Passport-G3-FoundationMax-Maths-FY_opt

Shapes Fractions 3 6 5 8 Example 10: Colour the shapes according to the given fractions. Shapes Fractions 1 5 2 7 3 4 Solution: We can colour the shapes according to the fractions as – Shapes Fractions 1 5 2 7 3 4 Fractions 145 L09_V2_PPS_Maths_G3_TB.indd 145 1/12/2017 5:22:08 AM

Train My Brain What fraction of the collection is: a) Chocolate cupcakes b) Strawberry cupcakes c) Butterscotch cupcakes 9.2 I Apply We can apply the knowledge of fractions in many real-life situations. Let us see a few examples. Example 11: Raju brought a bag of 30 marbles. Out of these, 10 marbles are blue. How many marbles are blue? Solution: Total number of marbles = 30 1 Fraction of blue marbles = of 30 = 30 ÷ 3 = 10 3 Total number of blue marbles = 10 Example 12: A basket has 64 flowers. Half of them are roses, a quarter of them are marigolds and a quarter of them are lotus. How many each of roses, marigolds and lotus are there in the basket? Solution: Total number of flowers = 64 Half of the flowers are roses. 1 The number of roses = of 64 = 64 ÷ 2 = 32 2 A quarter of the flowers are marigolds. 146 L09_V2_PPS_Maths_G3_TB.indd 146 1/12/2017 5:22:10 AM

1 The number of marigolds = of 64 = 64 ÷ 4 = 16 4 A quarter of the flowers are lotus. 1 The number of lotus = of 64 = 64 ÷ 4 = 16 4 Therefore, there are 32 roses, 16 marigolds and 16 lotus in the basket. Example 13: A set of 48 pens have 13 blue, 15 red and 11 black ink pens. The remaining are green ink pens. What fraction of the pens is green? Solution: Total number of pens = 48 Total number of blue, red and black ink pens = 13 + 15 + 11 = 39 Number of green ink pens = 48 – 39 = 9 Fraction of green ink pens = = Number of green ink pens = 9 Totalnumberofpens 48 Example 14: A bunch of 15 balloons has 2 green balloons, 3 blue balloons and 10 red balloons. Write the fraction of balloons of each colour. Solution: Total number of balloons= 15 Number of green balloons = 2 So, fraction of green balloons = 2 15 Number of blue balloons = 3 So, fraction of blue balloons = 3 15 Number of red balloons = 10 So, fraction of red balloons = 10 15 Fractions 147 L09_V2_PPS_Maths_G3_TB.indd 147 1/12/2017 5:22:12 AM

9.2 I Explore (H.O.T.S.) In some real-life situations, we need to find a fraction of some goods such as fruits, vegetables, milk, oil and so on. Let us now see some such examples. Example 15: One kilogram of apples costs ` 16 and one kilogram of papaya costs ` 20. If Rita buys 1 kg of apples and 1 kg of papaya, how much did 2 4 she spend? Solution: Cost of 1 kg apples = ` 16 1 1 Cost of kg apples = of ` 16 = ` 16 ÷ 2 = ` 8 2 2 (To find a half, we divide by 2) Cost of 1 kg papaya = ` 20 1 1 Cost of kg papaya = of ` 20 = ` 20 ÷ 4 = ` 5 4 4 (To find a fourth, we divide by 4) Therefore, the money spent by Rita = ` 8 + ` 5 = ` 13 2 Example 16: Sujay completed of his Maths homework. If he had to solve 25 5 problems, how many did he complete? Solution: Fraction of homework completed = 2 5 Total number of problems to be solved = 25 2 Number of problems Sujay solved = of 25 = (25 ÷ 5) × 2 = 5 × 2 = 10 5 Therefore, Sujay has solved 10 problems. 148 L09_V2_PPS_Maths_G3_TB.indd 148 1/12/2017 5:22:13 AM

Maths Munchies Egyptians have a different way to represent fractions. 1 2 3 To represent 1 as numerator, they use a mouth picture which literally means ‘part’. So, the fraction one-fifth will be shown as On the other hand, fractions were only written in words in Ancient Rome. 1 was called unica 6 was called semis 12 12 1 1 24 was called semunica 144 was called scripulum Connect the Dots Science Fun Around 7 out of 10 parts of air is nitrogen. Oxygen comes at the second position. 2 out of 10 parts of air is oxygen. Fractions 149 L09_V2_PPS_Maths_G3_TB.indd 149 1/12/2017 5:22:14 AM

English Fun Here is a poem about fractions. The Fraction Jingle (Sing to the tune of “The Wheels on the bus”) The numerator is the top number, Top number, top number. The numerator is the top number. In a fraction. The numerator tells how many parts, How many parts, how many parts. The numerator tells how many parts are In a fraction The denominator is the bottom number. Bottom number, bottom number. The denominator is the bottom number In a fraction The denominator tells the total parts, The total parts, the total parts, The denominator tells the total parts, In a fraction. A Note to Parent Fractions are present all around us. The easiest way to make a child relate to fractions is through food items. Cut fruits such as apples and oranges in different equal parts and use it to help your child understand fractions. 150 L09_V2_PPS_Maths_G3_TB.indd 150 1/12/2017 5:22:15 AM

Drill Time Concept 9.1: Fractions as a Part of a Whole 1) Find the numerator and the denominator in each of these fractions. 2 1 2 4 5 a) b) c) d) e) 5 7 3 9 7 2) Identify the fractions of the shaded parts. a) b) c) d) e) Concept 9.2: Fraction of a Collection 3) Find fraction of coloured parts. a) b) c) d) e) 1 4) Find 1 and of the following collection. 2 4 5) Word Problems 1 a) A circular disc is divided into 12 equal parts. Venu shaded of the disc pink 4 1 and of the disc green. How many parts of the disc are shaded? How 3 many parts are not shaded? 1 1 b) Rajesh has 24 notebooks. of them are unruled and of them are four- 6 2 ruled. How many books are (a) unruled and (b) four-ruled? Fractions 151 L09_V2_PPS_Maths_G3_TB.indd 151 1/12/2017 5:22:17 AM

Mo Moneyney I Will Learn Concepts 10.1: Convert Rupee into Paise 10.2: Add and Subtract Money with Conversion 10.3: Multiply and Divide Money 10.4: Make Rate Charts and Bills PPS_Class 3_Maths_ch-10.indd 152 1/13/2017 12:46:42 PM

Concept 10.1: Convert Rupee into Paise I Think Neena has ` 38 in her piggy bank. She wants to know how many paise she has. Do you know? To answer this question, we must know how to convert rupees to paise. 10.1 I Recall We have learnt to identify different coins and currency notes. We have also learnt that 100 paise make a rupee. Let us learn more about money. 1 rupee = 100 paise 100 p = 1 rupee Let us revise the concept about money. a) The value of the given coin is: [ ] (A) ` 1 (B) ` 2 (C) ` 5 (D) ` 10 b) The ` 500 note among the following is: [ ] (A) (B) (C) (D) Money 153 PPS_Class 3_Maths_ch-10.indd 153 1/13/2017 12:46:56 PM

c) The combination that has the greatest value is: [ ] (A) (B) (C) (D) 10.1 I Remember and Understand Let us understand the conversion of rupees to paise through an activity. Activity: The students must take their play money (having all play notes and coins). As the teacher writes the rupees on the board, each student picks the exact number of paise in it. There can be many combinations for the same amount of rupees. For example, 1 rupee is 100 paise. So, the students may take two 50 paise coins. Let us understand the conversion through some examples. Example 1: Convert the given rupees into paise: a) ` 2 b) ` 5 c) ` 9 Solution: We know that 1 rupee = 100 paise a) ` 2 = 2 × 100 paise = 200 paise 154 PPS_Class 3_Maths_ch-10.indd 154 1/13/2017 12:47:12 PM

b) ` 5 = 5 × 100 paise = 500 paise c) ` 9 = 9 × 100 paise = 900 paise Similarly, we can convert paise into rupees. Converting paise into rupees is the reverse process of conversion of rupees into paise. Example 2: Convert 360 paise to rupees. Solution: We can convert paise to rupees as: Solved Solve this Steps 360 paise 380 paise Step 1: Write the given paise 360 paise = 300 paise + as hundreds of paise. 60 paise Step 2: Rearrange 300 paise 300 paise = (3 × 100) as a product of 100 paise. paise + 60 paise Step 3: Write in rupees. ` 3 + 60 paise = ` 3.60 Train My Brain Convert as given. a) 550 paise to rupees b) 25 rupees to paise c) 110 paise to rupees 10.1 I Apply Let us see some real-life examples involving conversion of rupees into paise and that of paise into rupees. Example 3: Anil has ` 10 with him. How many paise does he have? Solution: 1 rupee = 100 paise So, 10 rupees = 10 × 100 paise Money 155 PPS_Class 3_Maths_ch-10.indd 155 1/13/2017 12:47:20 PM

= 1000 paise Anil has 1000 paise with him. Example 4: Raj has 670 paise. How many rupees does he have? Solution: Amount with Raj = 670 paise = 600 paise + 70 paise = (6 × 100) paise + 70 paise = ` 6 + 70 paise = ` 6.70 Therefore, Raj has ` 6.70. 10.1 I Explore (H.O.T.S.) Observe these examples where conversion of rupees to paise and that of paise to rupees are mostly useful. Example 5: Vani has ` 4.30, Gita has ` 5.50 and Ravi has 470 paise. Who has the least amount of money? Solution: Money Vani has = ` 4.30 Money Gita has = ` 5.50 Money Ravi has = 470 paise To compare money, all the money must be in the same unit. So, let us first convert the amounts in rupees to paise. ` 4.30 = (4 × 100) + 30 = 430 paise ` 5.50 = (5 × 100) + 50 = 550 paise Now, arranging the money in ascending order, we get 430 < 470 < 550. Therefore, Vani has the least money. 156 PPS_Class 3_Maths_ch-10.indd 156 1/13/2017 12:47:23 PM

Example 6: Ram has ` 1.10, Shyam has ` 1.40 and Rishi has ` 2.00. Arrange the amounts in ascending order. Who has the most money? Solution: Amount Ram has = ` 1.10 Amount Shyam has = ` 1.40 Amount Rishi has = ` 2.00 To compare the money, all of them must be in the same unit. So, let us convert the amounts in rupees to paise. ` 1.10 = (1 × 100) + 10 = 110 paise ` 1.40 = (1 × 100) + 40 = 140 paise ` 2.00 = (2 × 100) = 200 paise Arranging the money in descending order we get, 200 > 140 > 110. Therefore, Rishi has more money than Ram and Shyam. Maths Munchies Punch marked coins were the first ever coins documented between 7 – 6 century BC and 1 century th st th AD. Most of the coins were made of silver. Concept 10.2: Add and Subtract Money with Conversion I Think Neena’s father bought a toy car for ` 56 and a toy bus for ` 43. How much did he spend altogether? How much change does he get if he gives ` 100 to the shopkeeper? To answer this question, we must know how to add and subtract money. Money 157 PPS_Class 3_Maths_ch-10.indd 157 1/13/2017 12:47:26 PM

10.2 I Recall Recall that two or more numbers are added by writing them one below the other. This method of addition is called the column method. We know that rupees and paise are separated using a dot or a point. In the column method, we write money in such a way that the dots or points are placed exactly one below the other. The rupees are under rupees and the paise are under the paise. Let us recall a few concepts about money through these questions. a) 50 paise + 50 paise = ________________ b) ` 20 + ` 5 + 50 paise = ______________ c) ` 50 – ` 10 = _______________ d) ` 20 + ` 10 = _______________ e) ` 50 – ` 20 = _______________ 10.2 I Remember and Understand Addition and subtraction of money is similar to addition and subtraction of numbers. In column method, we write numbers one below the other and add or subtract as needed. Paise is always Let us understand this through some examples. written in two digits after the Example 7: Add: ` 14.65 and ` 23.80 point. Solution: We can add two amounts as: 158 PPS_Class 3_Maths_ch-10.indd 158 1/13/2017 12:47:27 PM

Steps Solved Solve these Step 1: Write the given numbers ` p ` p with the points exactly one below 1 4. 6 5 4 1. 5 0 the other, as shown. + 2 3. 8 0 + 4 5. 7 5 ` p Step 2: First add the paise. Regroup 1 the sum if needed. Write the sum 1 4. 6 5 ` p under paise. Place the dot just + 2 3. 8 0 below the dot. . 4 5 3 8. 4 5 + 3 5. 6 0 ` p Step 3: Add the rupees. Add the 1 carry forward (if any) from the 1 4. 6 5 previous step. Write the sum under + 2 3. 8 0 ` p rupees. 3 8. 4 5 2 3. 6 5 + 1 4. 5 2 Step 4: Write the sum of the given ` 14.65 + `23.80 amounts. = ` 38.45 Example 8: Write in columns and subtract: ` 56.50 from ` 73.50 Solution: We can subtract the amounts as: Steps Solved Solve these Step 1: Write the given numbers ` p with the dots exactly one below the 7 3. 5 0 ` p other, as shown. − 5 6. 5 0 8 0. 7 5 Step 2: First subtract the paise. ` p − 4 1. 5 0 Regroup if needed. Write the 7 3. 5 0 difference under paise. Place the − 5 6. 5 0 dot just below the dot. 0 0 Money 159 PPS_Class 3_Maths_ch-10.indd 159 1/13/2017 12:47:29 PM

Steps Solved Solve these Step 3: Subtract the rupees. Write the ` p difference under rupees. 6 13 7 3. 5 0 ` p − 5 6. 5 0 1 7. 0 0 6 0. 7 5 − 3 2. 5 0 Step 4: Write the difference of the given amounts. ` 73. 50 - ` 56. 50 = ` 17.00 Train My Brain Solve the following: a) ` 28.65 + ` 62.35 b) ` 32.35 + ` 65.65 c) ` 70.75 – ` 62.45 10.2 I Apply Look at some real-life examples where we apply addition and subtraction of money. Example 9: Arun has ` 45.50 with him. He gave ` 23.50 to Amar. How much money is Arun left with? Solution: Amount Arun has = ` 45.50 ` p 4 5. 5 0 Amount Arun gave to Amar = ` 23.50 − 2 3. 5 0 Difference in the amounts 2 2. 0 0 = ` 45.50 – ` 23.50 = ` 22 Therefore, the amount left with Arun = ` 22 Example 10: Ramu has ` 12.75 with him. His friend has ` 28.50 with him. What is the amount both of them have? Solution: Amount Ramu has = ` 12.75 160 PPS_Class 3_Maths_ch-10.indd 160 1/13/2017 12:47:38 PM

Amount Ramu’s friend has = ` 28.50 ` p 1 1 To find the total amount we have to add both the 1 2. 7 5 amounts. + 2 8. 5 0 Total amount with Ramu and his friend is ` 41.25. 4 1. 2 5 10.2 I Explore (H.O.T.S.) In some situations, we may need to add and subtract amounts together. In such cases, we need to identify which operation is to be carried out first. Let us see a few examples. Example 11: Surya went to a water park with his parents. The ticket for each ride is as given. Roller coaster: ` 35 Surya went on two rides. He gave ` 60 and got a change of ` 5. Which two rides did he go on? Break dance: ` 32 Water ride: ` 20 Solution: Surya gave ` 60. The change he got is ` 5. The money spent for two rides = ` 60 – ` 5 = ` 55 So, we must add and check which two tickets cost ` 55. Train My Brain ` 35 + ` 32 = ` 67 which is not ` 55. ` 32 + ` 20 = ` 52 which is not ` 55. ` 35 + ` 20 = ` 55 Therefore, the two rides that Surya went on are roller coaster and water ride. Example 12: Add ` 20 and ` 10.50. Subtract the sum from ` 40. Solution: First add ` 20 and ` 10.50. ` p ` 20 + ` 10.50 = ` 30.50 2 0. 0 0 + 1 0. 5 0 Now, let us find the difference between ` 30.50 3 0. 5 0 and ` 40. Money 161 PPS_Class 3_Maths_ch-10.indd 161 1/13/2017 12:47:38 PM

Therefore, ` 40 – ` 30.50 = ` 9.50 ` p 4 0. 0 0 − 3 0. 5 0 Maths Munchies 0 9. 5 0 It is easier to add money without actually doing addition. If you want to know the exact amount in rupees, you can just equally group the coins. Suppose you have eight 50 paise coins, we group it to find the total amount. Make groups of 2 coins together as two 50 paise = 1 rupee. So, 1 group = 1 rupee. For eight 50 paise coins, you will have 2 + 2 + 2 + 2. As you have got 4 groups, the total money you have is ` 4. Concept 10.3: Multiply and Divide Money I Think Neena's father gave her ` 150 on three occasions. Neena wants to share the total amount equally with her brother. How should she find the total amount? How much will Neena and her brother get? To answer this question, we must learn how to multiply and divide money. 10.3 I Recall While multiplying, we begin from ones place and move to the tens and hundreds places. Sometimes, we may need to regroup the products. We begin division from the largest place and move to the ones place of the number. 162 PPS_Class 3_Maths_ch-10.indd 162 1/13/2017 12:47:39 PM

Let us answer these to revise the concept. a) 32 × 4 = _____ b) 11 × 6 = _____ c) 20 ÷ 2 = _____ b) 48 ÷ 3 = _____ e) 10 × 6 = _____ f) 24 ÷ 8 = _____ 10.3 I Remember and Understand Multiplication and division of money is similar to that of numbers. To multiply money, first multiply the numbers under In multiplication, start paise, and place the point. Then multiply the number multiplying from the under rupees. To divide money, we divide the numbers rightmost digit. under rupees and place the point in the quotient. Then, In division, start dividing divide the number under paise. from the leftmost digit. Now, let us understand multiplying and dividing money through a few examples. Example 13: Multiply ` 72.50 by 8. Solution: Follow the steps to find the total amount. Step 1: Multiply the paise. Regroup if needed. ` . p Place the point in the product, just below the 2 4 point in the given number. 7 2 . 50 Step 2: Multiply the rupees. Regroup if needed. × 8 5 8 0 . 00 Example 14: Divide: ` 35.70 by 7 510. Solution: Follow the steps to divide the amount. 7 35 70 . ) Step 1: Divide the rupees. − 35 07 Step 2: Place point. − 7 Step 3: Divide the paise. 00 − 00 00 Money 163 PPS_Class 3_Maths_ch-10.indd 163 1/13/2017 12:47:53 PM

Train My Brain Solve the following: a) ` 28.20 × 5 b) ` 70 ÷ 2 c) ` 44.10 × 5 10.3 I Apply We apply multiplication and division of money in many real-life situations. Let us see some examples. Example 15: A dozen bananas cost ` 48. a) What is the cost of three dozen bananas? b) What is the cost of one banana? Solution: One dozen = 12 a) Cost of one dozen bananas = ` 48 2 Cost of three dozen bananas = ` 48 × 3 = ` 144 4 8 b) Cost of one dozen (12) bananas = ` 48 × 3 1 4 4 Cost of one banana = ` 48 ÷ 12 = ` 4 (Recall that 10 × 4 = 40. Then 11 × 4 = 44 and 12 × 4 = 48) Example 16: Rahul went to buy chocolates. If a chocolate costs ` 20.60, how much money would 4 such chocolates cost? ` p Solution: Cost of one chocolate = ` 20.60 2 2 0. 6 0 Cost of 4 chocolates = ` 20.60 × 4 = ` 82.40 × 4 8 2. 4 0 10.3 I Explore (H.O.T.S.) In some situations, we have to carry out more than one operation on money. Consider the following examples. 164 PPS_Class 3_Maths_ch-10.indd 164 1/13/2017 12:47:54 PM

Example 17: Nidhi buys 4 bunches of flowers each costing ` 54. She buys 6 candy bars for her brothers at the cost of ` 5.50 each. If she has ` 7.50 left with her, how much did she have in the beginning? Solution: Cost of a bunch of flowers = ` 54 Cost of 4 bunches = ` 54 × 4 = ` 216 Cost of each candy bar = ` 5.50 Cost of 6 candy bars = ` 5.50 × 6 = ` 33 Total cost of the things she bought = ` 216 + ` 33 = ` 249 Amount she is left with = ` 7.50 Therefore, amount she had in the beginning = ` 249 + ` 7.50 = ` 256.50 Example 18: Bhanu bought some items for ` 362. She has some ` 100 notes. How many notes should she give the shop keeper? Solution: Cost of the items ` 362 = ` 300 + ` 62 = (` 100 x 3) + ` 62 As ` 362 has to be paid, Bhanu has to give 3 + 1 = 4 notes of ` 100. Maths Munchies 1 When we deposit our money in banks, the money increases. The bank 2 3 gives us money as reward based on amount of money we deposit. It is called Interest. This is one of the way money multiplies. So, instead of saving money in piggy bank we should put money in banks. Money 165 PPS_Class 3_Maths_ch-10.indd 165 1/13/2017 12:47:54 PM

Concept 10.4: Make Rate Charts and Bills I Think Neena went to a mall with her parents. She buys a pair of jeans, 2 shirts, a story book and a ball. How much should she pay? She was given a bill for what she has bought. Can you prepare a bill similar to the one given to her? To answer this question, we must know how to prepare rate charts and bills. 10.4 I Recall Recall that we make lists of items when we go shopping. The lists can be of provisions, stationery and items like vegetables or fruits. We can compare the list of items and the items we received. We can compare their rates and add them to get the total amount to be paid. Let us answer these to revise addition and multiplication of money. a) ` 12 × 2 = __________ b) ` 20 × 3 = __________ c) ` 25 × 4 = __________ d) ` 12 + ` 20 = __________ e) ` 30 + ` 40 = __________ f) ` 21 + ` 10 = 10.4 I Remember and Understand 1) Making bills To make a bill of items, we write the rate of the object and the quantity in the bill. We write the product of the rate and the quantity. We add the products to find the 166 PPS_Class 3_Maths_ch-10.indd 166 1/13/2017 12:47:55 PM

total bill amount. Addition of amounts is similar to the addition of numbers of two or more digits. Let us understand how to make bills through a few examples. Example 19: The rates of some items in a stationery shop are given in the box. Sunil buys a few items as given in the list. Make a bill for the items he bought. Item Quantity Pencil box 1 Erasers 2 Sharpeners 4 Pens 3 Notebooks 4 Solution: Follow the steps to find the bill. Step 1: Write the items and their quantity in the bill. Step 2: Then write the cost per item. Step 3: Find the total cost of each item by multiplying the number of items by its rate. Step 4: Find the total bill by adding the amount for all the items bought. Money 167 PPS_Class 3_Maths_ch-10.indd 167 1/13/2017 12:47:57 PM

Bill S.No Item Quantity Rate per Amount item ` p 1 Pencil box 1 `24.50 24 50 2 Erasers 2 `5.00 10 00 3 Sharpeners 4 `3.00 12 00 4 Pens 3 `4.00 12 00 5 Notebooks 4 `10.00 40 00 Total 98 50 2) Making rate charts When rates of all items are written on the item, it is difficult to see and compare them. So, we need to make a rate chart. In this chart, we write the rate of each item. Example 20: Anil and his friends are playing with play money. Anil runs a supermarket. Some items in his supermarket are given below with their rates. ` 275/- ` 280/- ` 50/- ` 34/- ` 102/- ` 149.50/- ` 24.50/- ` 140/- per kg ` 45/- per kg ` 130/- per kg ` 50/- ` 40/- per dozen 168 PPS_Class 3_Maths_ch-10.indd 168 1/13/2017 12:49:27 PM

He makes a rate chart to display the price of each item. How will the rate chart look? Solution: 1. Draw a table. 2. Write each item and its rate in columns. Item Rate ` Item Rate ` Boost 275.00 1kg rice 45.00 Kitkat 50.00 1kg dal 140.00 Tea powder 102.50 1 biscuit packet 24.50 Horlicks 280.00 paneer 50.00 Soap 34.00 1 kg apples 130.00 Honey 149.50 1 dozen bananas 40.00 Train My Brain Answer the following: a) If you buy 4 items from a shop, how will you decide the amount to be paid? b) Suppose you need to buy 10 items from the shop, how will you remember the names? What will you do? How will the shopkeeper prepare the bill of items? c) Make a bill for the following items. Cake - ` 100, candle - ` 25, 10 birthday caps - ` 5 each, 10 small gifts - ` 15 each. 10.4 I Apply Let us learn how to make rate charts and bills and use them in our daily life with an activity. Go to a vegetable store. Suppose you see the rate chart of all vegetables with their rates per kg. Buy some vegetables and make the bill. Money 169 PPS_Class 3_Maths_ch-10.indd 169 1/13/2017 12:49:27 PM

Rate per kg Vegetables Bill in ` Cabbage 24.00 Item Rate per kg ` Paise Brinjal 30.00 1 kg brinjal 30.00 30 00 Okra 40.00 2 kg potato 40.00 80 00 Potato 40.00 2 kg tomato 20.00 40 00 Tomato 20.00 1 kg onion 22.00 22 00 Onion 22.00 Total 172 00 The bill for the items you bought would be as shown. Write the rates carefully, by considering the quantity. Find the total bill by adding total cost of each vegetable. Here, the total bill is ` 172.00. Example 21: Ashish went to Amar Bakery with his friends. The rate chart of the items available there is as given. Item Rate in ` Cheese Burger 55.00 Chicken Burger 60.00 Veg Burger 50.00 Cheese Pizza 125.00 Chicken Pizza 150.00 170 PPS_Class 3_Maths_ch-10.indd 170 1/13/2017 12:49:30 PM

Item Rate in ` Veg Pizza 110.00 Hot Dog 45.00 Veg Roll 40.00 Chicken Roll 50.00 What can they buy in this bakery, if they have ` 250? (Write 3 different options and make a bill for one of the options.) Solution: To write three different options for Ashish and his friends to choose, see that the sum of the rates does not exceed ` 250. The three options could be: a) 2 Chicken Burgers and 1 Cheese Pizza b) 2 Cheese Pizzas c) 2 Veg Rolls, 1 Veg Pizza, 1 Chicken Burger Let us now make a bill for 3 option. Find the cost and write the total. rd Amar Bakery Bill Item Rate per item ` p 2 Veg. rolls ` 40.00 80 00 1 Veg. pizza ` 110.00 110 00 1 Chicken burger ` 60.00 60 00 Total 250 00 Money 171 PPS_Class 3_Maths_ch-10.indd 171 1/13/2017 12:49:32 PM

10.4 I Explore (H.O.T.S.) Seeing the rate chart in a shop, we calculate mentally the amount for the items we buy and give money to the shopkeeper. Let us now see an example. Example 22: Sneha went to an ice cream 1000 ml tub of ice-cream Rate in ` shop and saw the rate chart given. Sneha took 2 Butter Scotch 150.00 Butter Scotch, 2 Mango, 1 Vanilla 120.00 Chocolate and 1 Vanilla Strawberry 130.00 ice cream tubs. What is the Mango 140.00 total bill ? Make the bill. If Chocolate 160.00 she gave ` 1000, how much did she get as change? Solution: Write the items, number of each item and their rates. Multiply them to find cost of each flavour of ice-cream. Find the total by adding all the amounts. Ice cream shop Item Quantity Rate per tub ` paise Butter Scotch 2 ` 150.00 300 00 Mango 2 ` 140.00 280 00 Chocolate 1 ` 160.00 160 00 Vanilla 1 ` 120.00 120 00 Total 860 00 Amount Sneha gave = ` 1000 Total bill amount = ` 860 The amount she received as change = ` 1000 – ` 860 = ` 140 172 PPS_Class 3_Maths_ch-10.indd 172 1/13/2017 12:49:32 PM

Maths Munchies Why is it important to always take a bill of the items we buy? Bills are a proof that we bought the things from a particular seller. The bill acts as a record that must be submitted as a proof of our purchase. Connect the Dots English Fun Here is a poem about Indian rupee. Very odd are the things A rupee coin can make, A pleasure to give and take. Toss it up for head or tail, Buy a stamp for your mail, Offer it to god and pray, It can buy you toys of clay, Use it for a call you make, Or to check your body weight Social Studies Fun Different countries have different type of money. Like we have Rupees and Paise, Americans have Dollars and Cents 1 rupee = 100 paise and 1 Dollar = 100 cents. Money 173 PPS_Class 3_Maths_ch-10.indd 173 1/13/2017 12:49:37 PM

A Note to Parent Take your child shopping and show him or her what a bill looks like. Make him or her calculate the total using addition, subtraction and multiplication. Drill time Concept 10.1: Convert Rupee into Paise 1) Convert rupees to paise. a) ` 34 b) ` 12 c) ` 80 d) ` 29 e) ` 10 2) Convert paise to rupees. a) 320 paise b) 140 paise c) 450 paise d) 298 paise e) 100 paise Concept 10.2: Add and Subtract Money with Conversion 3) Add: a) ` 23.24 + ` 10.80 b) ` 31.20 + ` 19.16 c) ` 61.21 + ` 29.20 d) ` 11.10 + ` 12.90 e) ` 60.90 + ` 24.23 4) Subtract: a) ` 87.10 – ` 23.20 b) ` 20.12 – ` 10.13 c) ` 31.55 – ` 22.44 d) ` 99.99 – ` 22.22 e) ` 56.13 – ` 12.03 174 PPS_Class 3_Maths_ch-10.indd 174 1/13/2017 12:49:37 PM

Drill time Concept 10.3: Multiply and Divide Money 5) Multiply: a) ` 23.14 × 2 b) ` 10.13 × 3 c) ` 99.99 × 1 d) ` 34.10 × 4 e) ` 54.29 × 5 6) Divide: a) ` 21 ÷ 7 b) ` 44 ÷ 2 c) ` 84 ÷ 4 d) ` 10.50 ÷ 5 e) ` 63.33 ÷ 3 Concept 10.4: Make Rate Charts and Bills 7) The rates of some vegetables and fruits per kg are given in the box. ` 10 ` 18 ` 15 ` 20 ` 7 ` 12 Raj buys a few items as given in the list. Make a bill for the items he bought. Item Quantity in kg Tomato 2 Carrot 3 Pumpkin 1 Cabbage 1 Money 175 PPS_Class 3_Maths_ch-10.indd 175 1/13/2017 12:49:38 PM

M Measurementeasurement I Will Learn Concepts 11.1: Conversion of Standard Units of Length 11.2: Conversion of Standard Units of Weight 11.2: Conversion of Standard Units of Volume Ch_11.indd 176 1/12/2017 12:48:04 AM

Concept 11.1: Conversion of Standard Units of Length I Think Neena went with her mother to a shop to buy a cloth. Her mother asked the shopkeeper to give two metres of the cloth. How do you think the shopkeeper should measure two metres of the cloth? To answer this question, we must know the concept of standard unit of length. 11.1 I Recall We know that people sometimes measure lengths of objects using their hands or feet. But the size of the body parts differ from person to person. So, the length of the same object also differs when measured by different people. Suppose a boy and a grown-up measure the same object. We see that the measures of the object are different. So, measures such as hand span, cubit, leg span and so on are called non-standard units. To express measurement in an exact way, standard units were developed. The measurement of objects remains the same anywhere in the world when these standard units are used. Measurement 177 Ch_11.indd 177 1/12/2017 12:48:05 AM

Measures of Length: Centimetre: It is a unit of length used to measure the length of pencil, the sides of a book and so on. We write centimetres as cm. Metres: It is the standard unit of length. It is used to measure length of a piece of cloth, a wall and so on. We write metres as m. Kilometre: It is a unit of length larger than metre. It is used to measure the distance between two places, length of a river and so on. We write it as km. By using our hand span, we can measure the lengths of the following objects. Fill in the blanks with the measurements obtained. a) Window of your class room - _____________. b) The benches on which you sit - _____________. c) The blackboard - _____________. d) Your math notebook - _____________. e) School bag - ____________. 11.1 I Remember and Understand Measure the length of a blackboard with your hand span. Ask your friends to do the same and note the readings. Did everyone get the same measurement? What do you observe by this? We observe that the readings are different. So, we need a standard measurement. If all of us use the same standard instrument to measure length, there will be no dif- ference in the measurements. Instruments such as scale, tape and so on, are used to measure lengths throughout the world. These are known as standard instruments. 178 Ch_11.indd 178 1/12/2017 12:48:06 AM

A scale is used to measure length in centimetres and inches. A measuring tape is used to measure longer lengths in like metres and kilometres. Can we use a measuring tape to measure smaller lengths? Yes, for that we should know to convert the measurements. Conversion of length We can convert one unit of measurement into another using the relation between them. Relation between Larger units to smaller units units of length Let us understand the conversion through a few examples. 1 m = 100 cm Example 1: Convert: 1 km = 1000 m a) 4 m into cm b) 8 m 6 cm into cm c) 5 km into m d) 6 km 4 m into m Solution: a) To convert metre into centimetre, multiply by 100. b) To convert kilometre into metre, multiply by 1000. c) To convert kilometre and metre into metre, convert kilometre to metre and add it to the metre. Solved Solve these a) Conversion of m into cm 7 m = _______________ cm 4 m = ___________ cm 1 m = 100 cm 4 m = 4 ×100 cm = 400 cm 4 m = 400 cm Measurement 179 Ch_11.indd 179 1/12/2017 12:48:07 AM

Solved Solve these b) Conversion of m and cm into cm 4 m 5 cm = ___________ cm 8 m 6 cm = ____________ cm 1 m = 100 cm So, 8 m = 8 ×100 cm = 800 cm 8 m 6 cm = (800 + 6) cm = 806 cm c) Conversion of km to m 7 km = ___________ m 5 km = __________ m 1 km = 1000 m 5 km = 5 ×1000 m = 5000 m 5 km = 5000 m c) Conversion of km and m into m 4 km 9 m = ___________ cm 6 km 4 m = ___________ m 1 km = 1000 m So, 6 km = 6 ×1000 m = 6000 m 6 km 4 m = (6000 + 4) m = 6004 m We can add or subtract lengths just as like we add or subtract numbers. Remember to write the units beside the sum or difference. Note: Introduce ‘0’ in the hundreds place, if the number in the metre of the kilometre have only 2 digits. Addition of lengths Example 2: Add: a) 25 m 16 cm and 32 m 30 cm b) 34 km 450 m and 125 km 235 m 180 Ch_11.indd 180 1/12/2017 12:48:07 AM

Solution: We can add the lengths as: Steps Solved Solved Solve these Step 1: Write m cm km m m cm the numbers 2 5 1 6 3 4 4 5 0 1 9 2 7 in columns as + 3 2 3 0 + 4 0 2 0 shown. + 1 2 5 2 3 5 Step 2: Add the m cm km m km m numbers under 2 5 1 6 3 4 4 5 0 1 2 1 5 0 the smaller unit + 3 2 3 0 and write the + 1 2 5 2 3 5 + 1 4 3 4 0 sum. 4 6 6 8 5 Step 3: Add m cm km m km m the numbers 2 5 1 6 3 4 4 5 0 1 0 1 0 0 under the + 3 2 3 0 + 1 0 0 1 0 0 larger unit and + 1 2 5 2 3 5 write the sum. 5 7 4 6 1 5 9 6 8 5 Subtraction of lengths Example 3: Subtract: a) 125 m 20 cm from 232 m 30 cm b) 234 km 15 m from 425 km 35 m Solution: We can subtract the lengths as: Steps Solved Solved Solve these m cm km m km m Step 1: Write the 2 3 2 3 0 4 2 5 0 3 5 1 4 3 5 0 numbers in columns − 1 2 5 2 0 − 2 3 4 0 1 5 − 1 2 1 5 0 as shown. Measurement 181 Ch_11.indd 181 1/12/2017 12:48:07 AM

Steps Solved Solved Solve these Step 2: Subtract m cm km m m cm the numbers under the 2 3 2 3 0 4 2 5 0 3 5 2 6 4 2 smaller unit − 1 2 5 2 0 − 2 3 4 0 1 5 − 1 3 2 1 and write the 1 0 0 2 0 difference. m cm km m m cm Step 3: Subtract the numbers 2 12 3 12 under the larger 2 3 2 3 0 \ 4 2 5 0 3 5 5 9 2 6 \ \ \ unit and write − 1 2 5 2 0 − 2 3 4 0 1 5 − 3 9 1 4 the difference. 1 0 7 1 0 1 9 1 0 2 0 Train My Brain Solve the following: Convert: a) 5 m 7 cm into cm b) 8 km into m c) 10 km 20 m + 20 km 10 m d) 42 m 30 cm – 30 m 20 cm 11.1 I Apply Let us solve some real-life examples where addition and subtraction of lengths is mostly used. Example 4: Reema rode her cycle for 9 km 6 m. How many metres did she ride? Solution: The distance travelled by Reema on her cycle = 9 km 6 m We know that 1 km = 1000 m So, 9 km = 9 ×1000 m = 9000 m 9 km 6 m = (9000 + 6) m = 9006 m Therefore, Reema rode for 9006 metres. 182 Ch_11.indd 182 1/12/2017 12:48:07 AM

Example 5: Sunny bought a rope of length 20 m 12 cm. Bunny bought another rope of length 12 m 20 cm. What is the total length of the rope they bought? Solution: The length of the rope bought by Sunny = 20 m 12 cm The length of the rope bought by Bunny = 12 m m cm 20 cm 2 0 1 2 + 1 2 2 0 The total length of the ropes = 20 m 12 cm + 12 m 3 2 3 2 20 cm Therefore, the total length of the rope bought by both of them = 32 m 32 cm Example 6: Raj’s house was at a distance of 36 km 119 m from his uncle’s house. He travelled by a car for 14 km 116 m from his uncle’s house. How much more distance has to be covered by Raj to reach his home? Solution: Distance between Raj’s house and his uncle’s house = 36 km 119 m Distance travelled by Raj to his house = 14 km 116 m Distance left to be covered km m = 36 km 119 m – 14 km 116 m 3 6 1 1 9 − 1 4 1 1 6 Therefore, the distance yet to be covered to reach 2 2 0 0 3 Raj’s home is 22 km 3 m. 11.1 I Explore (H.O.T.S.) Let us now see some more examples where we use the concept of standard units of lengths. Example 7: Ramu’s height is 134 cm and Somu’s height is 1 m 50 cm. Who is taller and by how many centimetres? Solution: To compare heights of two persons, they must be in the same units. Measurement 183 Ch_11.indd 183 1/12/2017 12:48:08 AM

Height of Somu = 1 m 50 cm = 100 cm + 50 cm = 150 cm Height of Ramu = 134 cm The difference in their heights is (150 – 134) cm = 16 cm 150 cm > 134 cm Therefore, Somu is taller than Ramu by 16 cm. Example 8: The figure given below is a map. It shows the different ways to reach different places from the house. Post office Airport 3 km \ House School Market 3 km Railway Station Look at the map and answer these questions. a) How far is the post office from the house? b) What is the distance between the market and the railway station? c) Find the distance between the house and the airport through the post office? d) Which is closer to the house – post office or market? e) How far is the railway station from the school? 184 Ch_11.indd 184 1/12/2017 12:48:08 AM

Solution: From the map, we see that a) The post office is 3 km from the house. b) The distance between the market and the railway station is 3 km. c) Through the post office, the distance between the house and the airport is 3 km + 6 km = 9 km d) Post office is closer to the house. e) The railway station is 10 km from the school. Maths Munchies A yard was originally the length of a man’s belt or girdle, as it was called. 2 3 1 In the 12 th century, King Henry I of England fixed the yard as the distance from his nose to the thumb of his out-stretched arm. Today it is 36 inches. Concept 11.2: Conversion of Standard Units of Weight I Think Train My Brain Neena went to the market with her father. They bought several things like vegetables, sweets and fruits. The shopkeeper measured the vegetables with a machine. He used some units to tell the weight. Do you know which units he used? To know the answer, we have to learn the concept of standard unit of weight. 11.2 I Recall The weight of an object is the measure of its heaviness. Different objects have different weights. We use standard units to measure the weights of objects around us. Measurement 185 Ch_11.indd 185 1/12/2017 12:48:08 AM

The standard unit of weight is kilogram. We write kilogram as ‘kg’. Another unit of weight is gram. We write gram as ‘g’. The smallest unit of weight is milligram. We write milligram as ‘mg’. Milligram (mg) is the unit used for weighing medicines, tablets and so on. Gram (g) is used for weighing objects such as pencils, books, and spices. Kilogram (kg) is used for weighing heavier objects such as rice, wheat, and flour. 11.2 I Remember and Understand Sometimes, to measure the weight of an object, we need the smaller unit instead of the larger unit. For this, we need to convert the units for appropriate Relation between units measurement. Let us see how we can convert of weight weights. 1 g = 1000 mg Conversion of weights 1 kg = 1000 g We can convert one unit of measurement into another using the relation between them. 186 Ch_11.indd 186 1/12/2017 12:48:10 AM

Larger units to smaller units Let us understand the conversion through a few examples. Example 9: Convert into grams: 4 kg Solution: To convert kilogram into gram, multiply by 1000. Solved Solved this 4 kg to grams 6 kg to grams 1 kg = 1000 g So, 4 kg = 4 × 1000 g = 4000 g Example 10: Convert into grams: 3 kg 150 g Solution: To convert kilogram and gram into gram, convert kilogram to gram and add it to the gram. Solved Solved this 3 kg 150 g to grams 4 kg 20 g to grams 1 kg = 1000 g So, 3 kg = 3 × 1000 g = 3000 g 3 kg 150 g = 3000 g + 150 g = 3150 g We add or subtract weights just as we add or subtract numbers. Remember to write the unit beside the sum or difference. Introduce ‘0’ in the hundreds place if the number in the milligram of gram and gram of kilogram has only 2 digits Addition of weights Example 11: Add: a) 15 g 150 mg and 23 g 285 mg b) 17 kg 706 g and 108 kg 189 g Solution: We can add the weights as: Measurement 187 Ch_11.indd 187 1/12/2017 12:48:10 AM

Steps Solved Solved Solve these Step 1: Write g mg kg g kg g the numbers in 1 5 1 5 0 1 7 7 0 6 1 1 2 3 0 the columns as + 2 3 2 8 5 + 1 0 8 1 8 9 + 8 7 6 0 shown. Step 2: Add the g mg kg g g mg numbers under 1 1 the smaller unit 1 5 1 5 0 1 7 7 0 6 2 6 1 9 0 and write the + 2 3 2 8 5 + 1 0 8 1 8 9 + 2 3 2 6 0 sum. 4 3 5 8 9 5 Step 3: Add the g mg kg g g mg numbers under 1 1 1 the larger unit 1 5 1 5 0 1 7 7 0 6 3 3 3 3 3 and write the + 2 3 2 8 5 + 1 0 8 1 8 9 + 2 2 3 3 3 sum. 3 8 4 3 5 1 2 5 8 9 5 Subtraction of weights Example 12: Subtract: a) 153 g 100 mg from 262 g 300 mg b) 234 kg 150 g from 355 kg 305 g Solution: We can subtract the weights as: Steps Solved Solved Solve these g mg kg g kg g Step 1: Write 2 6 2 3 0 0 3 5 5 3 0 5 5 0 5 6 0 0 the numbers in − 2 3 4 1 5 0 − 2 0 0 4 0 0 columns as shown. − 1 5 3 1 0 0 Step 2: Subtract g mg kg g g mg the numbers 2 10 \ \ under the smaller 2 6 2 3 0 0 3 5 5 3 0 5 1 5 2 6 0 unit and write the − 1 5 3 1 0 0 − 2 3 4 1 5 0 − 1 5 2 6 0 difference. 2 0 0 1 5 5 188 Ch_11.indd 188 1/12/2017 12:48:10 AM

Steps Solved Solved Solve these Step 3: Subtract g mg kg g g mg the numbers 5 12 2 10 \ \ under the larger \ 2 6 2 3 0 0 3 5 5 3 0 5 2 3 5 5 5 \ unit and write − 1 5 3 1 0 0 − 2 3 4 1 5 0 − 1 6 4 5 4 the difference. 1 0 9 2 0 0 1 2 1 1 5 5 Train My Brain Solve the following: a) Convert 5 kg into g b) Convert 10 kg 250 g into g c) Add 124 kg and 200 kg d) Subtract 120 g 50 mg from 325 g 70 mg 11.2 I Apply Look at some real-life examples where addition and subtraction of weights is used. Example 13: Rahul had a bag full of vegetables which weighed 17 kg 241 g. His friend had another bag of vegetables weighing 21 kg 243 g. What is the total weight of the vegetables in both the bags? Solution: Weight of the vegetables in Rahul’s bag = 17 kg 241 g Weight of the vegetables in friend’s bag = 21 kg 243 g kg g 17 241 The total weight of the vegetables in both the + 21 243 bags = 17 kg 241 g + 21 kg 243 g = 38 kg 484 g 38 484 Therefore, the weight of vegetables in Rahul’s and his friend’s bag is 38 kg 484 g. Measurement 189 Ch_11.indd 189 1/12/2017 12:48:10 AM

Example 14: Reena got a box of pins which weighed 43 g 132 mg. She took out 11 g 100 mg of pins. What is the weight of the pins left in the box? Solution: The weight of pins in the box = 43 g 132 mg g mg The weight of pins taken out from the box = 11 g 100 43 132 mg − 11 100 The weight of the remaining pins in the box = 32 032 43 g 132 mg – 11 g 100 mg = 32 g 032 mg Therefore, the weight of the remaining pins is 32 g 32 mg 11.2 I Explore (H.O.T.S.) Let us now see how we use standard units of weight in real-life situations. Example 15: Kiran weighs 13 kg and Venu weighs 11 kg 750 g. Who weighs more and by how many grams? Solution: To compare the weights, they must be in the same units. Weight of Venu = 11 kg 750 g = 11 × 1000 g + 750 g (As 1 kg = 1000 g) = 11000 g + 750 g = 11750 g Weight of Kiran = 13 kg = 13 × 1000 g = 13000 g = 13000 g > 11750 g Therefore, Kiran weighs more than Venu. The difference in their weights is (13000 – 11750) g = 1250 g. Example 16: Suresh bought apples, grapes and watermelon. The total weight of the fruits in his bag is 3 kg 750 g. The weight of apples is 1 kg 100 g and grapes is 1 kg 150 g. What is the weight of watermelon? Solution: Suresh had 3 kinds of fruits: apples, grapes and watermelon in his bag. 190 Ch_11.indd 190 1/12/2017 12:48:11 AM

Weight of apples = 1 kg 100 g Weight of grapes = 1 kg 150 g kg g 1 100 Total weight of apples and grapes + 1 150 = 1 kg 100 g + 1 kg 150 g 2 250 Therefore, the weight of apples and grapes together is 2 kg 250 g. Weight of watermelon = weight of the bag − total weight of apples and grapes Weight of the bag = 3 kg 750 g kg g 3 750 Weight of apples and grapes together = 2 kg 250 g − 2 250 Weight of watermelon = 3 kg 750 g – 2 kg 250 g 1 500 Therefore, the weight of watermelon is 1 kg 500 g. Maths Munchies One of the instruments used to measure weight of an object is a simple 2 3 1 balance. The simple balance is seen in the hand of our blind lady of justice. It means that the law is equal for everyone. Concept 11.3: Conversion of Standard Units of Volume I Think Neena’s 10 cousins visited her during their summer vacation. Neena bought two big bottles of cold drink. If each takes a glassful, can she serve equally to all? To answer this question, we have to learn the concept of the measurement of capacity. Measurement 191 Ch_11.indd 191 1/12/2017 12:48:12 AM

11.3 I Recall Bottles and glasses come in different sizes. We cannot specify the quantity of cold drink served in bottles and glasses as they are non-standard units. So, we need a standard unit of measuring capacity of liquids. Standard units of capacity are millilitres, litres and kilolitres. Commonly used containers for measuring the quantity of liquids are shown in the figure. The quantity of liquid (water, oil, milk and so on) that a container can hold is called its capacity or volume. The standard unit of capacity or volume is litre, denoted by ‘ℓ’. The unit smaller than a litre that is used for measuring capacity is called millilitre. We write it as ‘mℓ’. 11.3 I Remember and Understand To find the measure of the quantity of the smaller units, we need to convert the larger unit to smaller unit. Conversion of units of capacity Relation between units of capacity We can convert one unit of measurement into another using the relation between them. 1 litre = 1000 millilitres Let us understand the conversion through a few 1 kilolitre = 1000 litres examples. 192 Ch_11.indd 192 1/12/2017 12:48:12 AM

Larger units to smaller units To convert litres into millilitres, multiply by 1000. Example 17: Convert into millilitres: 3 ℓ Solution: Multiply the litres by 1000 to convert it to millilitre. Solved Solve this 3 ℓ to mililitres 7 ℓ to mililitres 1 ℓ = 1000 mℓ 3 ℓ = 3 × 1000 mℓ = 3000 mℓ Example 18: Convert into millilitres: 2ℓ 269 mℓ Solution: To convert litres and millilitres into millilitres, convert litres to millilitres and add it to the millilitres. Solved Solve this 2ℓ 269 mℓ to millilitres 3 ℓ 750 mℓ to millilitres 1 ℓ = 1000 mℓ So, 2 ℓ = 2 × 1000 mℓ = 2000 mℓ 2 ℓ 269 mℓ = 2000 mℓ + 269 mℓ = 2269 mℓ We add or subtract volumes just as we add or subtract numbers. Remember to write the unit beside the sum or difference. Introduce ‘0’ in the hundreds place if the millilitre in litre and litre in kilolitre if there are only two digits. Addition of volumes Example 19: Add: 13 ℓ 450 mℓ and 32 ℓ 300 mℓ Solution: We can add the volume as: Measurement 193 Ch_11.indd 193 1/12/2017 12:48:12 AM

Steps Solved Solve these ℓ mℓ ℓ mℓ Step 1: Write 13 450 21 200 the numbers in columns as shown. + 32 300 + 11 303 Step 2: Add the ℓ mℓ ℓ mℓ numbers under the 13 450 24 129 smaller unit and + 32 300 + 31 110 write the sum. 750 Step 3: Add the ℓ mℓ ℓ mℓ numbers under 13 450 52 000 the larger unit and + 32 300 + 41 000 write the sum. 45 750 Subtraction of volumes Example 20: Subtract: 351 ℓ 200 mℓ from 864 ℓ 350mℓ Solution: We subtract the volume as: Steps Solved Solve these ℓ mℓ ℓ mℓ Step 1: Write the 864 350 316 186 numbers in columns as shown. − 351 200 − 116 205 Step 2: Subtract the ℓ mℓ ℓ mℓ numbers under the 864 350 119 209 smaller unit and write − 351 200 − 11 101 the difference. 150 Step 3: Subtract the ℓ mℓ ℓ mℓ numbers under the 864 350 119 209 larger unit and write − 351 200 − 11 101 the difference. 513 150 194 Ch_11.indd 194 1/12/2017 12:48:12 AM