30 days = ............... months(d) 4 months = ............... days(e) .......... days = 1 year(f) 2 years = ............... days(g) 24 months = ............... years(h) 5 years = ............... monthsExercise 3.11. Convert the given weeks into days:(a) 20 weeks (b) 35 weeks (c) 50 weeksI know all.I have read it.Do you?
Acme Mathematics-4 1772. Convert the following as indicated:(a) 9 months into days (b) 20 months into days(c) 6 years into months (d) 25 years into months(e) 5 years into days (f) 15 years into days3. Convert the following units as indicated:(a) 30 days into months (b) 90 days into months(c) 50 days into months and days (d) 220 days into months and days(e) 21 days into weeks (f) 273 days into weeks(g) 37 days into weeks and days (h) 250 days into weeks and days4. Convert the unit as indicated units:(a) 96 months into years(b) 144 months into years(c) 58 months into years and months(d) 2234 months into years and months(e) 1095 days into years(f) 1295 days into years and days5. Convert the following:(a) 3 weeks 6 days into days (b) 10 weeks 2 days into days(c) 3 months 10 days into days (d) 14 months 2 days into days(e) 2 years 7 months into months (f) 15 years 6 months into months2. Relation between days, hours, minutes and secondsA. Days and hours12 o'clock at night 12 o'clock at noon 12 o'clock at night1 day12 hours 12 hours
178 Acme Mathematics-4Example 1 : Convert 5 days into hours.Solution : 1 day = 24 hours5 days = 5 × 24 hours= 120 hours.Example 2 : Convert 72 hours into days.Solution : 24 hours = 1 day72 hours = (72 ÷ 24) days = 3 daysExample 3 : Convert 290 hours into days and hours.Solution : 24 hours = 1 day290 hours = (290 ÷ 24) daysNow,290 hours = 12 days and 2 hours.B. Hours and minutesIn the clock, 1, 2, 3, ........, 12, numbers indicate hours. Small divisions (lines) indicate minutes. There are 60 small lines. There are 60 minutes in an hour.Minutes÷ 60× 60Hours1 hour = 60 minutes60 minutes = 1 hour 24) 7 2 (3 – 7 2 ×dayshours 24) 2 9 0 (12 – 2 4 5 0 – 4 8 0 2
Acme Mathematics-4 179Example 4 : Convert 8 hours into minutes.Solution : 1 hour = 60 minutes8 hours = 8 × 60 minutes = 480 minutesExample 5 : Convert 720 minutes into hours.Solution : 60 minutes = 1 hour720 minutes = (720 ÷ 60) hoursNow,720 minutes = 12 hoursC. Minutes and seconds1 minute = 60 seconds60 seconds = 1 minuteNow, remember this relation.Example 6 : Convert 5 minutes into seconds.Solution : 1 minute = 60 seconds5 minutes = 5 × 60 seconds= 300 secondsExample 7 : Convert 600 seconds into minutes.Solution : 60 seconds = 1 minute600 seconds = (600 ÷ 60) minutes= 10 minutes 60) 7 2 0 (12 – 6 0 1 2 0 – 1 2 0 × Rough 6 0 × 5 3 0 0 60) 6 0 0 (10 – 6 0 0
180 Acme Mathematics-4Example 8 : Convert 5 minutes 20 seconds into seconds.Solution : 1 minute = 60 seconds5 minutes = 5 × 60 seconds= 300 seconds20 seconds ⇒Now, 5 minutes 20 seconds = 320 seconds.Remember!× 24Day hours× 60Hour minutes× 60Minute seconds÷ 24Hours day÷ 60Minutes hour÷ 60Seconds minuteClasswork1. Fill in the blanks:(a) 2 days = ...................... hours(b) 48 hours = ...................... days(c) 6 minutes = ...................... seconds(d) 60 minutes = ...................... hours(e) 120 seconds = ...................... minutesExercise 3.21. Convert as indicated:(a) 24 hours into minutes(b) 7 days into hours(c) 1 day into seconds(d) 30 hours 10 minutes into minutes(e) 10 days 14 hours into hours(f) 20 minutes 20 seconds into seconds + 20 320 secondsAll are easy. Just remember their relations.
Acme Mathematics-4 1812. Convert into hours:(a) 360 minutes (b) 180 minutes (c) 600 minutes (d) 540 minutes3. Convert into minutes:(a) 120 seconds (b) 240 seconds (c) 300 seconds (d) 360 seconds4. Convert into days and hours:(a) 40 hours (b) 100 hours (c) 75 hours (d) 125 hours5. Convert into hours and minutes:(a) 70 minutes (b) 140 minutes (c) 155 minutes (d) 180 minutes3. Addition and subtractionLook at the examples carefully and try to understand the idea.Example 1 : Add: 4 years 7 months and 7 years 8 months.Solution : Here,Example 2 : Add 8 days 15 hours and 3 days 10 hourSolution : Here,Example 3 : Subtract 7 hours 45 minutes from 9 hours 15 minutes.Solution : Here, It is carryover 12 months = 1 yearyears months 4 7 + 7 8 11 15 + 1 – 12 12 3 15 months is equal to 1 year 3 months.Carry from the hour, 24 hour = 1 daydays hour 8 15 + 3 10 11 25 + 1 – 24 12 1hours minutes 9 15 – 7 45hours minutes 8 75 – 7 45 1 30 60 + 15 = 75 9 – 1 = 8 borrowed by minutes
182 Acme Mathematics-4Example 4 : Hardik completed Maths homework in 1 hour and 40 minutes, Nepali homework in 2 hours and 15 minutes. How long did he take to complete the homework?Solution : Here, the problem is related to addition of the time.Example 5 : Your first period starts at 10:15 am and ends at 11:00 am. How long is the period?Solution : Here, the problem is related to subtraction.Since we cannot subtract 15 from 00 minute. We borrow 1 hour (60 minutes) from 11.Classwork1. Look at the clock:(a) What is the time now?(b) Write the time after 3 hours.(c) Write the time 30 minutes before.(d) Write the time before 5 hours.2. Fill in the blanks:(a) 3 minutes + 60 seconds = ......... minutes(b) 25 minutes + 55 minutes = ......... hours and ......... minutes(c) 5 hours + 60 minutes = ......... hoursSo, hours minutes 1 40 Math's homework time + 2 15 Nepali's homework time 3 55Hardik took 3 hours 55 minutes to complete both the homeworks.So, 11 : 00 end of period – 10 : 15 starting of periodSo, 10 : 60 – 10 : 15 0 : 45The first period is 45 minutes long.
Acme Mathematics-4 1833. Complete the following.(a) 6 days – 20 hours = ......... days and ......... hours(b) 1 hour – 45 minutes = ......... minutes(c) 1 year – 8 months = ......... monthsExercise 3.31. Fill in the blanks:(a) 12 hours + 13 hours = ......... days and ......... hours(b) 40 hours + 13 days = ......... days and ......... hours(c) 50 days + 10 days = ......... months and ......... days(d) 29 days + 20 days = ......... months and ......... days(e) 7 weeks + 15 days = ......... weeks and ........... days(f) 4 am + 7 hours = ..............................2. Complete the following.(a) 1 week – 2 days = ......... days(b) 1 month – 10 days = .............(c) 7 am – 2 hours = .............(d) 11:30 am – 10 hours = .............(e) 3 pm – 7 hours = .............3. The route of micro-bus and its time is given below:Now complete the table.Narayangarh Malekhu Naubise45 min30 min1 hour1hr 10 min45 minKathmanduMuglin Galchhi
184 Acme Mathematics-4Places Time takenNarayangarh to Malekhu .........................Muglin to Galchhi .........................Malekhu to Kathmandu .........................Narayangarh to Kathmandu .........................4. Add the following:(a) years months 12 10 + 19 09(b) years months 112 09 + 12 07(c) months days 12 20 + 9 25(d) months days 20 15 + 25 20(e) weeks days 13 4 + 4 6(f) weeks days 21 06 + 10 05(g) days hours 5 16 + 6 8(h) days hours 15 10 + 30 20(i) hours minutes 7 02 + 9 28(j) hours minutes 14 30 + 15 29(k) minutes seconds 20 10 + 44 46(l) minutes seconds 50 40 + 8 205. Subtract the following:(a) years months 27 03 – 10 10(b) years months 61 06 – 3 8
Acme Mathematics-4 185(c) months days 32 20 – 12 29(d) months days 19 19 – 08 29(e) weeks days 18 6 – 2 7(f) weeks days 52 28 – 1 29(g) days hours 13 10 – 7 8(h) days hours 15 09 – 10 10(i) hour minutes 22 50 – 3 10(j) hours minutes 28 34 – 20 47(k) minutes seconds 112 55 – 10 55(l) minutes seconds 100 50 – 58 686. Solve the following verbal problems:(a) Bishal is 20 years 3 months old and Binaya is 19 years 10 months old. What is the sum of their ages?(b) Our school starts at 9:45 am and closes at 3:20 pm. How long is our school time?(c) The sum of the ages of Kundan and Kushal is 25 years 9 months. If the age of Kundan is 17 years 10 months, find the age of Kushal.(d) A bus starts its journey from Tandi to Kathmandu at 7:15 am. If it reaches Kathmandu at 11:45 am, how long is the journey?(e) Sarathi is 12 years 7 months old. Arjun is 14 years 9 months old. Find the difference of their ages.(f) Raman started reading a book at 6:20 pm and finished at 10:10 pm. How long time did he read?(g) Bhabana started cooking at 7:30 am and finished at 11:00 am. How long time did she cook for?(h) Kaushal completed the English homework in 2 hours 24 minutes, Nepali's homework in 1 hour 30 minutes and Social studies homework in 1 hour 25 minutes. How long did he take to complete all the homework?
186 Acme Mathematics-43.2 MoneyWarm-up:Fill in the blanks.1. Our coins are: One rupee coin, ....................2. Our notes are: One rupee note, ....................3. Small unit of our money is ....................4. Large unit of our money is ....................5. Look at the pictures and write their cost in paisa.(a) (b)(c) (d)6. Look at the pictures and write their cost in rupees.(a) (b) (c)Rs 17Rs 5Rs 15 Rs 2.50200 paisa700 paisa600 paisa
Acme Mathematics-4 1871. Conversion of moneyOur unit of money is paisa and rupees. In short form, paisa is denoted by P. Rupees is denoted by Rs.Try to remember 100 paisa = 1 rupee P and Rs.1 rupee = 100 paisaPaisa Rupees× 100÷ 100One rupee is written as Re. 1. Ten rupees is written as Rs. 10. One rupee and 50 paisa is written as Rs. 1.50. Eight rupees and 25 paisa is written as Rs. 8.25. Two rupees and 5 paisa is written as Rs. 2.05.Example 1 : Convert Rs. 7 into paisa.Solution : Here, 1 rupee = 100 paisa 7 rupees = 7 × 100 paisa= 700 paisaExample 2 : Convert 900 paisa into rupees.Solution : Here, 100 paisa = 1 rupee900 paisa = 900100 rupee= 9 rupees= Rs. 9Example 3 : Convert Rs. 6.50 into paisa.Solution : Here, 1 rupee = 100 paisa6 rupees = 6 × 100 paisa= 600 paisa + 50 paisa650 paisaRs. 6.50 = 650 paisaOh! Rupees is multiplied by 100.I know it, Rs. 6.50 is 6 rupees and 50 paisa.
188 Acme Mathematics-42. Addition and subtraction of moneyAddition and subtraction of money is similar to the addition and subtraction of numbers. Look at the examples carefully.Example 1 : Add Rs. 5.30 and Rs. 6.80Solution :Example 2 : Subtract 3 rupees 70 paisa from 9 rupees 20 paisaSolution :3. Multiplication and division of moneyExample 1 : Multiply 12 rupees 25 paisa by 8Solution :Example 2 : Divide Rs. 20.58 by 6.Solution:Rs. 20.58 divided by 6 = Rs 3.43 paisa.1 rupee is carried here.Here, Rs. Paisa 5 30 + 6 80 11 110 + 1 –100 12 10 it is 1 rupeeHere, Rs. Paisa 9 20 – 3 70Rs. 1 rupee paisa 8 120– 3 70 5 50Yes! 200 paisa= 2 rupees. 2 is carry over.Here, Rs. Paisa 12 25 × 8 96 200 + 2 – 200 98 0 Remainder is Rs. 2. Rs. 2 = 200 paisa. 200 paisa + 58 paisa = 258 paisa.Here, 3 43 Rs. Paisa 20 58– 18 2 58 – 2 418 – 18 ×6
Acme Mathematics-4 189Classwork1. Fill in the blanks.(a) Rs. 3 = .............. paisa (b) Rs. 10 = .............. paisa(c) 200 paisa = Rs. .............. (d) 900 paisa = Rs. ..............(e) 50 paisa + 40 paisa = .............. paisa(f) Rs. 7 + Rs. 9 = Rs. .............. (g) Rs. 12 – Rs. 2 = Rs. ..............(h) 10 × Rs. 11 = Rs. .............. (i) 18 × Rs. 5 = Rs. ..............(j) Rs. 30 ÷ 5 = Rs. .............. (k) Rs. 100 ÷ 10 = Rs. ..............(l) Rs. 9.50 = .............. rupees and .............. paisa(m) Rs. 19.17 = .............. rupees and .............. paisa(n) Rs. 5 and 13 paisa = .............. (o) Rs. 13 and 13 paisa = ..............Exercise 3.41. Convert into paisa.(a) Rs. 25 (b) Rs. 75 (c) Rs. 90(d) Rs. 20 and 25 p (e) Rs. 30 and 50 p (f) Rs. 50 and 80 p2. Convert into rupees.(a) 700 paisa (b) 1200 paisa (c) 1500 paisa(d) 50 paisa (e) 70 paisa (f) 100 paisa3. Add the following.(a) Rs. Paisa26 60+ 24 20(b) Rs. Paisa107 80+ 12 70(c) Rs. Paisa18 2020 70+ 39 20(d) Rs. Paisa217 05200 95+ 100 70(e) Rs. 233 and 60 paisa and Rs. 700 and 70 paisa(f) Rs. 548.50 and Rs. 300.60
190 Acme Mathematics-44. Subtract:(a) Rs. Paisa79 20– 12 60(b) Rs. Paisa90 70– 12 80(c) Rs. Paisa111 05– 93 65(d) Rs. Paisa700 42– 599 26(e) Rs. 78 and 62 paisa from Rs. 90 and 62 paisa(f) Rs. 108.87 from Rs. 109.785. Multiply:(a) Rs. Paisa25 20× 12(b) Rs. Paisa112 15× 75(c) Rs. Paisa215 75× 70(d) Rs. Paisa501 07× 95(e) Rs. Paisa710 09× 70(f) Rs. Paisa955 56× 1006. Divide:(a) Rs. Paisa12 36 48(b) Rs. Paisa20 100 80(c) Rs. Paisa15 200 40(d) Rs. Paisa35 467 60(e) Rs. Paisa18 286 02(f) Rs. Paisa27 121 77
Acme Mathematics-4 1914. Verbal problems on moneyStudy the given examples carefully.Example 1 : Nitesh got Rs. 20 and 25 paisa from his mother and Rs. 25 and 75 paisa from his uncle. How much money does he have now?Solution: This problem is related to addition of money.Nitesh has Rs. 46 now.Example 2 : Amara gave the shopkeeper a 100 rupees note for the payment of Rs. 60.75. How much did she get back from the shopkeeper?Solution : This problem is related to subtraction.So,Amara got back Rs. 39.25.Example 3 : Roman earns Rs. 102.60 per day, how much does he earn in 9 days?Solution : This problem is related to multiplication.So,Roman earns Rs. 923.40 in 9 days.100 paisa = 1 rupeeI know how to add. Add paisa first then rupees.Rs. Paisa99 100– 60 7539 25Rs. Paisa100 00– 60 75Rs. Paisa102 60× 9918 540+ 5 – 500923 40
192 Acme Mathematics-4Example 4 : If Mr Bhandari gave Rs. 150.50 to his son Kiran for pocket money for 7 days. Find his pocket money for 1 day.Solution : This problem is related to division.So,The pocket money for Kiran is Rs. 21.50 for 1 day.Classwork1. Price of certain goods are given below :Rs. 195 Rs. 700 Rs. 250.50 Rs. 3Find the total amount spent on:(a) 2 balls, 3 bags and 4 pencils. (b) 5 books and 3 balls.(c) 3 books, a ball and 3 pencils.Exercise 3.51. Read the price list of \"Tarkari Bazar\" at Narayangarh and give the answers to the following questions:2 1 5 0Rs. Paisa7 1 5 0 5 0 – 1 4 1 0 – 7 3 5 0 – 3 5 0 0Potato - Rs. 35 per kgTomato - Rs. 50 per kgCauliflower - Rs. 40 per kgPea - Rs. 30 per kgChilli - Rs. 100 per kgParwal - Rs. 40.50 per kgCarrot - Rs. 50 per kg
Acme Mathematics-4 193(a) How much does Mrs. Tara have to pay for 1 kg potato and 1 kg cauliflower?(b) Find the total bill for the following items.1 kg tomato1 kg chilli1 kg peaMadan's bill1 kg parwal1 kg carrot1 kg peaPramila's bill(c) How much is the difference between the price of potato and parwal?(d) How much is the difference between the lowest price and the highest price?(e) Find the total bill for the given items.Carrot 5 kgHari's billParwal 10 kgUma's billPotato 2 kgTomato 1 kgAnjan's bill2. Fill in the blanks (use price list of your book):Rs. PaisaThe cost of Science book = ................ ................The cost of Maths book = ................ ................The cost of Nepali book = ................ ................Total cost = ................ ................3. (a) Birat had 500 rupees note. He went for shopping and spent Rs. 416.40. How much money is left with him?(b) Pitamber has to buy a book for Rs. 515.50. He has only Rs. 200.50. How much more money does he need to pay?(c) Hemraj has Rs. 1500.60. He gave Rs. 966.75 to his daughter. How much money is left with him?4. Study the figures given below and calculate the following. Rs.112 Rs.1650 Rs.2500 Rs.415
194 Acme Mathematics-4Study the above price and calculate the following:(a) The cost of 12 balls.(b) The cost of 9 T-shirt.(c) The cost of 5 Geometry box and 6 balls.(d) The cost of 2 balls, 3 T-Shirt and 1 pen.5. Complete the table:S. No. Number of goods Total cost Per unit cost1Rs.9.60....................................2Rs.12000....................................3Rs.16....................................4Rs.31....................................6. (a) If the cost of 7 books is Rs. 927.50, what is the cost of 1 book?(b) Find the monthly fee of Kushal, if he pays Rs. 13392.60 yearly.(c) The yearly salary of a teacher is Rs. 150000. Find his 1 month's salary.(d) Thakur pays Rs. 120 for 10 copies, how much does he pay for 1 copy?
Acme Mathematics-4 1953.3 DistanceWarm-up:1. Name 2 instruments measuring the length...................................... and .................................. .2. Guess and write 'Yes' or 'No' in the blanks.(a) Your black board (white board) is 10 cm long. ..............(b) Your height is 3 m. ..............(c) Length of your Maths book is 3 cm. ..............(d) Length of eraser is 10 cm. ..............(e) Length of your scale is 15 cm. ..............3. Fill in the blanks.(a) 100 cm = .............. m (b) 1000 m = .............. km(c) 200 cm = .............. m (c) 4000 m = .............. km(e) (f)It is ..................... cm long It is ..................... cm long(g) Length of your tooth brush is ............... long.4. Find the sum.(a) 7 cm + 6 cm = ........... cm (b) 10 cm + 12 cm = ........... cm(c) 4 km + 9 km = ........... km (d) 14 m + 13 m = ........... m5. Subtract:(a) 20 m – 6 m = ........... m (b) 10 cm – 2 cm = ........... cm(c) 30 km – 28 km = ........... km (d) 28 cm – 20 cm = ........... cm0 1 2 3 4 5 6 7 8 9 105 4 3 2 10 1 2 3 4 5 6 7 8 9 105 4 3 2 1mm cm× 10÷ 10
196 Acme Mathematics-41. Unit of lengthWe use scale (ruler) to measure the length of books, pencils, erasers, pens, white boards, etc.0 1 2 3 4 5 6 7 8 9 105 4 3 2 10 to 1 is 1 cmeach line indicates millimeter (mm)It is starting point.It is a scale.In 0 to 1, there are 10 small lines.So, 10 mm = 1 centimeter (cm).The scale given above is centimeter scale. It is your scale. Your scale is either 15 cm long or 30 cm long. It measures the small lengths only.We use measuring tape to measure the length.Meter and kilometer are also units of length.100 cm = 1 meter (m)1000 m = 1 kilometer (km)Kilometer is the largest unit of length in metric system.2. Relation between units of lengthA. Millimeter and centimeter10 mm = 1 cm1 cm = 10 mmIt is a measuring tapeHow long is 1 km?centi multiply by 10milli divide by 10Is it?
Acme Mathematics-4 197Conversion of millimeter and centimeterExample 1 : Convert 5 cm into mm.Solution : 1 cm = 10 mm5 cm = 5 × 10 mm = 50 mmExample 2 : Convert 40 mm into cm.Solution : 10 mm = 1 cm40 mm = 40 ÷ 10 cm= 4 cmExample 3 : Convert 66 mm into cm and mm.Solution : 10 mm= 1 cm66 mm= (66 ÷ 10) cmDivide 66 by 10Now,So, 66 mm = 6 cm and 6 mmB. Centimeter and meter100 cm = 1 meter (m)1 m = 100 cmConversion of meter and centimeterExample 4 : Convert 15 m into cm.Solution : 1 m = 100 cm15 m = 15 × 100 cm= 1500 cmDivide 40 by 10. 10 ) 6 6 ( 6 – 6 0 6It is cm.It is mm.cm m× 100÷ 100 Oh! meter is 100 times greater than cm.Remember 1 0 0 × 1 5 5 0 0 1 0 0 1 5 0 0
198 Acme Mathematics-4Example 5 : Convert 900 cm into meter.Solution : 100 cm = 1 m900 cm = (900 ÷ 100) cm= 9 mC. Meters and kilometers1000 m = 1 kilometer (km)1 km = 1000 mConversion of m and kmExample 6 : Convert 7 km into meter.Solution : 1 km = 1000 m7 km = 7 × 1000 m= 7000 mExample 7 : Convert 12000 m into km.Solution : 1000 m = 1 km12000 m = (12000 ÷ 1000) km= 12 kmExample 8 : Convert 1423 m into kilometer and meter.Solution : 1000 m = 1 km1423 m = (1423 ÷ 1000) kmNow,So, 1423 m = 1 km and 423 m. 100 9 0 0 9 – 9 0 0 0m km× 1000÷ 1000 1000 1 2 0 0 0 12 – 1 0 0 0 2 0 0 0 – 2 0 0 0 0 1000 ) 1 4 2 3 ( 1 – 1 0 0 0 4 2 3Remember!× 1000 × 100 × 10km m cm mm÷ 10 ÷ 100 ÷ 1000mm cm m km
Acme Mathematics-4 199Classwork1 Fill in the blanks:(a) 3 cm = .............. mm (b) 10 cm = .............. mm(c) 10 mm = .............. cm (d) 20 mm = .............. cm(e) 200 cm = .............. m (f) 700 cm = .............. m(g) 3000 m = .............. km (h) 6000 m = .............. km2. Measure the length of the following objects:(a) (b)It is ..................... It is .....................(c) (d)It is ..................... It is .....................Exercise 3.61. Estimate the length (use mm, cm, m or km):(a) Length of the white board. .................. .(b) Length of your school building .................. .(c) Length of the road near your home. .................. .(d) Thickness of your eraser. .................. .(e) Height of your Maths teacher. .................. .2. Convert the following as indicated:(a) 30 mm (cm) (b) 90 m (cm) (c) 120 mm (cm)(d) 13 cm (mm) (e) 15 cm (mm) (f) 39 cm (mm)(g) 200 cm (m) (h) 700 cm (m) (i) 1900 cm (m)(j) 5 m (cm) (k) 11 m (cm) (l) 17 m (cm)(m) 8000 m (km) (n) 4 km (m) (o) 12 km (m)3. Convert as indicated in the bracket:(a) 5 cm 9 mm (mm) (b) 12 cm 7 mm (mm) (c) 7 m 12 cm (cm)A B
200 Acme Mathematics-4(d) 8 m 80 cm (cm) (e) 1 km 200 m (m) (f) 3 km 500 m (m)3. Addition and subtractionLook at the examples carefully and try to understand the addition and subtraction.Example 1 : Add: 30 cm 4 mm and 14 cm 8 mm.Solution : Here,Example 2 : Add: 4 m 17 cm 2 mm, 7 m 83 cm 4 mm and 10 m 50 cm 6 mm.Solution : Here,Example 3 : Add: 4 km 700 m 29 cm and 14 km 800 m 80 cm.Solution : Here,Example 4 : Subtract: 14 m 20 cm from 20 m 12 cmSolution : Here,cm mm30 4+ 14 844 12+ 1 – 1045 210 mm = 1 cm1 cm is carry over m cm mm 4 17 2 7 83 4+ 10 50 6 21 150 12 + 1 – 10 21 151 2+ 1 – 10022 51 2It is carry over. 100 cm = 1 mYes, addition is so easy.km m cm 4 700 29+ 14 800 8018 1500 109 + 1 – 10018 1501 9+ 1 – 1000 19 501 9I know 1000 m = 1 kmm cm20 12– 14 20m cm19 112– 14 20 5 92100 cm