The HCF and LCM of two numbers is 48 and 288 respectively. One of the numbers is 144. Find the other number.
HCF = 48
LCM = 288
First number = 144
Second number = ?
Since, HCF X LCM = Product of the two numbers
Therefore, 48 X 288 = 144 X second number
= 48 X 2
= 96
Thus, the other number is 96.
Find the smallest number which when divided by 42 or 147 leaves a remainder of 5 in each case.
The smallest number which when divided by 42 and 147 without a remainder is the LCM of 42 and 147.
LCM = 2 X 3 X 7 X 7
= 294
Therefore, the smallest number which when divided by 42 and 147 leaves a remainder of 5 is
294 + 5 = 299.
Find the greatest number which divides 149 and 101, leaving a remainder of 5.
The number must divide 149 and leave 5 as remainder.
Therefore, it must divide, (149 - 5) that is 144 without a remainder.
The number must also divide 101 and leave 5 as remainder.
Therefore, it must divide, (101 - 5) that is 96 without a remainder.
Therefore, we have to find the HCF of 144 and 96.
Thus, the HCF of 144 and 96 is 48.
Find the largest number that exactly divides 280 and 490.
To find the largest number that divides 280 and 490, we need to find the HCF of 280 and 490.
Therefore,
Thus, the HCF of 280 and 490 = 70
Thus, the largest number that exactly divides 280 and 490 is 70.
Find the smallest number which, on adding 10 to it, is exactly divisible by 28, 36 and 45.
The smallest number which is exactly divisible by 28, 36 and 45 is the LCM of 28, 36 and 45.
LCM = 2 X 2 X 3 X 3 X 5 X 7
= 1260
Therefore, the smallest number which when on adding 10 to it, is exactly divisible by 28, 36 and 45 is
1260 - 10 = 1250.
Fill in the missing blocks.
Omar bought 18 bunches of bananas. There were a dozen bananas in each bunch. How many bananas did Omar buy?
Number of bunches of bananas= 18
Number of bananas in each bunch = 1 dozen = 12
Total number of bananas bought= 12 x 18 = 216
So, Omar bought 216 bananas
Khathu filled 8 vases. She put 16 roses in each vase. How many roses did Khathu use?
Number of vases that are filled = 8
Number of roses in each vase = 16
Total number of roses used = 16 x 8 = 128
Number of roses used by Khatu are 128
Complete the pattern.
Colour the numbers which are the multiples of 3 with red colour and multiples of 5 with green colour and common multiples with blue colour.
Each boy has 5 candies and each girl has 6 candies.
How many candies do ____________ have altogether?
1. 5 boys
2. 9 girls
3. 4 boys and 4 girls
4. 7 girls and 2 boys
1. Number of candies consumed by 5 boys = 5 x 5 = 25 candies
2. Number of candies consumed by 9 girls = 9 x 6 = 54 candies
3. Number of candies consumed by 4 boys and 4 girls = 4 x 5 + 4 x 6 = 20 + 24 = 44 candies
4. Number of candies consumed by 7 girls and 2 boys = 7 x 6 + 2 x 5 = 42 + 10 = 52 candies
Total number of candies = 25 + 54 + 44 + 52
= 175 candies
Total number of candies is 175
I am less than 20. One of my multiples is 42. My second digit is four times the first digit. What number am I?
Number less than 20 = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19
Second digit is four times the first digit = 14
Multiples of 14 = 14, 28, 42
Hence, 14 is the required number.
Dali is thinking of a number that is divisible by both 11 and 5. What is the smallest possible number that Dali could be thinking of?
First number = 11
Second number = 5
Number divisible by 11 and 5 = 11 x 5 = 55
So, 55 is a number that is divisible by both 11 and 5
Find the common multiples of 12 and 14.
Multiple of 12 = 12, 24, 36, 48, 60, 72, 84, 96
Multiple of 14 = 14, 28, 42, 56, 70, 84, 98
Common multiples
Multiple of 12 = 12, 24, 36, 48, 60, 72, 84, 96
Multiple of 14 = 14, 28, 42, 56, 70, 84, 98
Common multiple of 12 and 14 = 84
Lefa wants to paint a wall. The wall is divided into 4 parts. Each part contains 20 tiles. Find the total number of tiles that Lefa have to paint.
Wall is divided into 4 parts
Each part contain 20 tiles
Total numbers of tiles are 20 x 4 = 80 tiles
Lizza needs to pack snack bags for a picnic. She has 30 bottles of juices, 28 packets of chips and 40 toffees. If the snack bags needs to be identical without any item left over, what is the greatest number of bags Lizza can make?
Number of bottles of juices = 30
Number of packets of chips = 28
Number of toffees = 40
Factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30
Factors of 28 = 1, 2, 4, 7, 14, 28
Factors of 40 = 1, 2, 4, 5, 8, 10, 20, 40
Common factors
Factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30
Factors of 28 = 1, 2, 4, 7, 14, 28
Factors of 40 = 1, 2, 4, 5, 8, 10, 20, 40
Common factors = 1, 2
Hence she can make 2 snack bags of juices, chips and toffees.
A shopkeeper is arranging 11 strawberry pastries, 43 chocolate pastries and 23 vanilla pastries in the plates. He wants same number of strawberry, chocolate and vanilla pastries in each plate. He also wants to make sure that no pastries are left. What is the maximum number of plates, the shopkeeper can arrange?
Number of strawberry pastries = 11
Number of chocolate pastries =43
Number of vanilla pastries = 23
Factors of 11 = 1, 11
Factors of 43 = 1, 43
Factors of 23 = 1, 23
Common factors
Factors of 11 = 1, 11
Factors of 43 = 1, 43
Factors of 23 = 1, 23
Common factor = 1
Hence, he can arrange only 1 plate to keep all three pastries.
Abhinav is making flower arrangements. He has 38 white roses and 48 red roses. If Abhinav wants to make all the arrangements identical and have no flowers left over, what is the greatest number of flower arrangements that he can make?
Answer.
Number of white roses = 38
Number of red roses = 48
Factors of 38 = 1, 2, 19, 38
Factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Common factors
Factors of 38 = 1, 2, 19, 38
Factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Common factors = 1, 2
Hence, he can make 2 flower arrangements of white roses and red roses.
Lefa is putting equal numbers of mango slices and grapes for snacks. Lefa arranges the mango slices in groups of 42 and the grapes in groups of 36. What is the greatest number of mango and grapes slices she can pack?
Number of mango slices = 42
Number of grapes slices = 36
Factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42
Factors of 36 = 1, 2, 3, 4, 9, 18, 36
Common factors
Factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42
Factors of 36 = 1, 2, 3, 4, 9, 18, 36
Hence, Lefa can arrange three packs of mango slices and grape slices.
Anesu is making kits to share with friends. She has 57 bottles of water and 67 cans of food, which she would like to arrange equally among the kits, with nothing left over. What is the greatest number of kits Anesu can make?
Number of water bottles = 57
Number of cans of food = 67
Factors of 57 = 1, 3, 19, 57
Factors of 67 = 1, 67
Common factors
Factors of 57 = 1, 3, 19, 57
Factors of 67 = 1, 67
Hence, Anesu can make only one kit with equal number of water bottles and cans of food.
Complete the flow chart.
If the 3rd factor of 82 is subtracted from the 5th factor of 98, which number do we get? (HINT: first arrange the factors in ascending order).
Factors of 82 = 1, 2, 41, 82
Factors of 98 = 1, 2, 7, 14, 49, 98
Subtraction = 49 41 = 8
Fill in the chart with the missing factors or products.
What is the sum of the 4th factor of 77, 69, and 85? (HINT: first arrange the factors in ascending order).
Factors of 77 = 1, 7, 11, 77
Factors of 69 = 1, 3, 23, 69
Factors of 85 = 1, 5, 17, 85
Sum of 4th factor of 77, 69, 85 = 77 + 69 + 85
= 231
A number is a common factor of 40 and 80. When divided by 6, it gives a remainder of 2. What is the number?
Factors of 40 = 1, 2, 4, 5, 8, 10, 20, 40
Factors of 80 = 1, 2, 4, 5, 8, 10, 20, 40, 80
Common factors
Factors of 40 = 1, 2, 4, 5, 8, 10, 20, 40
Factors of 80 = 1, 2, 4, 5, 8, 10, 20, 40, 80
Number when divided by 6 gives remainder 2 = 20
Using divisibility test, find whether 2896 is divisible by 9 or not.
Sum of the digits = 2 + 8 + 9 + 6
= 25
Since, 25 is not a multiple of 9
So, the number 2896 is not divisible by 9.
Using divisibility test, Complete the table.
Using Divisibility Test, show that 9873 is divisible by 9.
9 + 8 + 7 + 3 = 27
Since, 27 is a multiple of 9
So, 9783 is divisible by 9.
Fill in the box with the appropriate symbols >, < or = after completely working out the problem using the cross multiplication method.
Colour the required number of parts and say which is bigger?
So, Lefa scored more marks.
Write the fraction for the given numerators & denominators.
Shade the portion corresponding to the given fraction.
Identify the right fraction for the shaded portion.
James divided his birthday cake into 15 equal parts, and ate 3 of them. What fraction (in lowest term) of the cake was still left?
Write a fraction (in the lowest term) for the portion shaded in:
a. Red
b. Blue
c. yellow
What fraction of the whole is un-shaded? Also, reduce the fraction to its lowest term.
a) 3/6 = 1/2
b) 2/6 = 1/3
c) 4/7
Out of a group of 29 boys, 7 went away. What fraction of boys, left the group. Also, what fraction of the boys is still left in the group?
There are 14 girls in a class and five of them went for the swimming, calculate what fractions of them are at school?
What fractions of the ice-cream cones have vanilla flavour?
Hint: Total Number of ice-creams is 52.
Strawberry ice-cream is 13.
Vanilla ice-cream is 25.
Chocolate ice-cream is 14.
What fractions of the ice-cream cones are?
What fraction of the children are wearing skirt?
Write fractions for the shaded and un-shaded portion.
Draw a square on a sheet of paper. Divide it into four equal parts. Colour any one part. Write the fractional number for the coloured part.
Trace a bangle on a sheet of paper. Divide it into 8 parts. Colour any 5 parts. Write the fractional number for the coloured and the uncoloured part.
How many parts are there in a rainbow?
7
Lara divided her chocolate in four equal parts and ate one part. How much has she eaten?
She has eaten one-quarter of the whole.
How many quarters are there in a whole?
Four
How many one-thirds are there in a whole?
Three
How many halves are there in a whole?
Two
Which is smaller?
Which is greater?
Arrange the following in descending order.
Arrange the following in ascending order.
Compare mentally and use the appropriate symbol > or <.
Identify the numerator and the denominator of the given fraction.
What is the numerator of the given fraction?
What is the denominator of the given fraction?
What fraction of the following figure is shaded?
Write the fraction for the shaded part.
What fraction of the following figure is shaded?
What fraction of the following figure is shaded?
What fraction of the following figure is shaded?
Identify the numerator and the denominator of the fraction 5/6.
Numerator: 5
Denominator: 6
Identify the numerator and denominator of the fraction 7/9.
Numerator: 7
Denominator: 9
Identify the numerator and denominator of the fraction 4/5.
Numerator: 4
Denominator: 5
The numerator and denominator of a fraction is 2 and 5 respectively. Identify the fraction.
Ritu cuts the prantha in three equal pieces. What fraction is each piece?
Each piece is one-third of the whole. That is, 1/3.
Julia and Mary's teacher gave them 6 word problems. She told them to divide them equally between themselves. How many questions did each of them get?
Chip found 12 nuts under a tree; he gave half of them to Dale. What fraction of nuts did Chip and Dale have?
Robert and David walked past 33 cars. One – elevenths of the cars had bumper stickers. How many of those cars were without stickers?
Tia counted 27 children in the park. One – third of them were playing basketball. How many children were playing basketball?
Piya put 20 flowers in a vase on the table. One – half flowers out of them are yellow. How many flowers are of yellow colour?
